Six Sigma ASQ Book

Six Sigma Black Belt

Six Sigma Black Belt Introduction

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Six Sigma Black Belt | Introduction Introduction: Home

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Course Introduction

Six Sigma Black Belt | Introduction Concept: Course Introduction

Welcome to the American Society for Quality (ASQ) Six Sigma Black Belt (SSBB) certification preparatory course. This is the first step in your journey to Six Sigma Black Belt certification. This course will cover the following topics: • Enterprise-wide deployment • Business process management • Project management • Define • Measure • Analyze • Improve • Control • Lean enterprise • Design for Six Sigma Becoming an SSBB empowers you to make a difference in your organization. Six Sigma’s focus on customer satisfaction and operational excellence brings a new level of business credibility to your role as a quality expert. As a Black Belt, you will be relied upon as one of the leaders in your organization’s quality movement.    

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ASQ Overview

Six Sigma Black Belt | Introduction Concept: ASQ Overview

The American Society for Quality (ASQ) is the world's leading authority on quality. With more than 100,000 individual and organizational members, this professional association advances learning, quality improvement and knowledge exchange to improve business results and create better workplaces and communities worldwide. As champion of the quality movement, ASQ offers technologies, concepts, tools and training to quality professionals, quality practitioners and everyday consumers, encouraging all to Make Good Great™. ASQ is grateful for the contributions and dedication of subject matter  experts who provided their assistance in the development and design of this course. This course is based on the ASQ Six Sigma Black Belt Body of Knowledge. To download a copy of the Body of Knowledge, roll over Page Resources at the bottom of this page.

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Course Overview

Six Sigma Black Belt | Introduction Concept: Course Overview

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Six Sigma Black Belt Enterprise-Wide Deployment

Lesson Introduction

Six Sigma Black Belt | Enterprise-Wide Deployment Introduction: Lesson Introduction

The nature of a Six Sigma project is enterprise-wide. Particularly for companies beginning down the Six Sigma path, the investigation of which projects will be deployed based on data analysis often leads to activities that will affect the entire organization. To begin this journey, an enterprise-wide view will be established. To better understand this view and deploy a project of this magnitude, the ASQ Body of Knowledge provides the following topics: Enterprise view • Understand the organizational value of Six Sigma and its philosophy, goals and definition. • Understand and distinguish interrelationships between business systems and processes. • Describe how process inputs, outputs and feedback of the system impact the enterprise system as a whole. Leadership • Understand leadership roles in the deployment of Six Sigma. • Understand the roles and responsibilities of Black Belts, Master Black Belts, Green Belts, Champions, Executives and Process Owners. Organizational goals and objectives • Understand key drivers for business. • Understand key metrics and scorecards. • Describe the project selection process including knowing when to use Six Sigma improvement methodology as opposed to other problem-solving tools, and confirm link back to organizational goals. • Document the objectives achieved and manage the lessons learned to identify additional opportunities. Organizational improvement and Six Sigma foundations history • Understand the origin of continuous improvement tools used in Six Sigma.

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Lesson Overview

Six Sigma Black Belt | Enterprise-Wide Deployment Introduction: Lesson Overview

The tools and objectives of the Enterprise-Wide Deployment lesson are illustrated below.

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Six Sigma Black Belt Enterprise-Wide Deployment Enterprise View

Learning Objectives

Six Sigma Black Belt | Enterprise-Wide Deployment | Enterprise View Concept: Learning Objectives

At the end of this Enterprise-Wide Deployment topic, all learners will be able to: • understand the organizational value of Six Sigma, its philosophy, goals and definition. • understand and distinguish interrelationships between business systems and processes. • describe how process inputs, outputs and feedback of the system impact the entire enterprise system as a whole.             Portions of this topic were taken from the ASQ Six Sigma Green Belt web-based Certification Preparation Course.

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Why Use Six Sigma

Six Sigma Black Belt | Enterprise-Wide Deployment | Enterprise View Concept: Why Use Six Sigma

Depending on whom you ask, Six Sigma may be referred to as a philosophy, a methodology or a tool. In Donald W. Benbow and T.M. Kubiak's The Certified Six Sigma Black Belt Handbook, it is defined as "a fact-based, data-driven philosophy of improvement that values defect prevention over defect detection." The term “Six Sigma” is a measure of quality. Sigma (σ) is a Greek letter used by statisticians to show the variation in a process. For example, if a hospital process for admitting a new patient is supposed to take five to ten minutes, a variation occurs not only when it takes more or less time but also for each mistake that is made in collecting the patient's information. If the hospital is operating at 4 sigma (4σ), there may be as many as 6,000 problems per million opportunities for a mistake. For example, if a patient admission form has 50 questions, for every 20,000 patients admitted there could be 6,000 errors in the information. In a Six Sigma (6σ) environment, the standard for variability is reduced to 3.4 problems per million opportunities. Moving from 6,000 data errors at 4σ to just 3.4 data errors at 6σ is real progress! Imagine bringing this concept to life in your own home. The image below shows how your home would be affected if the power company ran at 4σ vs. 6σ:

 

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Philosophy and Goals

Six Sigma Black Belt | Enterprise-Wide Deployment | Enterprise View Concept: Philosophy and Goals

The philosophy of Six Sigma goes beyond the reduction of errors in a single department. Six Sigma is a business initiative, not a quality initiative. It is a way of doing business that improves quality and productivity, increases competitiveness and reduces cost. There are three major components to Six Sigma: • Culture of the organization • Improvement tools • Support systems for the tools By controlling the amount of variation beyond the upper and lower allowable limits of a process, one minimizes the frequency of out of control conditions. In real terms, building Six Sigma into a way of doing business can reduce errors, identify and correct flaws in processes and have a dramatic impact on the success of the organization.  

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Business Systems and Processes

Six Sigma Black Belt | Enterprise-Wide Deployment | Enterprise View Concept: Business Systems and Processes

Understanding the mindset of business is crucial to the success of any quality project. In this topic you will gain an understanding of and distinguish interrelationships between business systems and processes. Systems and processes and the relationships that define them will be first discussed and then applied to business. The American Heritage Dictionary defines system as “a group of interacting, interrelated, or interdependent elements forming a complex whole." The ASQ Glossary defines system as "a group of interdependent processes and people that together perform a common mission." This latter definition highlights an important aspect of systems, namely that a system operates in unity toward a unified purpose. Without a true understanding of a system's purpose, elements and interdependencies, it is difficult to know what improvements would truly benefit the system as a whole, rather than benefiting only one of its elements at the possible expense of others.

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System Example

Six Sigma Black Belt | Enterprise-Wide Deployment | Enterprise View Concept: System Example

To understand a system, go no further than your computer. The personal computer (PC) exemplifies a system by providing desired functionality to the user via its monitor, keyboard, mouse, software, hard drive, processor and other peripherals. Each of these PC components is an independent member of the PC system, and each interrelated module “works together” in unity toward a purpose set by the user. Many other systems exist in nature that allow an understanding of this interrelation concept. In this example, the various elements mentioned would be considered subsystems of the greater PC system, as seen from the perspective of the PC as a whole. If you were to focus your attention on just the mouse, the PC subsystem could be considered a system on its own, its elements being the left button, the right button, the navigation wheel, the casing and the cord.

Knowledge check • • •

What is another example of a system in nature? What are its elements? How could a PC be considered a subsystem?

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System Functions

Six Sigma Black Belt | Enterprise-Wide Deployment | Enterprise View Concept: System Functions

The American Heritage Dictionary defines function as “the action for which a person or thing is particularly fitted or employed.” For a system is to fulfill its purpose, one or more actions must occur. Thus, the functions of a system are those associated actions that allow a system to work as a unit toward its stated purpose. In the PC example, think about how multiple functions must work together to open an email program. To oversimplify the functions, when a user drags the mouse, an electronic signal must transmit the action of the mouse moving into a related motion recognizable to the user. The monitor allows the user to see this motion and the software and signal work together to display the cursor moving on the screen. Working in harmony, the user drags the cursor over the program icon and double-clicks the left mouse button. This transmits the instruction to the software: open the email program. To fully document this simple action across all subsystems within the PC would take volumes if you went to the deepest levels. To diagram the opening email example: Example

Concept

The Personal Computer

System

is made up of a monitor, keyboard, mouse, software and other hardware

Subsystems/Elements

which function together to allow the user to open email software

Unified Purpose

by executing the process of navigating and opening the program.

Process

The process will be discussed next.

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Processes

Six Sigma Black Belt | Enterprise-Wide Deployment | Enterprise View Concept: Processes

Process is defined by The American Heritage Dictionary as “a series of actions, changes, or functions bringing about a result.” For an experienced computer user, moving the mouse is a simple step, an action that is commonplace. For an inexperienced user this could be a more complicated process until he or she becomes acclimated to using the mouse. For a multidisciplined engineer studying the mouse in order to create a new model and replicate its features and functions, moving the mouse could be seen as a very complicated process. Each process, as outlined above, will share the following elements that affect its function: • inputs • process • outputs

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Applying a Systems View to Business

Six Sigma Black Belt | Enterprise-Wide Deployment | Enterprise View Concept: Applying a Systems View to Business

Now that the groundwork for the concepts has been established, how does this translate into designing a quality project for a business? Say, for example, that a business considers the following its core functions: • Sales • Marketing • Engineering • Production • Customer Service

 

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Functional Processes

Six Sigma Black Belt | Enterprise-Wide Deployment | Enterprise View Concept: Functional Processes

Each of these core functions has its own set of defined processes, which that particular department uses to accomplish its goals.

 

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Support Functions

Six Sigma Black Belt | Enterprise-Wide Deployment | Enterprise View Concept: Support Functions

The business also has various functions that support the core functions. These include: • Human Resources • Finance • Information Technology (IT) • Warehousing

At this point, the analysis of the business system looks vertical. Individuals inside a particular functional area have full view of their own process but have difficulty seeing outside of these “silos” except when they intersect with another functional area. For example, an intersection between functional areas occurs when a tracking system managed by the Information Technology support function is used by the Warehousing support function to deliver a product to a customer (internal or external). This limited perspective is why it is crucial to understand the business processes that cut across these functional process areas.

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Business Process View

Six Sigma Black Belt | Enterprise-Wide Deployment | Enterprise View Concept: Business Process View

A business process is a collection of related activities that produce something of value to the organization, its stakeholders or its customers. Examples of business processes throughout an organization can be defined as follows: • Quote-to-cash • Procure-to-pay • New product/service development • Order fulfillment

Becoming familiar with cross-functional business processes greatly increases understanding of the interrelationships between the core functions and clarifies how a quality project in one area of the company will affect other areas. To truly grasp the system, however, we must consider another aspect of the business process: its purpose.

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Managing the Purpose

Six Sigma Black Belt | Enterprise-Wide Deployment | Enterprise View Concept: Managing the Purpose

No business process can be effective unless its purpose is properly communicated to the rank-and-file. Executive leadership should drive management of the business purpose, and impress upon all members of the organization the importance of understanding and fulfilling that purpose. In addition, leadership must govern, manage, adjust and reset the purpose based on customer needs and other factors.

 

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Process Impact on the Organization

Six Sigma Black Belt | Enterprise-Wide Deployment | Enterprise View Concept: Process Impact on the Organization

The Six Sigma methodology recognizes that there are many input, output and feedback sources for an organization. Each output may have its own process dependent on the input from other processes. All inputs and outputs of a particular process should be measurable so that quality can be controlled. Suppliers, Inputs, Process, Outputs and Customers (SIPOC) is a tool that can be used to help identify these processes in an organization. Although this course will discuss SIPOC in more detail later, it is important to know that improvements in one area may create errors in another.

 

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Six Sigma Black Belt Enterprise-Wide Deployment Leadership

Learning Objectives

Six Sigma Black Belt | Enterprise-Wide Deployment | Leadership Concept: Learning Objectives

At the end of this Enterprise-Wide Deployment topic, all learners will be able to: • understand leadership roles in the deployment of Six Sigma (e.g., resources, organizational structure). • understand the roles and responsibilities of Black Belts, Master Black Belts, Green Belts, Champions, Executives and Process Owners.             Portions of this topic were taken from the ASQ Six Sigma Green Belt web-based Certification Preparation Course.

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Enterprise Leadership

Six Sigma Black Belt | Enterprise-Wide Deployment | Leadership Concept: Enterprise Leadership

Successfully implementing Six Sigma methodologies within an organization requires the commitment of the company's top leadership. Six Sigma focuses on cross-functional and enterprise-wide processes. Therefore, leadership and support from the executive staff, specifically the CEO, is crucial.  Without this support and leadership, the Six Sigma initiative will fail. An important leadership role within a Six Sigma project is the project Champion. According to Kim H. Pries in Six Sigma for the Next Millennium, the Champion: " ...is specifically tasked with the responsibility of planning the deployment of the Six Sigma process...[and] must understand the following: • Skills required • Data needed • Financial requirements (budgeting) • Specific people tied to the skills • Locations (meeting rooms, plant floor, and so on) • Tools or equipment (projectors, computers, ancillary tools, and so on) "

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Stakeholders

Six Sigma Black Belt | Enterprise-Wide Deployment | Leadership Concept: Stakeholders

In addition to their tactical qualifications, Champions and executive leadership must have a firm grasp of the company's stakeholders. A stakeholder is anyone who has an interest in the business. This broad group includes but is not limited to: • Investors • Customers • Vendors • Employees • Employees' families • Neighboring communities • Local, city and federal government Each stakeholder has different interests based on the stakeholder's relationship to the business. Identifying the overt and underlying interests of a stakeholder provides guidance on how a particular Six Sigma may positively or adversely affect them. Note: More detail on stakeholders may be found in the Business Process Management lesson.  

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Allocating Resources

Six Sigma Black Belt | Enterprise-Wide Deployment | Leadership Concept: Allocating Resources

Effective Six Sigma projects cannot happen without the appropriate decision makers taking ownership of the project. The project Champion as well as the group(s) funding the project must stay involved from the beginning and through completion. Working with the project Champion, the company leadership must provide resources in the form of personnel and funds to accomplish the project.

Staffing support Once the project is defined and the appropriate types of roles and skill sets are identified, specific personnel will be chosen to fulfill each role. During the selection process, leadership may find that those resources most needed are often the busiest. These resources cannot justify participation in the project unless its level of importance is appropriately elevated. Depending on workload, other individuals may be needed to backfill the work of someone dedicated to the Six Sigma project (Project roles will be discussed in more detail later in the course.) If Six Sigma is new to the organization, leadership must provide training in "the ways of Six Sigma," since use of these processes will affect each team member's performance on the project.

Other resources In addition to staffing dedication, the Champion must coordinate acquisition of other resources needed for the project, which could include: • Software • Hardware • Additional workspace (additional phone, Ethernet and wireless connectivity support) • Additional meeting space • Meeting room supplies • Office supplies The magnitude of these resource requirements will depend, of course, on the size and length of the project.

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Six Sigma Roles and Responsibilities

Six Sigma Black Belt | Enterprise-Wide Deployment | Leadership Concept: Six Sigma Roles and Responsibilities

In Implementing Six Sigma, Forrest Breyfogle outlines the following roles and responsibilities within a Six Sigma infrastructure: • Champion • Master Black Belt • Black Belt • Green Belt • Process Owner Again, depending on the organization, there may not be an individual to fill every role. In those cases, someone in another role must accept those responsibilities. Roll over Page Resources and select Six Sigma Roles and Responsibilities to view a chart of specific responsibilities per role.

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Six Sigma Hierarchy

Six Sigma Black Belt | Enterprise-Wide Deployment | Leadership Concept: Six Sigma Hierarchy

Historically, one of the unique features of a Six Sigma project is its associated organizational structure. By announcing a structure with designated roles, the company leadership and employees further declare their dedication to the project. In practical terms, a well-defined structure strengthens accountability and increases the project's chance of success. An example of a Six Sigma hierarchy is shown below. Keep in mind that every organization is different. Depending on the size of the organization or even the size of the project, the roles shown below may not be filled in the same manner.

   

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Six Sigma Black Belt Enterprise-Wide Deployment Organizational Goals and Objectives

Learning Objectives

Six Sigma Black Belt | Enterprise-Wide Deployment | Organizational Goals and Objectives Concept: Learning Objectives

At the end of this Enterprise-Wide Deployment topic, all learners will be able to: • understand key drivers for business, metrics and scorecards. • describe the project selection process including knowing when to use Six Sigma improvement methodology (DMAIC) as opposed to other problem-solving tools and confirm the link back to organizational goals. • describe the purpose and benefit of strategic risk analysis (e.g., strengths, weaknesses, opportunities, threats (SWOT), scenario planning) including the risk of optimizing elements in a project or process resulting in suboptimizing the whole. • document the objectives achieved and manage the lessons learned to identify additional opportunities.       Portions of this topic were taken from the ASQ Six Sigma Green Belt web-based Certification Preparation Course.

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Key Business Drivers

Six Sigma Black Belt | Enterprise-Wide Deployment | Organizational Goals and Objectives Concept: Key Business Drivers

In his book Insights to Performance Excellence 2006, Mark Blazey defines “key” as “the major or most important elements or factors, those that are critical to achieving the intended outcome…those that are most important to the organization’s success. They are the essential elements for pursuing or monitoring a desired outcome.” Defining the specific drivers of a particular business, then determining a performance target for the resulting business objects, is key to continued success. These drivers are determined by understanding the nature of the business at large, as well as the market forces driving the business. For example, the key business drivers for banks inside of grocery stores could include: • Existing store site population • Existing store site capability • Store expansion or plans to accommodate bank • New grocery store growth • Bank inclusion in new store plans • Performance feedback from existing sites Each driver has a degree of influence on continued growth for this specific banking business.

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Key Business Drivers

Six Sigma Black Belt | Enterprise-Wide Deployment | Organizational Goals and Objectives Concept: Key Business Drivers

Suppliers strive for performance on internal metrics (e.g., cycle time, cost or defects) to meet customers’ increasing expectations on external metrics (e.g., delivery, price or quality).  The following key drivers taken from the hospital example (used earlier in this lesson) are common to most businesses and allow management to gather data for comparison with competitors. Profit - An advantageous gain or return; a benefit. Hospital system profitability depends on managing costs down while increasing the efficiency and effectiveness of billing insurance payers. Market share - The proportion of industry sales of a good or service that is controlled by a single company. Our hospital system controls less than 20% of the market and that market share is decreasing due to a poor reputation for customer service. Customer satisfaction - Meeting and/or exceeding customers' spoken or unspoken needs and requirements as fast as possible with the lowest possible cost to the customer (i.e., offering consistent performance, on-time delivery, lower costs, etc.). Customers want the right prescriptions, shorter wait times in the various clinics and emergency room, and improved accessibility to services. Efficiency - A measure of desirability (i.e., improving availability, usability, features, design, etc.). Customers in the hospital system do not want to spend time filling out lengthy and repetitive forms. Patients do not want to lay on a gurney in a hallway after surgery waiting for a room to become available. Product differentiation - In marketing, product differentiation is the modification of a product to make it more attractive to the target market. This involves differentiating your product from competitors' products (i.e., creating robust designs, meeting customer requirements, increasing process and material capabilities, etc.). For a hospital system, the COO wants to find a way to distinguish the hospital's products and services from its competitors. This could be done by building a reputation for being focused on the patient, improving the availability of new advanced procedures and improving access to care.

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Metrics Introduction

Six Sigma Black Belt | Enterprise-Wide Deployment | Organizational Goals and Objectives Concept: Metrics Introduction

Metrics are an integral part of an organization's strategic planning and deployment. Metrics are numerical, and therefore quantifiable, measurements. They serve two valuable purposes: 1) assisting with organizational goal setting and 2) evaluating actual performance versus plan. According to Kim Pries in Six Sigma for the Next Millennium, examples of business metrics may include: " • • • • • • • "

Return on investment (ROI) Return on equity (ROE) Return on assets (ROA) Net present value (NPV) Payback time Internal rate of return (IRR) Economic value-added (EVA)

Pries also asserts that each enterprise will define its own key metrics to indicate the health of the business, however some metrics are more commonly used than others. For example, "cost of goods sold" is a standard division of a balance sheet within the Generally Accepted Accounting Practice (GAAP), and will therefore be found in the key metrics toolbox of many businesses. In general, "good" metrics will have the following characteristics: • Are customer centered • Measure performance across time • Provide direct information • Are linked with organizational goals • Are developed collaboratively by those who collect and use the data

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Metrics Classified

Six Sigma Black Belt | Enterprise-Wide Deployment | Organizational Goals and Objectives Concept: Metrics Classified

Metrics belong to one of two broad categories:

Customer-related and competitive performance metrics include: • • • • • • •

Gains or losses of customers and market share Survey results Percent of competitive awards received per applications submitted Recognition and ratings Certifications by customers Customer complaints Benchmark results

Operational improvement and financial performance quality metrics include: • • • • • • • • •

Defect levels Margin rates Operating profit rates Innovation rates Time to market Environmental or safety results Cycle time Lead time Setup time

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Linking Projects to Organizational Goals

Six Sigma Black Belt | Enterprise-Wide Deployment | Organizational Goals and Objectives Concept: Linking Projects to Organizational Goals

Project Champions face many challenges when introducing a new project to an organization. In situations where past projects fell short of their expected results, there may be considerable skepticism within the organization toward "another improvement project." This “historical project baggage” can result when these earlier project efforts took place in isolation, the silo mentality mentioned earlier. While one functional area may have been improved, not as many overall gains were achieved and sometimes other functional areas were negatively affected. Each improvement may have focused on a specific part of the business, and in the process ignored other departments. To combat skepticism and encourage a belief in the process, Six Sigma projects use metrics to make more comprehensive, company-wide improvements: • Improving product quality • Increasing service level • Reducing cost (overall) • Reducing cycle time (overall) Projects of this scope demand a link to organizational goals. The cross-functional business processes affected by these projects result in sweeping positive changes across the organization. It is important to note that not every project should be a Six Sigma project. An organizational strategy drives the organization in the right direction and serves as a basis for project selection. Many processes are available to develop and drive organizational strategy, but for the purpose of this course, we will focus on two: • Balanced Scorecard • Malcolm Baldrige National Quality Award (MBNQA) 2006 Criteria for Performance Excellence

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Balanced Scorecard

Six Sigma Black Belt | Enterprise-Wide Deployment | Organizational Goals and Objectives Concept: Balanced Scorecard

The balanced scorecard (BSC) is a strategic measurement and management system that translates an organization’s strategy into four perspectives: 1. 2. 3. 4.

Financial: To achieve financial success, “How should we appear to our shareholders?” Customer: To achieve our vision, “How should we appear to our customers?” Internal business processes: To achieve shareholder and customer satisfaction, “What business processes must we excel at?” Learning and growth: To achieve our vision, “How will we sustain our ability to change and improve?”

Robert Kaplan and David Norton created the BSC to move organizations away from focusing solely on financial data and toward balancing consideration of financial data with the creation of abilities and intangible assets required for long-term growth. To achieve this balance, the BSC translates an organization’s strategy into specific measures in each category. Note: Although BSC is not in the SSBB Body of Knowledge, it is a widely-accepted approach to establishing an organizational strategy.

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Baldrige Award Criteria

Six Sigma Black Belt | Enterprise-Wide Deployment | Organizational Goals and Objectives Task: Baldrige Award Criteria

In his book Insights to Performance Excellence 2006, Blazey states the "requirements for the Strategic Planning Category (MBNQA 2006 Criteria for Performance Excellence) are intended to encourage strategic thinking and acting – to develop a basis for achieving and maintaining a competitive position.”  Click strategy development and strategy deployment to learn about sample elements considered during the Strategic Planning Category (MBNQA 2006 Criteria for Performance Excellence). Strategy Development According to Blazey in Insights to Performance Excellence 2006, " sample elements considered during strategic planning include the following: • Customers: market requirements and evolving expectations and opportunities. • Competitive environment and capabilities relative to competitors: industry and market. • Technologies and other innovations that might affect products and services, and future business operations. • Internal strengths and weaknesses, including human resource capabilities and need, resource availability, and operational capabilities and needs. • Financial, societal, ethical, regulatory, and other potential risks that may affect business success. • Opportunities to redirect resources to higher-priority products, services, or business areas. • Changes in economic conditions (local, national, or global) that might affect the business. • Unique organizational factors such as supplier and supply chain, capabilities, and needs. • Clear strategic objectives with timetables that help leaders determine where the organization should be at given points in time so they can effectively monitor progress. " Strategy Deployment According to Blazey in Insights to Performance Excellence 2006, " sample elements considered during strategic deployment include the following: • Translate strategy into action plans and related human resource plans. • Align and deploy action-plan requirements, performance measures, and resources, throughout the organization to ensure changes or improvements are sustained. • Define measures for tracking progress on action plans and ensure actions are aligned throughout the organization. • Project expected performance results, including assumptions of competitor performance increases. "

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Key Components

Six Sigma Black Belt | Enterprise-Wide Deployment | Organizational Goals and Objectives Concept: Key Components

Once the organizational strategy has been established, it is time to implement a process system that aligns with the organization's strategic goals and objectives. All levels, from strategic to tactical, must be involved to truly understand the system's impact on the customer. A successful Six Sigma deployment depends on the project evolving systematically. Roll over each component of Six Sigma deployment below to learn more.   [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

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Project Selection Checklist

Six Sigma Black Belt | Enterprise-Wide Deployment | Organizational Goals and Objectives Concept: Project Selection Checklist

Careful project selection is key to the success of the Six Sigma quality initiative. Each industry and organization will have its own guidelines for deploying Six Sigma methodology. One approach to the dissemination of the Six Sigma culture is quality leaders (Master Black Belts, Black Belts, and the organizational leader) selecting projects that have the greatest impact on organizational goals. The following is an example of the type of criteria used to select Black Belt projects:

As discussed in the Business Process Management lesson, project selection criteria are customer driven and align with the company's strategic goals and objectives. An example of this customer driven goal would be to increase customer satisfaction scores or decrease customer wait time.  

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Strategic Risk Considerations

Six Sigma Black Belt | Enterprise-Wide Deployment | Organizational Goals and Objectives Concept: Strategic Risk Considerations

As discussed by Breyfogle in Implementing Six Sigma, differentiating between strategic and tactical planning is crucial. Strategic planning leads to "doing the right things"; while tactical planning leads to "doing things right." Strategic planning typically refers to a timeframe of three to five years, while tactical planning is more near-term in scope. To understand what the "right things" are, the method of choice is strategic risk assessment. Breyfogle further asserts that "with this strategic risk analysis, organizations can leverage the strength of the organization, improve any weakness, exploit opportunities and minimize potential impact of threats. Through this risk assessment organizations can then optimize their system as a whole." Once strategic risks are identified and, when possible, quantified, they can be used to determine the long-term strategic plan for the organization. The long-term plan is then broken down into strategic goals and subgoals, from which annual goals are created. Selection of projects may then be made based on each projects ability to meet these annual goals. When analyzing strategic risk, focus on the "big picture." A system should be thought of as the set of processes that makes up an enterprise. According to The Certified Six Sigma Black Belt Handbook by Benbow and Kubiak, when improvements are proposed, it is important to take a systems approach. Consideration should be given to the effect the proposed changes will have on other processes within the system and by association on the enterprise itself. Operating a system at less than its best mode is called suboptimization. Changes in a system may optimize individual processes but suboptimize the system as a whole.    

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Suboptimization Example

Six Sigma Black Belt | Enterprise-Wide Deployment | Organizational Goals and Objectives Concept: Suboptimization Example

When optimizing a system, remember that optimization is not just a local issue. Local optimization may actually have a negative impact on global optimization. The following is an example of local suboptimization.

Example The training department at ABC Corporation decided to "go paperless" by emailing course confirmations instead of sending a printed confirmation through interoffice mail. This new process would allow the department to cut down on paper and printer usage, as well as mail sorting time by the mail room staff. However, not all associates at ABC Corporation have access to email. Therefore, there is still a need to print some paper confirmations for those individuals. What the training department thought would save time and resources actually created two processes from one. The trainer now spends time looking up the name of each class participant in the company's global email address book. If the class participant is in the email system, then he or she receives an email confirmation. If a class participant does not have email, then a paper copy of the confirmation is mailed. In this example, paper use, copy machine wear and tear and mail room workload were reduced. However, an additional process was added thus creating more administrative work for the training department staff, resulting in time lost on other training projects. The net result is a waste of resources and an adverse effect on profits.

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Scenario Planning and FMEA

Six Sigma Black Belt | Enterprise-Wide Deployment | Organizational Goals and Objectives Concept: Scenario Planning and FMEA

Risk assessment uses several tools. We will consider three: scenario planning, FMEA and SWOT analysis.

Scenario planning Pioneered by the Royal Dutch/Shell petroleum company and distribution network, scenario planning involves constructing a scenario by drawing on current events, demographic trends and other statistics to compose a "story" describing possible sequences of events leading to a specific result (Kim Pries, Six Sigma for the Next Millennium). Pries states: " Typically, scenario planning groups will develop at least four scenarios: • Pessimistic • Moderate but pessimistic • Moderate but optimistic • Optimistic " Pries also notes that scenario planning serves "not so much to predict the future as to open the minds of planners and executive management to options and opportunities in the future." With scenario planning, risks that would otherwise never be considered can be uncovered, assessed and anticipated. The military has used scenario planning extensively.

Failure mode effects analysis (FMEA) According to the ASQ Glossary, failure mode effects analysis (FMEA) is a procedure that analyzes each potential failure point (or "mode") in every subitem of an item to determine the failure point's effect on each subitem and on the required function of the item itself. FMEA is used to determine high-risk process activities or product features based on the effect of a failure and the likelihood that a failure could occur without detection. In other words, FMEA is a systematic problem-prevention tool. Typically used during the analyze phase of DMAIC to prioritize process activities or product features prone to failure, FMEA can also be used during the improve phase of DMAIC or design phase of DFSS to identify high-risk process activities or product features in the proposed improvement. Note: FMEA is discussed in more detail in the DFSS lesson.

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SWOT

Six Sigma Black Belt | Enterprise-Wide Deployment | Organizational Goals and Objectives Concept: SWOT

The Strengths, Weaknesses, Opportunities, and Threats (SWOT) analysis provides a framework to identify elements that help or hinder an organization. While the SWOT is an effective tool to identify risk, remember that it does not quantify potential risks. A SWOT analysis has internal and external components. Strengths and weaknesses are considered part of an internal analysis of the organization, while opportunities and threats are part of an external analysis of the environment in which the organization operates. The external environment is essentially everything outside of an organization that might affect the organization.

     

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Strengths

Six Sigma Black Belt | Enterprise-Wide Deployment | Organizational Goals and Objectives Concept: Strengths

To identify organizational strengths, answer the question "What are the skills, capabilities and core competencies that help an organization achieve its goals and objectives?" In other words, "What is the organization really good at?" Organizational strengths might be any of the following: • Leadership • Research and development efforts • Innovative product designs • Breakthrough technology • Teamwork • Product development • Product assembly • Distribution channels One or more strengths can provide a competitive advantage and help an organization differentiate itself in the marketplace. For example, if a company is exceptional at research and development, the company might concentrate efforts and resources in that area to build or strengthen a competitive advantage. Conversely, spreading resources too thin across too many areas can weaken an organization's competitive stance. Every organization has distinct strengths. However, some organizations enter markets they do not belong in, produce products or services for which they lack expertise, or attempt to manage operations they do not understand. This does not mean an organization should never venture into new areas, but the organization should have a realistic understanding of what it will take to succeed.

46

Weaknesses

Six Sigma Black Belt | Enterprise-Wide Deployment | Organizational Goals and Objectives Concept: Weaknesses

Identifying organizational weaknesses answers the question "What skills, capabilities and competencies are lacking that prevent the organization from fully achieving its goals and objectives?" For example, an organization may discover that it has insufficient customer listening posts to support the desired level of customer service. Weaknesses are often considered opportunities for improvement. Any of the examples of strengths previously listed could become weaknesses. Given a deficiency, an organization generally has three choices: • Modify the goal and objective into something achievable • Invest the necessary capital to acquire the knowledge or skill required • Find another organization that has the expertise needed and outsource that requirement or develop an alliance It is common for organizations to readily identify strengths but struggle with weaknesses. However, weaknesses must be identified and addressed before an organization can plan for and achieve the performance levels necessary to meet its goals and objectives.

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Opportunities

Six Sigma Black Belt | Enterprise-Wide Deployment | Organizational Goals and Objectives Concept: Opportunities

Opportunities are generally described as those events and trends that help an organization grow to new levels. Opportunities are everywhere and are seen through changes in technology, government policy, and social patterns, to name a few. An opportunity could be found in a major situation or key trend present in the firm's business environment, or through identification of a previously overlooked market segment, changes in competitive or regulatory circumstances, technological changes or improved buyer-supplier relationships. Other examples of opportunities include: • New technologies • New markets for products or services • A collaborative partnership • Reduced labor costs through offshore resources • Increased customer relations through CRM technology • Increased product awareness through marketing

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Threats

Six Sigma Black Belt | Enterprise-Wide Deployment | Organizational Goals and Objectives Concept: Threats

Threats are barriers to an organization's growth that put the organization at a competitive disadvantage. No one likes to think about threats, but they must be addressed, even when they are external factors out of our control. It is vital to be prepared to face threats, especially during turbulent times. A threat is a major unfavorable situation in a firm’s environment. Threats are key impediments to the firm’s current or desired position. The entrance of new competitors, slow market growth, increased bargaining power of key buyers or suppliers, technological changes and new or revised regulations could represent threats to a firm’s success. Other examples might include: • Legal or regulatory issues • A new competitor • Changing demographics • A weakening economy • Tax increases • Introduction of new taxes • Dwindling workforce

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Managing Lessons Learned

Six Sigma Black Belt | Enterprise-Wide Deployment | Organizational Goals and Objectives Concept: Managing Lessons Learned

A Six Sigma project generates a wealth of information. Establishing a process to capture, document and share lessons learned infuses change in the organization. In the Quality Progress article, “Planning for Knowledge Management,” William Shockley discusses documenting for knowledge management purposes what an organization learns from processes and projects. Shockley recommends asking and documenting the answers to the following questions: • What went well? • What could have been done differently? • What could be improved? • What did we do that we should not have? • Did all our various departments interact efficiently and effectively? • Where were there gaps? • Where were there overlaps? • What can be done differently next time to make the situation easier for all parties involved? Documentation from lessons learned aids in continued improvement and identification of additional opportunities by: • enabling others to learn how the project was planned, implemented, and monitored. • helping resolve issues. • allowing resources to be tracked back to their work in the project. • creating an audit trail. • providing direction to revise or revive the project later.

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Closed-Loop Assessment

Six Sigma Black Belt | Enterprise-Wide Deployment | Organizational Goals and Objectives Concept: Closed-Loop Assessment

Once lessons learned are documented, they should be integrated into a process that ensures their implementation on future projects and within other parts of the organization. One approach is through a closed-loop assessment, where this type feedback enters into a process that will result in action. Consider the illustration below:

In the context of this discussion, the terms above could be understood as follows: • Assessment: The results of the lessons learned, perhaps as a part of the project final report. • Reporting: Delivery of the lessons learned to the appropriate group within the organization. (e.g., the project steering committee). • Remediation: Actions taken by the group in response to the lessons learned. These include corrective action and input for future projects. Organizations should establish a project repository or database to maintain records of projects completed and to provide a reference for future projects. Project repositories help to translate improvements and lessons learned to other processes within the organization.

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Six Sigma Black Belt Enterprise-Wide Deployment Org. Improvement and Six Sigma Foundations History

Learning Objectives

Six Sigma Black Belt | Enterprise-Wide Deployment | Org. Improvement and Six Sigma Foundations History Concept: Learning Objectives

At the end of this Enterprise-Wide Deployment topic, all learners will be able to understand the origin of continuous improvement tools used in Six Sigma (e.g., Deming, Juran, Shewhart, Ishikawa, Taguchi).             Portions of this topic were taken from the ASQ Foundations in Quality Learning Series: Certified Manager of Quality/Organizational Excellence.

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History of Six Sigma

Six Sigma Black Belt | Enterprise-Wide Deployment | Org. Improvement and Six Sigma Foundations History Concept: History of Six Sigma

The quality movement can trace its roots to medieval Europe, where, in the late 13th century, craftsmen began organizing into unions called "guilds". Six Sigma's role as a measurement standard has its ancestry in the 1800s introduction of Carl Frederick Gauss' concept of the normal curve. The harbinger of Six Sigma's measurement standard in product variation came about in the 1920's when Walter Shewhart showed that three sigma from the mean is the point where a process requires correction. 1940s

1950s

1970s

1980s

1990s

2000s

The U.S. Military, dependent upon product quality and consistency to support the war effort, becomes the primary proponent of quality. Inspection and sampling techniques are implemented and improved upon, and processes redesigned to increase production efficiency. Statistical quality control is an emerging quality approach. Following World War II, the quality revolution in Japan spurs the birth of total quality in the United States. The Japanese welcome the input of Americans Joseph M. Juran and W. Edwards Deming, and rather than concentrating on inspection, focus on improving all organizational processes at the worker level. Juran facilitates the move from statistical quality control (SQC) to total quality control (TQC) in Japan. Japan’s high quality products steadily steal market share from U.S. industries. The U.S. response, emphasizing not only statistics but approaches that embraced the entire organization, becomes known as total quality management (TQM). Six Sigma begins in 1986 as a statistically-based method to reduce defects in production processes at Motorola Inc. By the late 80s, it extends to critical business processes. In 1991 Motorola certifies its first 'Black Belt' Six Sigma experts, signifying the formalization of the accredited training of Six Sigma methods. In the same year, Allied Signal becomes the second to adopt Six Sigma, followed by GE in 1995. New quality systems evolve from the foundations of Deming, Juran and the early Japanese practitioners of quality. Quality moves beyond manufacturing into service, healthcare, education and government sectors.

Adapted from The History of Quality, by the American Society for Quality; and Quality Assurance and Reliability in the Japanese Electronics Industry, World Technology Evaluation Center. We will now discuss these Quality Pioneers and their approaches in more detail.  

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Origins of Continuous Improvement

Six Sigma Black Belt | Enterprise-Wide Deployment | Org. Improvement and Six Sigma Foundations History Concept: Origins of Continuous Improvement

Six Sigma contains a broad collection of concepts and tools used to discover organizational defects and their remedies. Each of these tools was pioneered by one person, who developed a particular facet of the quality effort, then tested and proved it to be useful to the global community. In this topic, we will discuss seven of the men behind the tools of Six Sigma and offer perspective on the tools any Black Belt will encounter and likely put to use.

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Philip B. Crosby

Six Sigma Black Belt | Enterprise-Wide Deployment | Org. Improvement and Six Sigma Foundations History Concept: Philip B. Crosby

Philip B. Crosby (1926-2001) is considered the business person of quality. He was one of ITT’s first vice presidents of corporate quality, and gained prominence in the quality field after publishing Quality Is Free in 1979. Subsequently, he founded Philip Crosby Associates, a quality management consulting firm, and the Quality College, an institute that provides quality training for top management. One of Crosby’s major contributions was making quality meaningful and accessible to American executives. He promoted addressing quality problems through existing management and organizational structures rather than from a statistical basis.    

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Crosby Four Absolutes

Six Sigma Black Belt | Enterprise-Wide Deployment | Org. Improvement and Six Sigma Foundations History Task: Crosby Four Absolutes

In Crosby's quality philosophy, the “four absolutes of quality management" are designed to answer the following questions: What is quality? Quality has to be defined as conformance to requirements, not as "goodness." Management’s job is to establish the requirements, supply the wherewithal, and encourage and help employees get the job done. The basis of this policy is DIRFT—“Do It Right the First Time.” Requirements for quality must be thoroughly understood and accepted. What system is needed to cause quality? The system for causing quality is prevention, not appraisal. The first step toward defect and error prevention is to understand the process responsible for creating the product. When a defect occurs, discovery and elimination are the top priorities. Prevention is a knowledge issue for quality-focused workers. What performance standard should be used? The performance standard must be zero defects, not “that’s close enough.” The only performance standard that makes sense for DIRFT is zero defects. Zero defects must be a performance standard of everyone in the company, from top management to line workers. What measurement system is required? The measurement of quality is the price of nonconformance, not indexes. A dollar figure can be established for the cost of quality (COQ) by determining the difference between the price of nonconformance (PONC) and the price of conformance (POC). PONC is the expense of doing things the wrong way and can account for 20% to 35% of revenues. POC is the expense of doing things right—typically 3% to 4%. COQ is not a standard to be met. Managers should spend time identifying where it occurs and address what makes it occur. Source: Quality Without Tears, by Philip B. Crosby.

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Crosby 14 Steps

Six Sigma Black Belt | Enterprise-Wide Deployment | Org. Improvement and Six Sigma Foundations History Concept: Crosby 14 Steps

Crosby also offered a guide to the implementation process. These steps were republished in ASQ’s Quality Progress (December 2005), adapted from Crosby’s Quality Is Free: The Art of Making Quality Certain. The steps are designed to help individuals and organizations understand the long-term effort needed and to persevere through the necessary change in order to receive the resultant benefits of quality improvement. 1.

2. 3.

4.

5. 6. 7.

8.

9.

10. 11. 12. 13. 14.

Management commitment: Management must understand and then commit to quality improvement. Then management must garner the commitment of each individual to live a work life of conforming to requirements and/or have the requirements updated to reflect true customer needs. Quality improvement team: A quality team representing the entire company is needed to enable and guide the improvement process decisively. Quality measurement: Bring the entire company under the some form of measurement. Measurement allows management to assess progress and determine improvement targets. Cost of quality evaluation: Organizations must identify the COQ in a formal and objective manner and then feed the identified costs into the regular management process. Quality awareness: People need to know about the organization’s quality policy, management’s commitment to quality and the costs of poor quality. Corrective action: Corrective action is required to identify and eliminate problems. Establish an ad hoc committee for the zero defects program: Form a subcommittee (from the original quality improvement team or other involved employees) to understand zero defects conceptually and determine how to apply the concepts specifically within the organization. Begin planning and working the plan as the company moves toward “Zero Defects Day” (Step 9) Supervisor training: Provide training to all levels of supervisors with the expectation that they will understand the program well enough to teach it to their employees. Zero defects day: On "zero defects day," management makes a commitment to quality in front of the entire organization and emphasizes that the entire organization must abide by it. Goal setting: While zero defects are the ultimate goal, individual groups should identify interim goals that are made public to the rest of the organization. Error cause removal: Organizations should ask employees to describe the problems they have so that something can be done about them. Recognition: Organizations should develop a recognition program for all employees, from executives to line workers. Quality councils: Quality professionals should come together periodically and learn from each other. Do it over again: By learning, watching, and participating, quality improvement teams can find ways to continue the quality improvement process.

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W. Edwards Deming

Six Sigma Black Belt | Enterprise-Wide Deployment | Org. Improvement and Six Sigma Foundations History Concept: W. Edwards Deming

Dr. W. Edwards Deming (1900-1993) is widely credited with starting the modern quality improvement movement. He introduced statistical methods to American industry during World War II, but these were largely abandoned after the war. Later, in the early 1950s, Deming introduced his statistical methods to the Japanese. The Japanese embraced Deming and his quality philosophy, ultimately naming the country’s quality prize after him. According to Deming, good quality does not necessarily mean high quality. A predictable degree of uniformity and dependability is suited to the market at low cost, such that quality is whatever the customer needs and wants. Deming’s quality management principles support a process-oriented approach to the production of goods and services: • Teach process improvement as the path to increased quality and performance. • Acknowledge the workers’ expertise and involve them in continuous process improvement (CPI). • Understand variation using statistical analysis. Overall, Deming emphasized that the key to quality is in management’s hands: 95% of quality problems are due to the system, while only 5% are due to employees.  

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Deming and The 14 Points

Six Sigma Black Belt | Enterprise-Wide Deployment | Org. Improvement and Six Sigma Foundations History Task: Deming and The 14 Points

The basis of Deming’s philosophy is a list of objectives he called “the 14 points for Management.” These are requirements for a business whose management plans to remain competitive, producing goods and services that will have a suitable market. Points 1 through 5: 1. Create constancy of purpose. Create constancy of purpose toward improvement of products and services with the aim of becoming competitive, staying in business, and providing jobs. 2. Adopt the new philosophy. We are in a new economic age. Western management must awaken to the challenge, learn their responsibilities and take on leadership for change. 3. Cease dependence on inspection. Eliminate the need for inspection on a mass basis by building quality into the product from the beginning. 4. End the practice of awarding business on the basis of price tag. Instead, minimize the total cost. Move toward a single supplier for any one item, based on a long-term relationship of loyalty and trust. 5. Improve constantly and forever. Make constant improvement part of the system of production and service, and you will experience a constant decrease in costs. Source: Out of the Crisis, by W. Edwards Deming.

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Deming and The 14 Points Cont.

Six Sigma Black Belt | Enterprise-Wide Deployment | Org. Improvement and Six Sigma Foundations History Task: Deming and The 14 Points Cont.

The basis of Deming’s philosophy is a list of objectives he called “the 14 points.” These are requirements for a business whose management plans to remain competitive producing goods and services that will have a suitable market. Points 6 through 10: 6. Institute training. Institute training on the job. 7. Institute leadership (see Point 12). Institute leadership to help people and machines and gadgets do a better job. Leadership in management is in need of an overhaul, not just the leadership of production workers. 8. Drive out fear. Eliminate fear, so everyone will work effectively for the company. 9. Break down barriers. Break down barriers between departments. People in research, design, sales, and production must work as a team to foresee problems of production and usage that may be encountered with the product and service. 10. Eliminate slogans, exhortations, and targets for the workforce. Eliminate slogans, exhortations, and targets for the workforce asking for zero defects and new levels of productivity. Source: Out of the Crisis, by W. Edwards Deming.

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Deming and The 14 Points Cont.

Six Sigma Black Belt | Enterprise-Wide Deployment | Org. Improvement and Six Sigma Foundations History Task: Deming and The 14 Points Cont.

The basis of Deming’s philosophy is a list of objectives he called “the 14 points.” These are requirements for a business whose management plans to remain competitive producing goods and services that will have a suitable market. Points 11 through 14: 11. Eliminate work standards; eliminate management by objective. Substitute leadership for work standards (quotas) on the factory floor. Substitute leadership for management by objective. Eliminate management by numbers, numerical goals. 12. Remove barriers that rob employees of the right to pride of workmanship. Remove barriers that rob the hourly worker of the right to pride of workmanship. The responsibility of supervisors must be changed from sheer numbers to quality. Remove barriers that rob people in management and engineering of their right to pride of workmanship. This means “inter-alias,” abolishment of the annual or merit rating, management by objective or management by numbers. 13. Institute a vigorous program of education. Institute a vigorous program of education and self-improvement. 14. Put everybody in the company to work to accomplish the transformation. The transformation is everybody’s job. Source: Out of the Crisis, by W. Edwards Deming.

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Dr. Armand V. Feigenbaum

Six Sigma Black Belt | Enterprise-Wide Deployment | Org. Improvement and Six Sigma Foundations History Concept: Dr. Armand V. Feigenbaum

Dr. Armand V. Feigenbaum (1920- ) is generally credited with developing the concept of “total quality control” during the late 1940s while an employee of General Electric. In the late 1960s, he started his own company, the General Systems Company, to provide consulting services for quality management and strategic planning. Feigenbaum placed major emphasis on the need for total quality control in order to achieve productivity, market penetration, and competitive advantage. In his book Total Quality Control, Feigenbaum defines total quality control as “an effective system for integrating the quality-development, quality-maintenance, and quality-improvement efforts of the various groups in an organization so as to enable marketing, engineering, production, and service at the most economical levels which allow for full customer satisfaction.”    

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Feigenbaum Four Fundamentals

Six Sigma Black Belt | Enterprise-Wide Deployment | Org. Improvement and Six Sigma Foundations History Concept: Feigenbaum Four Fundamentals

Feigenbaum’s quality philosophy emphasizes the need for everyone in the organization to focus obsessively on serving the external and internal customers. To this end, Total Quality Control provides Four management fundamentals of total quality: 1. 2. 3. 4.

Make quality a full and equal partner, with innovation starting from the inception of product development. Emphasize getting high-quality product design and process matches upstream, before manufacturing planning has frozen the alternatives. Make full-service suppliers a quality partner at the beginning of design rather than implementing a quality surveillance program later. Make the acceleration of new product introduction a primary measure of the effectiveness of a company’s quality program.

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Feigenbaum Ten Benchmarks

Six Sigma Black Belt | Enterprise-Wide Deployment | Org. Improvement and Six Sigma Foundations History Task: Feigenbaum Ten Benchmarks

In addition to the "Four Fundamentals," Feigenbaum offers Ten benchmarks that are key to implementing total quality control with success. Benchmarks 1 through 5: 1. Quality is an organization-wide process Quality is neither a specialist function, nor a department, nor an awareness or testing program alone. It is a disciplined system of customer-connected work processes implemented throughout the organization and integrated with suppliers. High quality products are the result of high quality work processes. If you do not improve the process, you cannot expect substantial improvement in results.  2. Quality is what the customer says it is. Quality is not what a developer, manager or marketer says it is. If you want to find out about your quality, ask your customer. No one can compress in a market research statistic or defect rate the extent of buyer frustration or delight. 3. Quality and cost are a sum, not a difference. Quality and cost are not adversaries. The quality costs of fixing failures are high compared to quality costs required to properly prevent such defects. True quality leaders are cost leaders, and commonly enjoy advantages of 10-20% for competitive cost. 4. Quality requires both individual and teamwork zealotry. Quality is everyone's job. Without a clear infrastructure that supports both the quality work of individuals and the teamwork among individuals and departments, however, quality is an orphaned responsibility. Too often quality improvement activities become islands without bridges. All the left hands must work effectively with all the right hands. 5. Quality is a way of managing. Good management today means empowering the quality knowledge, skills and attitudes of everyone in the organization to recognize that making quality right makes everything else in the organization right. The belief that quality travels under some exclusive national passport, or has some unique geographical or cultural identity, is a myth.

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Feigenbaum Ten Benchmarks cont.

Six Sigma Black Belt | Enterprise-Wide Deployment | Org. Improvement and Six Sigma Foundations History Task: Feigenbaum Ten Benchmarks cont.

In addition to the "Four Fundamentals," Feigenbaum offers Ten benchmarks that are key to implementing total quality control with success. Benchmarks 6 through 10: 6. Quality and innovation are mutually dependent. Quality requires product and process innovation, and the key to successful new products is to make quality the partner of development from the beginning, not to use it as a clean-up tool after problems surface. It is essential to fully include the customer in all phases of development. Paper studies cannot do the job. 7. Quality is an ethic. The pursuit of excellence with the understanding that what you are doing is right is the strongest human emotional motivator in any organization and is the basic driver in true quality leadership. Quality programs relying solely on cold metrics are never enough. 8. Quality requires continuous improvement. Quality is a constantly upward-moving target, while continuous improvement is an in-line, integral component of everyone's job responsibility. This requires more than just "better-than-last-year" internal incremental improvement. The marketplace defines world-class performance. 9. Quality is the most cost-effective, least capital-intensive route to productivity. Some of the world's strongest organizations have blindsided their competition by concentrating on eliminating their "hidden" plant or organization – the part that exists to find and fix mistakes and the associated waste. They have done this by changing their productivity concept from "more" to "good" (a quality leadership concept), creating the "more good quality productivity" concept. 10. Quality is implemented with a total system connected to both customers and suppliers. The relentless application of the systematic method that makes it possible for an organization to manage its quality and associated costs makes quality leadership real in an organization.

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Feigenbaum Crucial Elements of Total Quality

Six Sigma Black Belt | Enterprise-Wide Deployment | Org. Improvement and Six Sigma Foundations History Concept: Feigenbaum Crucial Elements of Total Quality

Feigenbaum also established nine elements of total quality that enable a total customer focus (internal and external): 1. 2. 3. 4. 5. 6. 7. 8. 9.

Making quality leadership a business center point for revenue growth and competitive strength. Achieving complete customer quality satisfaction and driving buyer acceptance. Developing effective supplier and other business quality partnerships. Maximizing the effectiveness of quality data. Accelerating sales and earnings growth through quality cost management. Forming an integrated company quality systems network through customer, producer and supplier relationships. Encouraging the tools and resources to create individual quality improvement emphasis. Recognizing quality as an international business language. Assuring quality leadership is a foundation for successful ethical behavior and social contribution.

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Dr. Kaoru Ishikawa

Six Sigma Black Belt | Enterprise-Wide Deployment | Org. Improvement and Six Sigma Foundations History Concept: Dr. Kaoru Ishikawa

Dr. Kaoru Ishikawa (1915-1989), considered the father of Japanese quality control efforts, was involved with the Japanese quality movement from its inception. He was instrumental in making the quality movement a nationwide phenomenon through his educational efforts and his work with the Union of Japanese Scientists and Engineers. Ishikawa states that quality control is the practice of developing, designing, producing and servicing a quality product that is most economical, most useful and always satisfactory to the consumer.  

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Ishikawa CWQC

Six Sigma Black Belt | Enterprise-Wide Deployment | Org. Improvement and Six Sigma Foundations History Concept: Ishikawa CWQC

Ishikawa developed the concept of company-wide quality control (CWQC) to distinguish the Japanese approach to total quality control from its Western counterpart. As stated in the Quality Engineering Handbook, First Edition, the concept of CWQC incorporates: • Participation by all members of the organization in quality control • Education and training in quality control • Quality control circle activities • Using advanced statistical methods and the 7M tools: ° ° ° ° ° ° ° •

Affinity diagram Interrelationship digraph Tree diagram Prioritization matrices Matrix diagram Process decision program (PDPC) chart Activity network diagram

Nationwide quality control promotion activities

In addition to CWQC, Ishikawa’s philosophy also promotes many of the ideas that are now associated with the quality movement, including: • Next operation as customer (i.e., internal departments serving one another as customers rather than treating each other as enemies) • Elimination of sectionalism (i.e., getting rid of the “it’s not our job” mentality) • Worker training and empowerment • Pursuit of customer satisfaction • Humanistic management of workers

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Dr. Joseph M. Juran

Six Sigma Black Belt | Enterprise-Wide Deployment | Org. Improvement and Six Sigma Foundations History Concept: Dr. Joseph M. Juran

Along with Deming, Dr. Joseph M. Juran (1904- ) is considered by many to be a co-founder of the 20th-century quality movement. His quality experience began in 1924 with an inspection job and evolved into a quality career of research, lecturing, consulting, and writing that spans more than 50 years. In that time, and through his affiliation with the American Management Association, he has taught the course “Managing for Quality” to over 100,000 people in more than 40 countries. Juran, like Deming, was instrumental in working with the Japanese to introduce quality concepts. In particular, he championed quality control as a management tool rather than a specialist's technique.    

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Juran Achieving Customer Satisfaction

Six Sigma Black Belt | Enterprise-Wide Deployment | Org. Improvement and Six Sigma Foundations History Concept: Juran Achieving Customer Satisfaction

In Juran's Quality Planning and Analysis for Enterprise Quality, 5E, Juran and Frank M. Gryna state that “quality is customer satisfaction,” or simply “fitness for use.” Customer satisfaction is achieved through two components: product features and freedom from deficiencies. Product features that meet the needs of customers and thereby provide product satisfaction. This component refers to the quality of design. Overall, product features have a major impact on sales income as they affect market share and premium price. Examples of product features in both the manufacturing and service industries include: Manufacturing industry

• • • • • • • •

Performance Reliability Durability Ease of use Serviceability Aesthetics Availability of options Reputation

Service industry

• • • • • • • •

Accuracy Timeliness Completeness Friendliness and courtesy Anticipating customer needs Knowledge of server Aesthetics Reputation

Source: Adapted from Juran's Quality Planning and Analysis for Enterprise Quality, 5E, by Joseph M. Juran and Frank M. Gryna Freedom from deficiencies. This component refers to the quality of conformance. Freedom from deficiencies has a major impact on costs through reduction in rejects, rework, repairs, complaints, etc.

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Juran Trilogy

Six Sigma Black Belt | Enterprise-Wide Deployment | Org. Improvement and Six Sigma Foundations History Concept: Juran Trilogy

In Juran on Quality by Design, Juran asserts that “managing for quality is done by use of the same three managerial processes of planning, control, and improvement that are used to manage finance.” Thus, • Quality planning is analogous to financial planning and budgeting. • Quality control is analogous to financial control. • Quality improvement is analogous to cost reduction. As mentioned, these three quality management processes have come to be known as the Juran Trilogy®. The Juran Trilogy® is a system that top management can use to institutionalize quality, just as they use systems for financial planning, control, and improvement. The process requires patience and persistence. As Juran emphasizes, incremental quality improvements must be made by the thousands, year after year. A narrative overview of the Juran Trilogy® follows on the next two pages. Source: Adapted from Juran on Quality by Design, by Joseph M. Juran.

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Juran Trilogy - Quality Planning and Control

Six Sigma Black Belt | Enterprise-Wide Deployment | Org. Improvement and Six Sigma Foundations History Concept: Juran Trilogy - Quality Planning and Control

Quality planning is the activity of developing products and processes required to meet customers’ needs. It involves the following universal steps: 1. 2. 3. 4. 5. 6.

Establish quality goals. Identify the customers (i.e., those who will be affected by the efforts to meet the goals). Determine the customers’ needs. Develop product features that respond to the customers’ needs. Develop processes that are able to produce those product features. Establish process controls and transfer the resulting plans to the operating forces.

Quality control refers to the process used to meet standards. The process is similar to a feedback loop and involves the following universal steps: 1. 2. 3. 4. 5. 6. 7.

Choose the control subject (i.e., what needs to be regulated). Choose a unit of measure. Set a goal for the control subject. Create a sensor that can measure the control subject in terms of the unit measure. Measure actual performance. Interpret the difference between actual performance and the goal. Take action on the difference (if any).

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Juran Trilogy - Quality Improvement

Six Sigma Black Belt | Enterprise-Wide Deployment | Org. Improvement and Six Sigma Foundations History Concept: Juran Trilogy - Quality Improvement

The quality improvement process is the means of raising quality to unprecedented levels (i.e., “breakthroughs”). The methodology consists of the following universal steps: 1. 2. 3. 4.

Establish the infrastructure needed to secure annual quality improvement. Identify the specific needs for improvement (i.e., the improvement projects). For each project, establish a project team with clear responsibility for conducting and concluding the project. Provide the resources, motivation, and training needed by the teams to: • diagnose the causes. • stimulate establishment of remedies. • establish controls to hold the gains.

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Walter A. Shewhart

Six Sigma Black Belt | Enterprise-Wide Deployment | Org. Improvement and Six Sigma Foundations History Concept: Walter A. Shewhart

Walter Andrew Shewhart (1891-1967) was a physicist, engineer and statistician who is considered by many the father of statistical quality control. While an employee of Western Electric and Bell Telephone Laboratories, Shewhart wrote, lectured and consulted on the subject of quality control. Most of Shewhart's professional career was spent at Bell Telephone Laboratories, where he served in several capacities as a member of the technical staff from 1925 until his retirement in 1956. While at Western Electric Company, Shewhart developed control chart techniques that helped to distinguish between "assignable-cause" and "chance-cause" variations. Shewhart stressed that bringing a production process into a state of "statistical control" is necessary to predict future output and to manage a process economically. Shewhart’s charts were adopted by the American Society for Testing and Materials (ASTM) in 1933 and advocated to improve production during World War II in American War Standards Z1.1-1941, Z1.2-1941 and Z1.3-1942. Shewhart was ASQ's first honorary member.  

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Walter A. Shewhart cont.

Six Sigma Black Belt | Enterprise-Wide Deployment | Org. Improvement and Six Sigma Foundations History Concept: Walter A. Shewhart cont.

Control chart The contribution for which Shewhart is most widely known is the control chart. Also known as the "Shewhart chart" or "process-behavior chart," the control chart is a statistical tool intended to assess the nature of variation in a process and to facilitate forecasting and management. The control chart is one of the seven basic tools of quality control discussed in the Control lesson of this course. The illustration below is one example of a control chart:

PDCA cycle Shewhart also gave us the Shewhart cycle (sometimes also attributed W. Edwards Deming as the Deming cycle). In his book, Statistical Method from the Viewpoint of Quality Control, Shewhart illustrates the continuous improvement cycle of Plan, Do, Check, Act (PDCA), as seen here:

   

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Dr. Genichi Taguchi

Six Sigma Black Belt | Enterprise-Wide Deployment | Org. Improvement and Six Sigma Foundations History Concept: Dr. Genichi Taguchi

Dr. Genichi Taguchi (1924- ) is often called the “Father of Quality Engineering.” Following World War II, Japan charged Taguchi with improving R&D productivity and enhancing product quality at its Electrical Communication Laboratories (ECL). The Japanese modeled ECL after the United States’ Bell Laboratories in an effort to develop a state-of-the-art communications system. Harold Kerzner, author of Project Management: A Systems Approach to Planning, Scheduling, and Controlling, writes that Taguchi noticed a great deal of time and money being spent on engineering experimentation and testing during his tenure at ECL. In response, Taguchi developed specific quality engineering techniques to optimize the process of engineering experimentation and product design. In the early 1980s, the American companies Ford and Xerox adopted Taguchi’s ideas as a way to improve product quality.  

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Taguchi Quality Loss Function

Six Sigma Black Belt | Enterprise-Wide Deployment | Org. Improvement and Six Sigma Foundations History Concept: Taguchi Quality Loss Function

Taguchi loss function, or "quality loss function," maintains that there is an increasing loss (both for producers and for society at large), which is a function of the deviation or variability from the ideal or target value of any design parameter. The greater the deviation from the target, the greater is the loss. The concept of loss being dependent on variation is well established in design theory, and at a systems level is related to the benefits and costs associated with dependability. Variability inevitably means waste of some kind, but operations managers also realize that it is impossible to have zero variability. The common response has been to set not only a target level for performance but also a range of tolerance about that target that represents "acceptable" performance. Thus if performance falls anywhere within the range, it is regarded as acceptable, while falling outside the range renders it unacceptable. The Taguchi methodology suggests that instead of this implied step function of acceptability, a more realistic function is used based on the square of the deviation from the ideal target, that is, that customers/users get significantly more dissatisfied as performance varies from ideal). Taguchi defines quality as the financial loss to society after an article is shipped – a departure from most customers’ perception that quality is positive or good. In this case, quality is used in a negative sense to indicate the degree of unacceptable product. As an example, consider a quality professional who reports a 3% quality level for a certain material. The 3% represents a loss to society due to unsatisfactory performance. Note: The Improve lesson of this course provides more details on the Taguchi Quality Loss Function. [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

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Taguchi Three Basic Concepts

Six Sigma Black Belt | Enterprise-Wide Deployment | Org. Improvement and Six Sigma Foundations History Concept: Taguchi Three Basic Concepts

While most statistical methods describe what has already happened, Taguchi’s philosophy emphasizes statistical methods that help make things happen. His view of product quality includes three basic concepts: 1. 2.

3.

Quality should be designed into a product, not inspected into it. Quality is best achieved by minimizing deviations from a target. The more “robust” the products, the less sensitive they are to variables that are either ill-controlled or non-controllable. The COQ should be measured as a function of deviation from the midpoint of the specification or tolerance limits; any losses should be measured system-wide.

Overall, Taguchi’s philosophy is technical in nature. While it does not require companies to undergo an internal revolution, it does provide concrete concepts to help them improve products and procedures.

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Lesson Summary

Six Sigma Black Belt | Enterprise-Wide Deployment Summary: Lesson Summary

Enterprise View As we think of how Six Sigma integrates into a business, we understand that Six Sigma is a business initiative, not a quality initiative. It is a way of doing business that improves quality and productivity, increases competitiveness and reduces cost. There are three major components to Six Sigma: • Understanding the culture of the organization • Knowing how to use improvement tools • Understanding support systems for the tools Building Six Sigma into a way of doing business can reduce errors, identify and correct flaws in processes and have a dramatic impact on an organization's success. Six Sigma allows for a cross-functional process focus (across departments) which reduces the likelihood that a positive change in one department will have an unanticipated negative impact on another department. The Six Sigma methodology recognizes that there are many input, output and feedback sources for an organization. Each output may have its own process that is dependent on the input from other processes. All inputs and outputs of a particular process should be measurable so that quality can be controlled. Leadership Successfully implementing Six Sigma projects within an organization requires the commitment of top leadership and a well-defined team with well-defined roles. All team members must be empowered to make the appropriate level of decisions and should be given the necessary time away from their normal work duties to execute their required tasks. Organizational goals and objectives Project goals and objectives should be demonstratively linked to the company’s overall mission. When selecting a Six Sigma project, use the appropriate analytical tools to ensure the appropriate and best project is selected to maximize the company’s return on the investment. Organizational improvement and Six Sigma foundations history To build a tall building, the work begins with a strong foundation. Understanding the roots of the tools and methods used within Six Sigma not only provides a perspective on how these tools integrate into the workplace but also enables an appropriate appreciation for the men who founded the principles.

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Lesson Bibliography

Six Sigma Black Belt | Enterprise-Wide Deployment Concept: Lesson Bibliography

American Society for Quality. ASQ’s Foundations in Quality Learning Series: Certified Manager of Quality/Organizational Excellence. Milwaukee, WI: ASQ, 2005. American Society for Quality. Six Sigma Green Belt Certification Preparation Course, Version 1 (web-based course). Milwaukee, WI, 2006. The American Heritage® Dictionary of the English Language. 4th ed. Houghton Mifflin Company, 2000. Analyzing Business Systems, International Council on Archives, General Editor, Michael Roper; Managing Editor, Laura Millar, International Records Management Trust, London, UK, 1999. Benbow, Donald W. and T.M. Kubiak.The Certified Six Sigma Black Belt Handbook. Milwaukee, WI: ASQ Quality Press, 2005. Blazey, Mark L. Insights to Performance Excellence 2006: An Inside Look at the 2006 Baldrige Award Criteria. Milwaukee, WI: ASQ Quality Press, 2006. Breyfogle III, Forrest W. Implementing Six Sigma: Smarter Solutions® Using Statistical Methods. 2nd ed. Hoboken, NJ: John Wiley & Sons, Inc, 2003. Crospy, Philip. "Crosby's 14 Steps To Improvement," Quality Progress Dec. 2005: 60-64. Crosby, Philip. Quality without Tears. New York: McGraw-Hill, 1984. Deming, W. Edwards. The New Economics for Industry, Government, Education. 2nd ed. Cambridge, MA: MIT Press, 1993. Deming, W. Edwards. Out of the Crisis. Cambridge, MA: MIT Press, 1986. Feigenbaum, Armand V. Total Quality Control. 3rd ed. New York: McGraw-Hill, 1991. Gryna, Frank M., Richard C.H. Chua, and Joseph A. DeFeo. Juran's Quality Planning and Analysis for Enterprise Quality. 5thed. New York: McGraw-Hill, 2005. Juran, Joseph M. Juran on Quality by Design. New York: The Free Press of the McMillan Inc., 1992. Kubiak, T. M., "Feigenbaum on Quality: Past, Present, and Future." Quality Progress. November 2005: 57-62 Pries, Kim H.Six Sigma for the Next Millennium: A CSSBB Guidebook. Milwaukee, WI: ASQ Quality Press, 2006. Pyzdek, Thomas. Quality Engineering Handbook. 1st ed. Milwaukee, WI: ASQ Quality Press, 1991. Pyzdek, Thomas. The Six Sigma Handbook: A Complete Guide for Green Belts, Black Belts, and Managers at All Levels, 2nded. New York: McGraw-Hill, 2003. Shockley III, William. "Planning for Knowledge Management." Quality Progress. March 2000: 57-62.

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Lesson Bibliography

Six Sigma Black Belt | Enterprise-Wide Deployment Concept: Lesson Bibliography

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Six Sigma Black Belt Business Process Management

Lesson Introduction

Six Sigma Black Belt | Business Process Management Introduction: Lesson Introduction

Business Process Management (BPM) is a fundamental Six Sigma concept. Rather than take an individual project-by-project approach to quality, Six Sigma requires that systematic methods are used to understand, control and improve business process results. The focus of efforts to improve quality are linked directly to business goals and care is given to ensure consistency in approach. Six Sigma takes both a holistic and project-specific focus. It is not one to the exclusion of the other. To better understand this concept, the ASQ Body of Knowledge provides the following topics: Process versus functional view • Understand process components and boundaries. • Identify process owners, internal and external customers and other stakeholders. • Understand the difference between managing projects and maximizing their benefits to the business. • Establish key performance metrics and appropriate project documentation. Voice of the customer (VOC) • Segment customers as applicable to a particular project. • Use various methods to collect customer feedback and understand the strengths and weaknesses of each approach. • Use graphical, statistical and qualitative tools to understand customer feedback. • Translate customer feedback into strategic project focus and establishing key project metrics that relate to the voice of the customer and yield process insights. Business results • Calculate process performance metrics and understand how metrics propagate upward and allocate downward. • Understand the importance of benchmarking. • Understand and present financial measures and other benefits of a project. • Understand and use basic financial models. • Describe, apply, evaluate and interpret cost of quality concepts.

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Lesson Overview

Six Sigma Black Belt | Business Process Management Introduction: Lesson Overview

The tools and objectives of the Business Process Management lesson are illustrated below.

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Six Sigma Black Belt Business Process Management Process versus Functional View

Learning Objectives

Six Sigma Black Belt | Business Process Management | Process versus Functional View Concept: Learning Objectives

At the end of this Business Process Management topic, all learners will be able to: • understand process components and boundaries. • identify process owners, internal and external customers and other stakeholders. • understand the difference between managing projects and maximizing their benefits to the business. • establish key performance metrics and appropriate project documentation.         Portions of this topic were taken from the ASQ Six Sigma Green Belt web-based Certification Preparation Course.

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Introduction

Six Sigma Black Belt | Business Process Management | Process versus Functional View Introduction: Introduction

An important concept in Six Sigma is business process management (BPM). BPM is the ability to define and improve business processes to create added value for all stakeholders. It requires the organization to focus on systemic approaches to improving quality in processes rather than taking a disjointed approach with competing methods, competing stakeholders and competing outcomes. As seen below, traditional management structures create vertical silos. For example, most manufacturing organizations have an operations group, a research and development group, a human resources group, a marketing group, an information technology group, a customer service group, a sales group, a finance group, and so on. If a product process flows in and through several of these groups, then each group may have very different ideas on defining the process, measuring it and improving it.

Similarly, W. Edwards Deming described the supplier – process – customer framework by emphasizing the importance of the interdependence of these system components. That, coupled with statistical methods and process feedback, can be used to improve business processes. The goal of BPM is to implement a systemic approach that overcomes the natural silo mentality that builds in an organization.

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Business Systems and Processes

Six Sigma Black Belt | Business Process Management | Process versus Functional View Concept: Business Systems and Processes

A Six Sigma project revolves around analyzing and improving a company's processes. This is why it is crucial to determine what a company's processes are, including where those processes start and stop and what they contain. According to Benbow and Kubiak in The Certified Six Sigma Black Belt Handbook: " A business system is designed to implement a process or, more commonly, a set of processes. Business systems make certain that process inputs are in the right place at the right time so that each step of the process has the resources it needs. Perhaps most importantly, a business system must have as its goal the continual improvement of its processes, products, and services. The diagram below illustrates the relationship between systems, processes, subprocesses, and steps. Each part of the system can be broken into a series of processes, each of which may have subprocesses. The subprocesses may be further broken into steps. "

   

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Process Components

Six Sigma Black Belt | Business Process Management | Process versus Functional View Concept: Process Components

Processes can be defined as a series of events that produce an output. They contain different elements, actions and steps. The objective of most business processes is to add value to the product or service being created, which, in turn, will be sold to a customer. Not every process adds value directly, but may be necessary for the business to support other value-adding processes. In assessing the organizations existing processes, those that are identified as not adding value or are not functioning efficiently may be selected for process improvement efforts or for elimination. Process components include everything it takes to get from "step A" to "step B," including inputs, process steps and outputs. It is important to identify specific process steps in order to determine those that add value to the process. The measurements captured for the inputs, process steps and outputs can be used to optimize (or eliminate) the particular process measured. The items to be measured can be controlled and changed. At a minimum, a process contains the following elements: • Inputs: The people or organizations that provide the raw material or resources to use in the process • Task or process steps: How raw materials and resources are transformed into a product or service • Outputs: The people or organizations that receive the product or service produced The diagram below illustrates an example of these elements.

   

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Process Boundaries

Six Sigma Black Belt | Business Process Management | Process versus Functional View Concept: Process Boundaries

As a variety of processes flow through an organization, there are points where one process ends and another begins. Process boundaries are the beginning and end points of a process. These boundaries are identified using flowcharts and process maps. Given the complex nature of most modern business processes, defining process boundaries is clearly important to the Six Sigma process. The transition points between boundaries are especially important. They can often represent a transition between people, departments or divisions. Any process is susceptible to inefficiencies at these points. This transition issue makes it all the more important to set clear boundaries for a process to be evaluated. The focus should be on a project with clear boundaries and endpoints as you will learn in the Define lesson of this course. When setting boundaries for a process under evaluation, be cautious where the boundary exists to avoid issues of transition (hand-offs) between departments or organizational levels. Mitigating potential issues at the "hand-off" points is key, and the following tools can help in the transition: • Control or action plans • Pilot or phased approach of implementing solutions • Training

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Process Hand-Offs

Six Sigma Black Belt | Business Process Management | Process versus Functional View Concept: Process Hand-Offs

A critical challenge to setting clear project boundaries is that many business processes cut across multiple departments. An example of such a process is quote-to-cash, shown below. The diagram depicts the process from one department to the next, showing how each transition is a potential "leaking point.” At any of these points, data are lost, waste increases, delays occur, information disappears and the process becomes less efficient.

It can be difficult from a people management perspective to work toward improving efficiencies across departments. Department leaders bring their own agendas and reward-based behavior to such meetings. In addition, this may be the first time two particular leaders have been in a room together working toward the same goal. Furthermore, by nature of the current processes, a naturally antagonistic relationship may exist between the two departments. Making this processes more efficient takes a great deal of cooperation and often major change. Cross functional area challenges include: • Stakeholders in various functional areas (they need to get "buy in" from different people in the organization) • Team members in various functional areas (the project is not their main job function) • Time commitment (team members may not have much time to spend on the project due to other expectations) • Departments with different opinions on “which process is most important to be fixed” may fight for their project and be unwilling to work on other projects • Departments unwilling to share information (processes) that would help a project  

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Introducing Owners and Stakeholders

Six Sigma Black Belt | Business Process Management | Process versus Functional View Concept: Introducing Owners and Stakeholders

Effective Six Sigma projects cannot happen without the appropriate decision makers taking ownership of the project. In addition to key resources "buying in" to the change, these and other resources must be available to give an appropriate level of input and make decisions. Often, the individuals who are needed are the busiest and cannot find time to participate in the project unless the level of importance is appropriately elevated. These individuals should be identified early on and informed of their role in the project as soon as practical. Who is a stakeholder? A stakeholder is anyone who has an interest in the business. This broad group might include:

Each stakeholder has a different interest based on their relationship to the business. Similar to stakeholders in the business, there are project stakeholders – those who have an interest in the process at issue. Examples of this group are usually employees, managers, department heads, customers, suppliers or vendors and process owners. What is an owner? Six Sigma narrows the definition of owner to a process owner, such as a member of the management team within the organization responsible for a specific process. The process owner leads the improvement effort for their area of responsibility by: • identifying all stakeholders within the process. • thoroughly understanding all the relevant process elements, process flows, and process boundaries as well as associated measurements to enable process improvement. • assigning team members or subject-matter experts (SMEs) from their respective department to the project.  

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Defining Owners and Stakeholders

Six Sigma Black Belt | Business Process Management | Process versus Functional View Task: Defining Owners and Stakeholders

To further illustrate the differences among the various types of stakeholders, click the title of the stakeholder in the list below: Primary Business Stakeholders • Investors • Owners or shareholders • Board of directors • Employee ownership groups Process Owners • Principal stakeholder of the selected process • Typically a member of the management team • Project sponsor with vested interest in its success Internal Customer Stakeholders • People or groups who are downstream from the selected process who receive value from its outputs • Other people or groups within the organization who are affected by the process outcomes • Those who serve external customers in some capacity External Customer Stakeholders • Those who purchase the product or service produced by the process Internal Supplier Stakeholders • People or groups who provide input to the selected process • Other people or groups affected in some way by the process and what supports the process External Supplier Stakeholder • Those who supply raw materials or resources used in the process Other Project Stakeholders • Project team members who have a vested interest in the success of the project • Other employees or groups who are affected by the process, but not directly involved in it • Senior management sponsors other than the process owner • Government agencies (in some circumstances)

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Introduction to Project Management

Six Sigma Black Belt | Business Process Management | Process versus Functional View Concept: Introduction to Project Management

Understanding project management basics is essential to successfully communicating the many facets of this complex process. This subtopic will illustrate how project management supports the objectives of BPM. Further details on Six Sigma project management may be viewed in the lesson entitled "Project Management." The foundation document that begins this process is the project charter. The definition and scope of the project is established differently in a Six Sigma project versus a traditional project. For example, a traditional project for IT solutions may be to develop, design and implement an automated system access form. On the other hand, a Six Sigma project may focus on very specific metrics such as reducing down-time for new hires by 20%. Six Sigma project goals line up directly with company strategic goals and objectives. Sometimes, the Black Belt or Master Black Belt defines the scope of the project. In other organizations, a process owner may define it. In still others, a strategic plan may define the scope. The scope can always be expanded or clarified by the project team. Regardless of how the scope is determined, the project charter documents the project scope.

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Project Manager Roles

Six Sigma Black Belt | Business Process Management | Process versus Functional View Concept: Project Manager Roles

Black Belts play multiple roles when managing a Six Sigma project. They: • develop the project plan and other tools to manage the project. • manage the project team by assigning tasks and ensuring their execution. • communicate progress and results to project stakeholders. • facilitate the project through difficult periods and transitions. • manage the project focus in addition to managing the project execution. The next lesson in this course, Project Management, outlines detailed information on project management for Six Sigma projects. For the purposes of this introduction, we will concentrate on the the difference between managing project execution and managing project focus. All projects require good management skills, but Six Sigma projects differ in that the focus of the project is paramount. The results of the process improvement effort must be connected to key and well-defined business results. While BPM is concerned with focusing on the "right projects" and the "right processes" with the greatest opportunities, project management is concerned with "doing things right." The foremost role for the Six Sigma project manager is to ensure that the focus on business results drives all decisions about the project.

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Project Benefits

Six Sigma Black Belt | Business Process Management | Process versus Functional View Concept: Project Benefits

The benefits realized from the project are often the starting point for selecting the project itself. Projects may be selected for a variety of reasons, including: • Customer complaints • Product defects • Waste and cost reduction • Cycle time improvement • Work flow improvement • Supplier quality improvement • Customer service improvement • Error reduction • Sales improvement The selection of the project should have anticipated benefits related to company strategies and customer needs. The project goal states the benefits in clear and specific language.The Project Management lesson provides further details about developing problem statements and goal statements. Example: Reduce production line defects to less than 1.5% for all products started on the line by October 1, 2007. Example: Reduce the exception processing steps contributing to inspection, rework and overtime resulting in a 20% reduction in the cost per unit by 4th quarter 2006.  

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Introduction to Performance Metrics

Six Sigma Black Belt | Business Process Management | Process versus Functional View Task: Introduction to Performance Metrics

Performance metrics fall into three categories: quality, time, and cost. These three metrics work within a delicate balance. Improving quality might require an increase in the time needed for production, which would also increase costs. Reducing the cycle time might reduce costs, but it also might reduce quality. Reducing costs might also reduce quality if source materials are less expensive because they are inferior in quality. Click the terms below to learn more about performance metrics. Quality • Fewer defects • Higher quality of material resources • Fewer warranty items or returns • Higher demand by customers for product or service • Customer survey scores increasing Time • Cycle-time reductions • Response time in a call center • Time-to-market • Response time to customer inquiries • Time to complete special orders Cost • Revenue realized due to increased sales of a product or service that, in turn, is due to lowered price, reduced costs of production, volume improvement, improved product quality, enhanced product features, better availability to the customer, fewer defects and so on. • Cost reductions realized through fewer defects, less scrap, fewer returns, fewer warranty items and so on.

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Performance versus Project Metrics

Six Sigma Black Belt | Business Process Management | Process versus Functional View Concept: Performance versus Project Metrics

Performance metrics are used to determine how effective or efficient a process is, and to establish goals for the project’s anticipated outcome. Performance metrics are determined as the Six Sigma process is applied to a specific process, and they are recorded in project documentation. Examples of performance metrics include defects per unit (DPU), cost of poor quality (COPQ) and cost of quality (COQ). Performance metrics describe the success of the selected process. Project metrics describe the success of the project’s execution. Project metrics might include: • Percent of tasks completed • Resource utilization • Timeliness of task completion or milestones reached • On budget • Project variances on budget, timeliness, or resource use Primary project metrics will respond clearly and specifically to management questions such as: • Are we on schedule using expected resources of people, equipment, facilities, and other resources? • Are we on budget using expected resources of people, equipment, facilities, and other resources? • Are we still expecting to yield the projected value/returns as described in the charter?

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Project Documentation

Six Sigma Black Belt | Business Process Management | Process versus Functional View Task: Project Documentation

Different organizations will elect to use different types of project documentation as demanded by the project. Click each term below to learn more about what project documentation might include. Project Charter As mentioned previously, the project charter is the central piece of documentation in the project management process. While project charters vary by organization, they often include common elements such as team members, business need and project description. More in-depth information on project charters may be viewed in the Project Management lesson. Status Reports • Written with a standardized format and formal tone, delivered periodically. Status reports are specific to each organization. • Provide high-level information on projects ° Where project stands in relation to plan ° Report any risks or issues affecting the time, scope or cost of the project and what is being done to address these issues ° Request management intervention as needed ° Tools used: • Milestone charts • Performance reports • Budget reports Management Reviews • Meetings between the project leader and management providing updates to the status of the project using a Gantt chart, status reports or performance reports. Budget Reviews • Written with a standardized format and formal tone, delivered periodically. Budget reviews are specific to each organization. • Evaluate actual resource and budget utilization • May involve budget revision Customer Audits • Are formal reviews conducted by a certified quality auditor (quality audits have their own Body of Knowledge, which is outside the scope of this course) • Play an active role in keeping the project on track to the stated goals • Should be updated as often as feasible for the project and the needs of the customer Note: In this context, “customer” is defined as the principal stakeholder or "owner of the process" in a project. Additional examples of data and fact-driven documentation are discussed in the Project Management lesson. 100

Six Sigma Black Belt Business Process Management Voice of the Customer

Learning Objectives

Six Sigma Black Belt | Business Process Management | Voice of the Customer Concept: Learning Objectives

At the end of this Business Process Management topic, all learners will be able to: • segment customers as applicable to a particular project. • list specific customers impacted by project within each segment. • show how a project impacts internal and external customers. • recognize the financial impact of customer loyalty. • use various methods to collect customer feedback (surveys, focus groups, interviews and observation) and understand the strengths and weaknesses of each approach. • recognize the key elements that make surveys, interviews and other feedback tools effective. • review questions for integrity (bias, vagueness, etc.). • use graphical, statistical, and qualitative tools to understand customer feedback. • translate customer feedback into strategic project focus areas using quality function deployment (QFD) or similar tools. • establish key project metrics that relate to the voice of the customer and yield process insights.   Portions of this topic were taken from the ASQ Six Sigma Green Belt web-based Certification Preparation Course.

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Voice of the Customer

Six Sigma Black Belt | Business Process Management | Voice of the Customer Concept: Voice of the Customer

Voice of the customer (VOC) is the term used to describe the stated and unstated needs or requirements of the customer. These can be captured in a variety of ways: direct discussion or interviews, surveys, focus groups, customer specifications, observations, warranty data, field reports, complaint logs and so on. Companies that effectively use VOC are proactive and innovative in capturing the changing requirements of the customers over time. They have a defined process to collect and analyze VOC to translate the data into specific requirements needed for a product or service. The VOC is critical to help an organization: • decide what products and services to offer. • identify critical features and specifications for those products and services. • decide where to focus improvement efforts. • determine a baseline measurement of customer satisfaction to measure improvement. • identify key drivers of customer satisfaction. The following are typical outputs of the VOC process: • Identification of customer markets and customer segments • Identification of relevant reactive and proactive sources of data • Verbal or numerical data that identify customer needs • Defined critical-to-quality requirements (CTQs) • Specifications for each CTQ The VOC is determined using four steps: 1. 2. 3. 4.

Identify the customer. Collect customer data. Analyze customer data. Determine critical customer requirements.

The process of collecting and using VOC is continual because customer opinions and attitudes change over time.

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Step 1: Customer Identification

Six Sigma Black Belt | Business Process Management | Voice of the Customer Concept: Step 1: Customer Identification

Customer identification is important for several reasons. A company that knows its customers can: • tailor its products and services accordingly. • become a customer-focused or customer-driven company. • acquire customers more readily. • retain existing customers more easily. • target its marketing efforts. • understand what drives the success of the company. • understand the needs of the customers, who support the company by purchasing its products and services. Customers may be classified as internal or external. To ensure the greatest positive impact to the business from the Six Sigma project, identifying the affected customers and their needs is an important step. [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

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Financial Impact of Customer Loyalty

Six Sigma Black Belt | Business Process Management | Voice of the Customer Concept: Financial Impact of Customer Loyalty

Thomas Pyzdek, in The Six Sigma Handbook, succinctly states: “Customers have value.” Quality management can directly affect customer satisfaction, share of spend and market share, which is why many Six Sigma projects are chosen for “their positive impact on customers.” The book, Six Sigma for the Next Millennium provides the fundamental basis for questions that should be addressed at the beginning of the improvement process: • Will this benefit external customers or only internal customers? • Is this change benefiting a high-value customer or low-value customer (is this a customer we want to keep)? • How will change be communicated, both internally and externally? In this process, it is important to identify how a change will impact a customer, both internally and externally. Will a process change? Will product numbers or documentation change? It is even possible that a customer may not want an improvement because of its negative affect on one or more of their other products or processes.

Evaluating customer value Pyzdek further explains that to determine the value of customer retention, and to help identify the customers most valuable to the firm, a company must evaluate the lifetime of the customer relationship, not each transaction. While it can be easy at times for management to perceive some transactions as a loss (e.g., returns, the cost of technical support), those interactions can lead to increased satisfaction and sales, or the converse. Therefore, the net cost and value to support the customer relationship should be the focus of any evaluation. Although net present value (NPV) analysis can vary by company, it commonly takes into account: • Net profit per year • Customer retention rates • Desired return on assets Extensive customer segmentation can make this analysis more insightful since long-term customers tend to spend more and have fewer bad debts, and new customers are often attracted by discounts. There are costs associated with attracting new customers and retaining long-term customers, but generally the costs to retain are lower than those to attract. The NPV of customers can be used to determine the cost of attracting new customers and leverage customer satisfaction offers. Roll over Page Resources and click Net Present Value to see detailed instructions on calculating NPV.  

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Net Present Value

Six Sigma Black Belt | Business Process Management | Voice of the Customer | Financial Impact of Customer Loyalty Example: Net Present Value

Calculating NPV Pyzdek gives the following calculation for NPV: " 1.

2.

3.

4.

Determine a meaningful period of time over which to do the calculation (e.g., a life insurer would track decades, whereas a diaper manufacturer would track only a few years). Calculate net profit (net cash flow) generated by customers each year. For the first year, subtract the cost of attracting the pool of customers. Specific numbers, such as profit per customer in year one, are more valuable because long-term customers tend to spend more. Chart the customer "life expectancy" using samples to fine out how much the customer base erodes each year. Again, specific numbers are more valuable. In retail banking, 26% of account holders defect in the first year, while in the ninth year, the rate drops to 9%. Pick a discount rate. If you want a 15% annual return on assets, use that.

Costs that should be considered when determining attraction and retention costs: • Advertising • Commissions • Account set up • Loyalty and customer satisfaction programs Calculations • NPV1 = Profit / 1.15 • • •

NPV2 = (Year 2 profit x retention rate) / (1.15)2 Last year: NPVn = (Year n's adjusted profit) / (1.15)n The sum of years 1 through n is how much your customer is worth. This is the NPV of all the profits you can expect.

  "

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External Customer Types

Six Sigma Black Belt | Business Process Management | Voice of the Customer Concept: External Customer Types

External customers fall into three general categories: 1.

2. 3.

Those who use the product or service. Customers in this category are sometimes referred to as end users. A person who purchases a grocery item in a food store is an end user, as is a consumer who purchases a software title. Individuals who resell or repackage the product or service. Customers in this category include distributors, wholesalers, and consulting firms. Anyone affected by the product or service who does not currently use, resell or repackage it. Customers who view advertising on television can be influenced by a product but not actually purchase it. A company whose competition just purchased a new complex software system is affected by that purchase. This group also includes society in general, which is affected by positive and negative attributes of a product, including: • increased traffic • real estate appreciation and depreciation and tax base fluctuations caused by organization relocations • taxpayer cost to treat chemical dependencies or control crime • environmental impact of products and services.

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Customer Segmentation

Six Sigma Black Belt | Business Process Management | Voice of the Customer Concept: Customer Segmentation

A popular method of identifying external customers is called customer segmentation. This method segments customers by characteristics such as geography, demographics (gender, race, income, occupation), brand preference and buying behaviors.

Benefits of customer segmentation After customer segmentation, some markets with specific customer types may be deemed most desirable and will subsequently have marketing dollars applied to them. The benefits of this segmentation approach include: • Multiple marketing programs • Targeted marketing programs with a greater percentage of “hits” • Effective use of marketing dollars • Effective identification of customers and customer needs

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VOC and Kano Model

Six Sigma Black Belt | Business Process Management | Voice of the Customer Task: VOC and Kano Model

VOC is also characterized by customers’ spoken and unspoken expectations, priorities and needs, all of which determine customer satisfaction. The VOC drives quality in both products and services. Dr. Noritaki Kano developed a model of the relationship between customer satisfaction and three levels of quality. Click each quality attribute to reveal the University of Cambridge/Royal College of Art definition and examples. Common alternate names for each category are in parentheses. Threshold Attributes (Basic) Attributes that must be present in order for the product to be successful, can be viewed as a 'price of entry.' However, the customer will remain neutral toward the product even with improved execution of these aspects. • Bank teller will be able to cash a check • Nurses will be able to take a patient's temperature • Mechanic will be able to change a tire • Keyboards will have a space bar Customers rarely mention this category, unless they have had a recent negative experience, because it is assumed to be in place.   One-Dimensional Attributes (Performance, Linear, Expected, Desired, Satisfiers) These characteristics are directly correlated to customer satisfaction. Increased functionality or quality of execution will result in increased customer satisfaction. Conversely, decreased functionality results in greater dissatisfaction. Product price is often related to these attributes. Examples are: • The shortest waiting time possible in the bank drive-up window • The shortest waiting time possible for the nurse to answer the patient call button • The auto mechanic performing the services on the car as efficiently and inexpensively as possible • Tech support being able to help with a problem as quickly and thoroughly as possible Customers give the most information on this category.

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VOC and Kano Model

Six Sigma Black Belt | Business Process Management | Voice of the Customer Task: VOC and Kano Model

Attractive Attributes (Delighters, Exciters) Customers get great satisfaction from a feature - and are willing to pay a price premium. However, satisfaction will not decrease (below neutral) if the product lacks the feature. These features are often unexpected by customers and they can be difficult to establish as needs up front. Sometimes called unknown or latent needs. • The drive-up bank teller greets you by name; remembers you from a previous visit • The nurse brings you a book that you mentioned you enjoy • The mechanic cleans and vacuums the car making it better than when you brought it in • The tech support individual emails you a $5 coupon to compensate for the issue Customers rarely provide VOC on this category because they don't know to expect it. Innovation is needed to provide this level of quality consistently.

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Kano Model Analysis

Six Sigma Black Belt | Business Process Management | Voice of the Customer Concept: Kano Model Analysis

Purpose The Kano analysis tool prioritizes customer requirements based on their affect on customer satisfaction. Although all requirements are important, they may not be equally important to the customer. Kano defines customer satisfaction based on threshold, one-dimensional and attractive attributes.

Features Moving from left to right, fulfillment increases. Moving from bottom to top, satisfaction increases. The three lines represent the three types of requirements. Looking at the threshold line, when the basics are missing, satisfaction plummets. With the one-dimensional attributes line, satisfaction increases as more "perks" are added. With the attractive attributes line, satisfaction is static when delighters are missing, but when they are added, satisfaction increases dramatically. Essentially, the better or more innovative the execution, the higher the customer satisfaction.

As mentioned briefly before, VOC changes over time. As industries become more innovative, features that were once "delighters" become "must haves." At one time an FM radio in a car was a delighter that moved to "more is better" if it was higher quality. Now it is a basic expectation. In the same manner, a car CD player was a delighter and is now "more is better" (more features, with changer, and so on), while accessories to integrate an MP3 player into the car stereo system are delighters.

Benefits • •

Gain a better understanding of the customer's desires Increase customer satisfaction

 

111

Using the Kano Model

Six Sigma Black Belt | Business Process Management | Voice of the Customer Concept: Using the Kano Model

Use When • • • •

Developing risk assessments about customer satisfaction Identifying customer needs Determining functional requirements Analyzing competitive products

User Tips 1.

Ask customers two key questions about each attribute • Rate your satisfaction if the product has this attribute • Rate your satisfaction if the product lacks this attribute

2.

Ask customers to answer with one of the following responses: • Satisfied • Neutral (all products have this; this is normal) • Dissatisfied • Don’t care

3.

Basic attributes generally receive the “neutral” response to Question 1 and the “dissatisfied” response to Question 2. Excluding these attributes in the product has the potential to severely affect the success of the product in the marketplace. Eliminate/include attributes whose presence or absence leads to customer dissatisfaction. This often requires a trade-off analysis against cost. As customers rate attributes or functionality as important, ask the question, “How much extra would you be willing to pay for this attribute or more of this attribute?” This will help determine which excitement attributes would provide the greatest returns on customer satisfaction.

4. 5.

The Kano model is often used in conjunction with quality functional deployment (QFD, discussed in a later section) and prioritization matrices, which are discussed next.

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Step 2: Collecting Customer Data

Six Sigma Black Belt | Business Process Management | Voice of the Customer Task: Step 2: Collecting Customer Data

Different data collection tools are available for determining the VOC. Tool selection must consider the study’s purpose and key decision factors, as well as match the desired evaluation level and data type. Even with a sound decision on these points, there can still be bias that will invalidate or skew the measurements. Click each term to learn more. Purpose • Identify urgent problems • Identify competitor's edge • Identify customer preferences • Determine the customer's desired level of quality • Determine customer needs • Measure customer satisfaction Key Decision Factors • Credibility • Staff skills • Cost/budget • Time constraints • Level of evaluation desired Levels of Evaluation • Knowledge • Behavior • Attitude • Opinion Types of Data Qualitative Data • Descriptive • Not quantifiable • Also called "discrete" data Quantitative Data • Measured • Numerical • Also called "continuous" data

113

Tool Selection

Six Sigma Black Belt | Business Process Management | Voice of the Customer Concept: Tool Selection

Four different levels of evaluation exist: 1. 2. 3. 4.

Knowledge – What facts do we know about the customer? Behavior – How does the customer act given certain events? Attitude – How favorable or unfavorable is this customer’s disposition toward a product or service? Opinion – What beliefs or conclusions are held by the customer?

Selecting the tool to match the desired level of evaluation (result) is one factor in gaining reliable data. For instance, customer service records may provide information about the number of complaints or service calls (knowledge) from a customer, but do not provide information about the customer’s behaviors, attitudes or opinions.

 

114

Data Collection Tools

Six Sigma Black Belt | Business Process Management | Voice of the Customer Concept: Data Collection Tools

Different data collection tools exist for listening to the VOC. Although each tool has strengths and weaknesses, the selected tool should be appropriate and bias free. [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

115

Bias and Error - Data Collection

Six Sigma Black Belt | Business Process Management | Voice of the Customer Concept: Bias and Error - Data Collection

Intentional or not, humans are prone to both bias and error. Culture, preconceived ideas, and perception are a few of the factors affecting any form of human interaction. Whether writing questions for a survey or leading a focus group discussion, researchers must guard against bias that can influence results, and take care not to make an error in judgment. Study the chart below. It contains examples of bias and how well each of the data collection tools compares to each form of bias. The "minus signs" indicate that the negative criteria can be problematic when using that tool. For instance, leading questions/wording are a source of error for interviews and surveys, and are not a problem when using focus groups and observations.

 

116

Step 3: Analyze Customer Data

Six Sigma Black Belt | Business Process Management | Voice of the Customer Task: Step 3: Analyze Customer Data

Customer data change over time because of the customer's attitude, situation, need, and market niche. Many tools analyze customer data. However, selecting the most appropriate tool optimizes the analysis. All of these tools will be discussed in greater detail in the following lessons. Click each tool for a brief description: Histogram According to The Quality Toolbox by Nancy R. Tague, "A frequency distribution shows how often each different value in a data set occurs. A histogram is the most commonly used graph to show frequency distributions." Tague states that histograms are used: " • •

• • • • •

When the data are numerical. When you want to see the shape of the data’s distribution, especially when determining whether the output of a process is distributed approximately normally. When analyzing whether a process can meet the customer’s requirements. When analyzing what the output from a supplier’s process looks like. When seeing whether a process change has occurred from one time period to another. When determining whether the outputs of two or more processes are different. when you wish to communicate the distribution of data quickly and easily to others.

" Line Graphs According to The Quality Toolbox by Nancy R. Tague, "A line graph is the simplest kind of graph for showing how one variable, measured on the vertical y-axis, changes as another variable, on the horizontal x-axis, increases. The data points are connected with a line. The x-axis variable is called the dependent variable, because its value depends on the value of the independent variable." Tague states that line graphs are used: " • • • "

When the pairs of data are numerical. When you want to show how one variable changes with another, continuous variable, usually time. Only when each independent variable is paired with only one dependent variable.

117

Step 3: Analyze Customer Data

Six Sigma Black Belt | Business Process Management | Voice of the Customer Task: Step 3: Analyze Customer Data

Control Charts According to The Quality Toolbox by Nancy R. Tague, "The control chart is a graph used to study how a process changes over time. Data are plotted in time order. A control chart always has a central line for the average, an upper line for the upper control limit and a lower line for the lower control limit. These lines are determined from historical data. By comparing current data to these lines, you can draw conclusions about whether the process variation is consistent (in control) or is unpredictable (out of control, affected by special causes of variation)." Tague states that control charts are used: " • • • • •

When controlling ongoing processes by finding and correcting problems as they occur. When predicting the expected range of outcomes from a process. When determining whether a process is stable (in statistical control). When analyzing patterns of process variation from special causes (non-routine events) or common causes (built into the process). When determining whether your quality improvement project should aim to prevent specific problems or to make fundamental changes to the process.

" Pareto Analysis According to The Quality Toolbox by Nancy R. Tague, "A Pareto chart is a bar graph. The lengths of the bars represent frequency or cost (time or money), and are arranged with longest bars on the left and the shortest to the right. In this way the chart visually depicts which situations are more significant." Tague states that Pareto charts are used: " • • • • "

When analyzing data about the frequency of problems or causes in a process. When there are many problems or causes and you want to focus on the most significant. When analyzing broad causes by looking at their specific components. When communicating with others about your data.

118

Step 3: Analyze Customer Data

Six Sigma Black Belt | Business Process Management | Voice of the Customer Task: Step 3: Analyze Customer Data

Affinity Diagram According to The Quality Toolbox by Nancy R. Tague, "The affinity diagram organizes a large number of ideas into their natural relationships. This method taps a team’s creativity and intuition. It was created in the 1960s by Japanese anthropologist Jiro Kawakita." Tague states that affinity diagrams are used: " • • • "

When you are confronted with many facts or ideas in apparent chaos. When issues seem too large and complex to grasp. When group consensus is necessary.

119

Step 3 Cont.: Analyze Customer Data

Six Sigma Black Belt | Business Process Management | Voice of the Customer Task: Step 3 Cont.: Analyze Customer Data

Click each tool for a brief description: Nominal Group Technique According to The Quality Toolbox by Nancy R. Tague, "Nominal group technique (NGT) is a structured method for group brainstorming that encourages contributions from everyone. "

Tague states that the nominal group technique is used: " • • • • • • "

When some group members are much more vocal than others. When some group members think better in silence. When there is concern about some members not participating. When the group does not easily generate quantities of ideas. When all or some group members are new to the team. When the issue is controversial or there is heated conflict.

120

Step 3 Cont.: Analyze Customer Data

Six Sigma Black Belt | Business Process Management | Voice of the Customer Task: Step 3 Cont.: Analyze Customer Data

Matrix Diagrams According to The Quality Toolbox by Nancy R. Tague, "The matrix diagram shows the relationship between two, three or four groups of information. It also can give information about the relationship, such as its strength, the roles played by various individuals or measurements."

There are several different types of matrix diagrmas. An L-shaped matrix is shown above. Tague states the following uses: " • • • • • •

An L-shaped matrix relates two groups of items to each other (or one group to itself). A T-shaped matrix relates three groups of items: groups B and C are each related to A. Groups B and C are not related to each other. A Y-shaped matrix relates three groups of items. Each group is related to the other two in a circular fashion. A C-shaped matrix relates three groups of items all together simultaneously, in 3-D. An X-shaped matrix relates four groups of items. Each group is related to two others in a circular fashion. A roof-shaped matrix relates one group of items to itself. It is usually used along with an L- or T-shaped matrix.

"

121

Step 3 Cont.: Analyze Customer Data

Six Sigma Black Belt | Business Process Management | Voice of the Customer Task: Step 3 Cont.: Analyze Customer Data

Prioritization Matrix A prioritization matrix is a decision making tool using a systematic process to narrow choices. It is a variation of an L-shaped matrix (discussed in Matrix Diagrams). A prioritization matrix allows raters to rank the options against pre-determined scales, weights and criteria to determine order of importance.

Prioritization matrices are used: • When prioritizing the variables with the greatest significance. • When reaching consensus in small teams. • When comparing a few options to specific standards. • When narrowing a list of options to one choice. • When making decisions based on multiple criteria (best when used for six to eight criteria). • When selecting one product, approach, supplier, option or problem.

122

Step 3 Cont.: Analyze Customer Data

Six Sigma Black Belt | Business Process Management | Voice of the Customer Task: Step 3 Cont.: Analyze Customer Data

Statistical Analysis Quantitative customer data may also be analyzed using basic statistical analysis in addition to using the other tools. Statistical evaluation quantifies and summarizes information and provides a basis for CTQ. Basic statistical analysis might include: • Central tendency (mean, median, and mode) • Variance of data from an established norm • Correlation between various sets of data

 

123

Translating VOC to Organizational Goals

Six Sigma Black Belt | Business Process Management | Voice of the Customer Concept: Translating VOC to Organizational Goals

In the preceding sections, the first three steps of the process to use VOC were discussed. 1. 2. 3.

The customer was identified. Customer data were collected. Customer data were analyzed.

VOC data have little value until they are translated into action, where they can increase quality, customer satisfaction and, ultimately, the bottom line.

124

Step 4: Determining Critical Customer Requirements

Six Sigma Black Belt | Business Process Management | Voice of the Customer Concept: Step 4: Determining Critical Customer Requirements

By use of analysis, the VOC is categorized into key customer issues, which are converted to critical customer requirements (CCRs) or specific, measurable targets. In this way, customer feedback is prioritized and linked directly to internal processes to create change. There are several key components to incorporating CCRs into strategy: • Define how meeting customer requirements will be measured • Determine any impacts or interrelations of CCRs on one another • Translate customer's terms into product features • Identify ways to deliver on customer needs

125

Functional Requirements

Six Sigma Black Belt | Business Process Management | Voice of the Customer Concept: Functional Requirements

Functional requirements (FRs) are the requirements the product or process must possess to satisfy the CCRs. The FRs need to be understood early in the design process in order to establish criteria for selecting a design based on the quality level and development costs that enable the product to service in a competitive marketplace. Along with establishing the FR early in the process, the FRs must be accurate and informative, since misinformation about the FRs can delay the development cycle.

126

CTQ

Six Sigma Black Belt | Business Process Management | Voice of the Customer Concept: CTQ

The next step is to translate the customer feedback into project goals and objectives, for which a “critical to” (CT), matrix is often created. The translation is accomplished by sorting the customer’s needs according to the following characteristics: • Critical-to-quality (CTQ) • Critical-to-delivery (CTD) • Critical-to-cost (CTC) The focus here will be on CTQ.

Benefits • • • • • •

Identifies focus areas Increases customer satisfaction, product quality, and level of business success Improves customer relations May identify an area for innovation Reduces cost of poor quality (COPQ) / cost of quality (COQ) (to be discussed later) Improves customer loyalty

127

CTQ Analysis

Six Sigma Black Belt | Business Process Management | Voice of the Customer Concept: CTQ Analysis

There are essentially two steps to identifying CTQs.

Step 1: Understand customer and technical requirements. • • •

Who are the customers? (Use VOC) What is important to them? (Use VOC to translate into CCRs) What are the technical requirements? (Use CCRs to determine functional/technical requirements)

Step 2: Transfer technical requirements to CTQs. • •

What are the parts and characteristics? What is critical?

By identifying the vital few qualities that outweigh the trivial many, a CT matrix can show where to obtain the greatest impact.

128

Using CT Matrices

Six Sigma Black Belt | Business Process Management | Voice of the Customer Concept: Using CT Matrices

Procedure 1. 2. 3. 4. 5.

Identify the customer. Identify the customer's needs. Identify the customer's basic requirements. Breakdown the requirements into additional detail. Validate the requirements with the customer.

Use When • • •

Working through the Define phase. Identifying methods for delivering customer needs. Preparing for the QFD.

User Tips • • • •

Use an interrelationship diagram to evaluate relationships between customer needs and CCRs. Determine the relative importance of each CCR. Coordinate with the use of the "House of Quality" matrix (to be discussed later). Use a CT matrix to lead into the QFD.

129

Moving to QFD

Six Sigma Black Belt | Business Process Management | Voice of the Customer Concept: Moving to QFD

QFD is a customer-driven planning tool for products and services that focuses on translating customer requirements into technical requirements to deliver products and services with features and capabilities that meet or exceed customer requirements. QFD matrices — a graphic representation often called a House of Quality — are used to display the results of the planning process. CCRs, FRs and CTQs are incorporated directly into QFD matrices such as the House of Quality, which are used to determine how the internal process will be affected. The application of QFD and the use of its matrices will be discussed at length in the DFSS lesson of the course.

130

Process Insights

Six Sigma Black Belt | Business Process Management | Voice of the Customer Concept: Process Insights

As projects or improvements are identified, the result and its improvement and its affect on customers and other stakeholders should constantly be considered. A few important questions to ask include: • Is there any reason a customer may NOT want this improvement? • Is there a change in the product that will require action from the customer, and is the customer prepared for this action (for example, new documentation, new part numbers)? • Has the issue of CTQs of external customers been balanced with concerns about cost, profit, and productivity from internal customers?

131

Six Sigma Black Belt Business Process Management Business Results

Learning Objectives

Six Sigma Black Belt | Business Process Management | Business Results Concept: Learning Objectives

At the end of this Business Process Management topic, all learners will be able to: • calculate defects per unit (DPU), rolled throughput yield (RTY) and defects per million opportunities (DPMO) sigma levels. • understand how metrics propagate upward and allocate downward. • compare and contrast capability, complexity and control. • manage the use of sigma performance measures (e.g., cost of poor quality 'COPQ', parts per million 'PPM', DPMO, DPU, RTY) to drive enterprise decisions. • understand the importance of benchmarking. • understand and present financial measures and other benefits (soft and hard) of a project. • understand and use basic financial models (e.g., net present value 'NPV', return on investment 'ROI'). • describe, apply, evaluate and interpret cost of quality concepts (COQ), including quality cost categories, data collection and reporting.

    Portions of this topic were taken from the ASQ Quality Process Analyst web-based Certification Preparation Course.

133

Introduction

Six Sigma Black Belt | Business Process Management | Business Results Concept: Introduction

As discussed earlier in this lesson, metrics may be categorized into three levels: 1.

2.

3.

Business level metrics are normally financial measures that provide information to shareholders and senior management regarding the organization’s performance. Operations level metrics provide information related to the quality, time, and cost of producing a product or providing a service. These metrics usually apply to departments or larger groups with aggregated information. Process level metrics provide information related to a specific process, its efficiency and effectiveness, and the quality the process yields. This information is typically related to only one process.

The use of these various metrics are discussed in this topic.  

134

Process Performance Metrics

Six Sigma Black Belt | Business Process Management | Business Results Concept: Process Performance Metrics

Process performance metrics establish the current situation of the process. When identifying which process to study for a project, performance indices compare the current status to the target. The project team then selects the process that delivers the least quality to the customer, or the process with the highest cost or variation. The upcoming modules will cover each of the following metrics in detail: • Defects per unit (DPU) • Parts per million (PPM) • Defects per million opportunities (DPMO) • First pass yield (FPY) • Rolled throughput yield (RTY) • Cost of poor quality (COPQ)

Tips • • •

Link the metrics to the needs of the identified stakeholders: shareholders, customers, and/or employees. This initial reference allows one to compare future measures to initial measures in order to gage improvement. Metrics are used to drive project decisions, but on a larger scale, they are used to make strategic management decisions.

135

Defects and Yield

Six Sigma Black Belt | Business Process Management | Business Results Concept: Defects and Yield

A stable process is defined as one that does not contain any special cause variation — it only contains common cause variation. Common cause variation is that which is normal to the process and doesn't change over time. To understand the effect of the overall quality throughout the process, the cumulative effect of throughput and defects through multiple steps must be known. Consider the following questions about a three-process operation. • If each stage has 90% throughput, is the throughput for the entire operation 90%? • If not, what is the overall throughput? • What is the yield? • Does the 10% lost for each stage have a monetary value? These are questions that will be answered in this section.  

136

Defects per Unit

Six Sigma Black Belt | Business Process Management | Business Results Concept: Defects per Unit

Introduction According to ASQ's Glossary and Tables for Statistical Quality Control, defects per unit (DPU) is the measure of capability for discrete (attribute) data, and is found by dividing the number of defects by the number of units: DPU = Defects / Units DPU refers to the average number of defects observed; it is a measurement of yield. A defect is defined as the non-fulfillment of a requirement related to an intended or specific use, such as: • A failure to meet a customer's requirement (characteristic or specification) • Any measured lack of performance needing improvement • Any dissatisfaction expressed by an internal or external customer • Anything prohibiting a service or a part from delivering its intended value to the customer A unit is defined as a quantity of product, material, or service forming a cohesive entity of which a measurement or observation can be made. Examples include: • An assembly • A quantity of time • A process step • A definable service • A product

Benefits DPU provides a common baseline (benchmark) for: • Describing the current situation in quantifiable terms • Evaluating processes for identifying improvement activities • Evaluating a process in an existing project

137

Using DPU

Six Sigma Black Belt | Business Process Management | Business Results Concept: Using DPU

Use When • • •

performing the Define phase, but also throughout the DMAIC process gaining an understanding of the problem generating a measurable statistic (number) for evaluating a process

Information Needed • • • •

A defined nonconformity or defect A defined unit Total number of non-conformances produced from the distribution being measured Total number of items in the distribution

Example Olivia's Toy Manufacturers produces toy cars. The company plans to analyze the finishing process and will start by measuring DPU. The finishing process involves three steps: • Apply paint • Affix decals • Apply clear coat/varnish A sample of 100 cars is used for the observation. DPU is measured for each step and then calculated for the entire process:   Step 1 - Apply paint

Step 2 - Affix decals

Step 3 - Apply clear coat

Final

Units = 100

Units = 100

Units = 100

 

Defects = 2

Defects = 1

Defects = 1

 

DPU = 2 ÷ 100 = .02

DPU = 1 ÷ 100 = .01

DPU = 1 ÷ 100 = .01

DPU = .02+.01+.01 = .04

138

DPU Tips

Six Sigma Black Belt | Business Process Management | Business Results Concept: DPU Tips

User Tips • •

Once you obtain the DPU, follow with an analysis to understand the problem by creating a Pareto chart or a DPU histogram Before collecting data to determine DPU: ° Define what a defect is ° Define the unit of work ° Check the capability of the measurement system (discussed in detail in the Measure lesson of this course).

139

Parts per Million (PPM)

Six Sigma Black Belt | Business Process Management | Business Results Concept: Parts per Million (PPM)

According to ASQ'sGlossary and Tables for Statistical Quality Control, parts per million (PPM or ppm) is a measurement that is expressed by dividing the data set into 1,000,000 or 106 equal groups. The equation is: PPM = DPU x 1,000,000 The quoted defect rate of a 6σ process is 3.4 parts per million (PPM or ppm), or 3.4 defects per million opportunities "although a normal distribution table will indicate the probability of exceeding six standard deviations (i.e., z = 6) is two times in a billion opportunities" according to Paul Keller in Six Sigma Demystified. Why the difference? Keller describes, "When Motorola was developing the quality system that would become Six Sigma, an engineer named Bill Smith, considered the father of Six Sigma, noticed external failure rates were not well predicted by internal estimates. Instead, external defect rates seemed to be consistently higher than expected. Smith reasoned that a long-term shift of 1.5σ in the process mean would explain the difference. In this way Motorola defined the Six Sigma process as one which will achieve a long-term error rate of 3.4 DPMO, which equates to 4.5 standard deviations from the average. While that may seem arbitrary, it has become the industry standard for both product and service industries."

140

PPM and Sigma Level

Six Sigma Black Belt | Business Process Management | Business Results Concept: PPM and Sigma Level

The following image shows the sigma quality level associated with various services (considering the 1.5σ shift of the mean):

According to Keller's Six Sigma Demystified, "most companies operate in the three to four sigma range, based on their published defect rates." Notice in the above image as the sigma level increases, the parts per million rate decreases. The table below shows the relationship between the sigma level and the defective ppm.

       

141

Defects per Million Opportunities (DPMO)

Six Sigma Black Belt | Business Process Management | Business Results Concept: Defects per Million Opportunities (DPMO)

According to the Glossary and Tables for Statistical Quality Control, defects per million opportunities (DPMO) is the measure of capability for discrete (attribute) data or continuous data (which is the more common application). It is calculated by dividing the number of defects by the opportunities for defects, and multiplying the result by 1,000,000 (or 106). It allows comparison of different types of product to be, in essence, an "apples to apples" comparison. DPMO transforms observed process data into a recognized and agreed upon standard representing the average number of defects a product, process, or service produces. As a yield measurement, DPMO indicates the number of defects in a process observed during a production of one million units. DPMO = (Defects/Total Opportunities) x 1,000,000 OR DPMO = DPO x 106

Benefits • • •

Defines the current baseline performance Provides a common measurement to use as a baseline in assessing a process' ability to produce defect-free products Provides data to help pick projects for future Six Sigma projects

142

Using DPMO

Six Sigma Black Belt | Business Process Management | Business Results Concept: Using DPMO

Example A Building upon the previous example for discrete data, calculate the DPMO. The bulleted list below indicates the number of opportunities for a defect during each step in the process: • Step 1 - Apply paint: two opportunities for defect • Step 2 - Affix decals: three opportunities for defect • Step 3 - Apply clear coat/varnish: five opportunities for defect Step 1 - Apply paint

Step 2 - Affix decals

Step 3 - Apply clear coat

Units = 100

Units = 100

Units = 100

Defects = 2

Defects = 1

Defects = 1

Opportunities/unit = 2

Opportunities/unit = 3

Opportunities/unit = 5

DPMO = (Totaldefects / Totalopportunities)(1,000,000) Totaldefects = 2 + 1 + 1 = 4 Totalopportunities = (Totalopportunities/unit)(Totalunits) Totalopportunities/unit = 2 + 3 + 5 = 10 Totalunits = 100 Totalopportunities = (Totalopportunities/unit)(Totalunits) = (10)(100) = 1,000 DPMO = (4/1,000)(1,000,000) = 4,000

Example B DPMO may be calculated for continuous data by multiplying the proportion defective or "out of specification" by 1,000,000. While normal distributions are covered in detail in the Probability Distributions section of the Measure lesson, an example of how to find the DPMO for continuous data is shown below. Consider the following scenario: Wait time in a bank's teller line is expected to be no more than five minutes. On average, the wait time for customers is three minutes with a standard deviation of one minute. Based on this information, let's calculate the z value: z value = (5 - 3)/1 = 2 From the normal table (which will be shown in the Measure lesson), you can estimate that customers will be waiting longer that five minutes .02275 or 2.275% of the time. To calculate to DPMO: DPMO = .02275 x 1,000,000 = 22,750 To translate DPMO to a sigma level, an abbreviated sigma conversion table is shown below. Based on these calculations, out of one million opportunities, you can estimate that customers will be waiting longer than five minutes 22,750 times, thus a sigma level of 3.5. Sigma

DPMO

6.0

3.4

5.5

30

143

Using DPMO

Six Sigma Black Belt | Business Process Management | Business Results Concept: Using DPMO

5.0

230

4.5

1,350

4.0

6,210

3.5

22,700

3.0

66,800

2.5

158,000

2.0

308,000

1.5

500,000

1.0

690,000

0.5

840,000

       

144

Introduction to Yield

Six Sigma Black Belt | Business Process Management | Business Results Concept: Introduction to Yield

Yield is defined as the percentage of products that successfully complete the production process. It is calculated by dividing the amount of product that finishes the process by the amount of product that started the process. In essence, yield is the output(s) divided by the input(s). Keep in mind that this does not mean that all products are necessarily free of defects or did/did not require rework. It simply means that the products completed the production process and are presumed to be good enough to ship to the customer. For example, if 1,000 units started production, and of these, 980 units successfully completed production, then the yield is calculated as: 980/1000 = 98% First pass yield (FPY) is the percentage of units that successfully complete a process with no rework. This statistic only considers the initial input data and the final output. FPY is typically used to express the process yield for an entire operation. In the case of processes with many steps, it is calculated by multiplying the yield of each step in a process.

Benefits • •

Provides a common measurement for evaluating a single process Provides a benchmark for measuring process improvement projects

145

First Pass Yield

Six Sigma Black Belt | Business Process Management | Business Results Concept: First Pass Yield

As mentioned previously, the FPY statistic does not consider rework; it only looks at the number of units that successfully complete production. However, FPY does not provide a completely accurate picture of the efficiency of a process and its ability to produce an error-free product. Consider the following examples: • Process A: 4,000 units started and 3,800 completed; 200 defective units • Process B: 4,000 units started and 3,800 completed; 200 defective units were scrapped and 600 additional units had one defect each that were successfully reworked • Process C: 4,000 units started and 3,500 completed with no defects; 300 units reworked with 420 defects (i.e., reworked 420 times); 200 units were scrapped In each of the scenarios, the FPY is calculated as: 3800 / 4000 = .95 or 95% The processes are very different; however, using the simple FPY statistic, you would not be able to differentiate the three.

146

Rolled Throughput Yield

Six Sigma Black Belt | Business Process Management | Business Results Concept: Rolled Throughput Yield

Rolled throughput yield (RTY or Yrt) is the probability that a single unit can pass through a series of process steps free of defects. RTY is calculated as the overall quality level after several steps in a process have been completed by multiplying the throughput yield of each step within the process.

Calculating Rolled Throughput Yield Apply the formula below. Note that rework is just that, rework. There is no distinction made regarding the complexity or number of times a product or service is reworked. RTY signals when a process or sub-process must be improved. RTY = N (units entering process) – (# of reworks + # in scrap) / N (units entering process)

Example Consider the following examples discussed earlier: • Process A: Of 4,000 units started and 3,800 completed, 200 defective units were scrapped, each had a single defect. RTY = (4,000 – 200 scrap)/4,000 = 3,800/4,000 = 0.95 • Process B: Of 4,000 units started and 3,800 completed, 200 defective units were scrapped, and 600 additional units had one defect each that were successfully reworked. RTY = (4,000 – (200 scrap +  600 rework))/4,000 = (4,000-800)/4,000 = 3,200/4,000 =  0.80 • Process C: Of 4000 units started and 3800 completed, 300 units reworked for 420 defects, 200 units scrapped for 580 defects. RTY = (4,000 – (200 scrap + 300 rework actions))/4,,000 = (4,000 – 500)/4,000 =  3,500/4,000

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Rolled Throughput Yield

Six Sigma Black Belt | Business Process Management | Business Results Concept: Rolled Throughput Yield

= 0.875 RTY A, B, and C = 0.95 x 0.80 x 0.875 = 0.665 or 66.5%.

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Cost of Poor Quality (COPQ)-Cost of Quality (COQ)

Six Sigma Black Belt | Business Process Management | Business Results Concept: Cost of Poor Quality (COPQ)-Cost of Quality (COQ)

Cost of poor quality (COPQ) are the costs associated with providing poor quality products or services. Cost of quality (COQ) is the original term coined by Philip Crosby referring to the cost of poor quality. Whichever term is used, it is important to understand more than the cost of the process improvement or quality department is involved. Quality-related costs should not be viewed merely as expenses of an organization’s process improvement or quality department. Today, strong quality and price competition require that organizations carefully manage all operations to constantly improve their quality and cost positions in the marketplace.

Benefits • •

•

Provides a statistic to quantify potential savings by measuring the actual cost associated with the poor quality of a product or service Provides a baseline: ° For assessing projected savings for a potential project ° During the Define stage when constructing the project charter and during project benefit impact tracking ° For showing the anticipated dollar impact of the generated project improvement Identifies hidden costs incorporated into the standard operating expenses of an organization

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COPQ - COQ Examples

Six Sigma Black Belt | Business Process Management | Business Results Concept: COPQ - COQ Examples

Examples • • • • • • • • • •

Number of defects produced over a selected timeperiod, lot, or unit size Cost of labor to rework material Cost of extra material used in the reworking process (if any) Cost of material that is now scrapped Cost of the labor applied to the part up to detection Cost of extra utilities to rework part Cost of the utilities used in the process up to detection (if part was scrapped) Cost of lost opportunity to process a new part when the rework part is using the machine Loss of sales/revenue (profit margin) Potential loss of market share

Use When • • • •

performing the Define stage to state the baseline, goal, and entitlement. developing the project charter. tracking the benefits after closing a project to assure sustained benefits. selecting future Six Sigma projects.

User Tips • •

If possible, collect current data to ensure an accurate measurement. COPQ includes: ° Labor cost ° Rework cost ° Disposition costs ° Warranty cost ° Material costs ° Others invested in the unit up to the point of detecting the nonconformance ° Lost opportunity cost due to the loss of resources used in rework

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COPQ (COQ) Advantages and Disadvantages

Six Sigma Black Belt | Business Process Management | Business Results Concept: COPQ (COQ) Advantages and Disadvantages

Advantages • Provides a snapshot of the health of the organization’s quality • Monitors the long-term effect of process changes • Increases the efficient allocation of resources • Creates a culture of quality and a continuous improvement mindset • Engages senior management and is useful for gaining commitment to quality improvement efforts

Disadvantages • The exact cause of movement in the data is not always easy to pinpoint • Hidden costs in the organization may not be reflected in the data • Data validity is often an issue debated among managers, rather than a focus on improving the processes

Monitoring the Cost of Quality (Cost of Poor Quality)  

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COPQ (COQ) Cost Category Overview

Six Sigma Black Belt | Business Process Management | Business Results Concept: COPQ (COQ) Cost Category Overview

Prevention, appraisal and failure are the traditional cost categories many organizations use to assess the effectiveness of their quality systems in financial terms. These categories include the following: 1. 2. 3.

Investments in the prevention of defectives (non-conformances) to requirements Appraisal of a product or service for conformance to requirements Failure to meet requirements

These three categories represent the classic way in which COPQ/COQ is analyzed. Total quality costs are the sum of prevention, appraisal, internal failure and external failure costs. Total quality costs represent the difference between the actual cost of a product or a service and what the reduced cost would be if there was no possibility of substandard service, product failures or manufacturing defects.

 

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COPQ (COQ) Cost Category Descriptions

Six Sigma Black Belt | Business Process Management | Business Results Task: COPQ (COQ) Cost Category Descriptions

Click each "classic" category of cost below to learn more. Prevention Prevention costs are all the costs expended to reduce or preclude errors from being made. Investments in this type of cost usually give the best return and include the costs involved in helping the employee do the job right every time. This type of cost can be viewed as an investment in the future; therefore, it is also considered a cost-avoidance investment. Prevention costs answer the question "What is the cost of doing it right the first time?" Examples of prevention costs include: • Market research • Field trials • Customer surveys • Development and implementation of a quality data-collecting and data-reporting system • Development of the process control plan • Job-related training • Quality-related education and training • Supplier surveys • Design specification reviews • Environmental impact planning • Quality improvement programs Appraisal Appraisal can be defined as testing, inspection and examination to assess whether requirements for quality are being fulfilled. Appraisal costs monitor ongoing quality. These costs are the results of evaluating already-completed output and then auditing the process to measure conformance to established criteria and procedures. Appraisal costs include all the costs expended to determine whether an activity was done right every time. Appraisal costs answer the question "Did you make or do it right? "Examples of appraisal costs include: • Testing • Inspection • Maintenance and calibration of testing and inspection equipment • Safety checks • Reviews of completed designs • Reviews of testing and inspection data • Internal audits of operation systems • Quality product or process audits

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COPQ (COQ) Cost Category Descriptions

Six Sigma Black Belt | Business Process Management | Business Results Task: COPQ (COQ) Cost Category Descriptions

Failure Management has control over prevention and appraisal costs. Other quality costs an organization incurs result from errors because all activities were not done right every time. These include internal and external failure costs. Where prevention and appraisal costs are considered to be investments, internal and external failure costs are considered losses. Whether the failure cost is internal or external simply differentiates where the problem surfaces. Internal failure Internal failure costs can be defined as those resulting from a product failure to meet the quality requirements prior to delivery (e.g., re-performing a service, reprocessing, rework, retest, scrap). Internal failure costs are the costs incurred by the organization as a result of noncompliance detected before a product or service is provided. It is the cost the company incurs because not everyone did the job right every time — the cost to redo a defective product or correct an unsatisfactory service. Included are the costs incurred from the time an item is shipped until it has been accepted by the final customer. Additional examples of internal failure costs include: • Engineering changes • Costs resulting when additional inventory is required to support poor process yields, potential scrap parts and rejected loss • Waste • Troubleshooting or failure analysis costs • Corrective action • Internal labor losses resulting from shutdowns, re-setups, line stoppages • Computer reruns • Document changes • Change orders due to errors

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COPQ (COQ) Cost Category Descriptions

Six Sigma Black Belt | Business Process Management | Business Results Task: COPQ (COQ) Cost Category Descriptions

External failure External failure can be defined as costs resulting from a product failing to meet the quality requirements after delivery (e.g., product maintenance and repair, warranties and returns, direct costs and allowances, product recall costs, liability costs). External failure costs are associated with a product or service failing to meet quality requirements after shipment or delivery to the external customer. These costs are incurred by the organization producing the product or the service because the appraisal process did not detect all the errors before the product or service was delivered to the customer. Additional examples of external failure costs include: • Costs of customer-rejected services or products • Complaint handling • Warranty costs • Training of repair and customer service personnel • Overhead costs required to maintain field service centers • Product upgrades or updates in the field • Customer goodwill • Missed sales

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COPQ (COQ) Models

Six Sigma Black Belt | Business Process Management | Business Results Concept: COPQ (COQ) Models

The most costly condition for an organization occurs when a customer finds defects in a product or service. If the manufacturer or service provider had found the defects through inspection, testing or checking, a less costly condition would have resulted. Better yet, had the organization been focused on quality improvement and defect prevention, defects and their resulting costs would have been minimized. In the classic model of optimum quality costs, prevention and appraisal costs are portrayed as rising asymptotically as defect-free levels are achieved—as prevention and appraisal costs increase, failure costs decrease until an optimum point is reached. It was believed that for any process, there was a trade off between cost and the resulting quality—that there was a theoretical optimum where the benefits were less than the cost. After this point, decreased failure costs did not offset further increases in appraisal and prevention costs. But this model underestimated the cost of poor quality. Recent successes in quality management programs supported by quality cost systems recognize that the full costs of poor quality have resulted in revisions to the classic model of optimum quality costs: • New technology has reduced inherent failure rates of materials and products. • Robotics and other forms of automation have reduced human error during production. • Automated inspection and testing have reduced the human error of appraisal. As with any enterprise-wide initiative, when launching a complete quality cost system, support from top management proves critical to its success. The quality cost curve is shown on the next page.

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Quality Cost Curve

Six Sigma Black Belt | Business Process Management | Business Results Concept: Quality Cost Curve

The revised model shows how these developments have resulted in the ability to achieve perfection at finite costs. The illustration below shows both the classic and revised models:

   

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Why Benchmark

Six Sigma Black Belt | Business Process Management | Business Results Concept: Why Benchmark

Benchmarking is the process of identifying best practices in organizations with comparable processes or comparable customer issues for the purpose of determining the current state and a desired future state. For example, customer satisfaction scores for a hotel may be compared to those for a bank or hospital. There are several important differentiating factors to consider: • Benchmarking is not just for acquiring competitive information for comparison. • Benchmarking involves setting objectives. • Just like Six Sigma, benchmarking should be considered a process that is ongoing and becomes a way of doing business.

Benefits • • • •

Meet customer expectations more efficiently and effectively Establish performance goals based on leaders in the industry Identify best practices to gain market share and improve performance Include as a critical component of a robust quality program in managing business processes

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What to Benchmark

Six Sigma Black Belt | Business Process Management | Business Results Concept: What to Benchmark

When considering what to benchmark, bring together a team positioned to respond to the following questions: • What can we benchmark (processes, methods, results, and so on)? • What are the most critical measures of success for the organization? ° ° ° ° ° • • • • • • • •

Revenue Production levels Marketing campaigns Customer satisfaction Maintaining cost levels

Of those areas, which are causing the most trouble? What does the customer desire in the organization’s marketplace? In which direction is the industry moving and how is the organization positioned to move in that direction? What competitive pressures affect the organization’s performance? What product features are critical for customers? What issues exist in the manufacturing process? What issues exist for customer service? What performance trends in the organization may signal problems ahead?

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The Benchmarking Process

Six Sigma Black Belt | Business Process Management | Business Results Concept: The Benchmarking Process

At a high level, the core process steps for a benchmarking program might be: 1. 2. 3. 4. 5. 6. 7. 8.

Identify what to benchmark. Select organizations with comparable processes or comparable customer issues. Determine data collection methods. Analyze the data and findings. Establish goals based on the data analysis. Develop action plans to obtain the goals. Implement the action plans. Conduct ongoing evaluation and re-evaluation of goals and benchmarking data.

Companies must be meticulous when going through the benchmarking process. By no means is benchmarking a "do-it-yourself" process. It is recommended that companies enlist the help of an expert to do the job right and to help avoid the potential for legal issues (e.g., conflicts of interest).

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Project Financial Benefits

Six Sigma Black Belt | Business Process Management | Business Results Concept: Project Financial Benefits

When determining whether a Six Sigma project has been successful, the bottom line is often the factor that matters most. The key question is, “How much value does the organization realize as a direct result of this project’s success?” The financial factors defined in this subtopic are: • Cost benefit analysis • Return on assets • Return on investment • Net present value

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Financial Benefits

Six Sigma Black Belt | Business Process Management | Business Results Concept: Financial Benefits

Just as there are costs associated with poor quality (see COPQ) there are also financial benefits of implementing changes that result from successful Six Sigma projects. These financial benefits may include: • Additional revenue from increased sales • Cost avoidance or mitigation • Faster return on investments • Lower production costs • Lower costs associated with customer service • Increased cash flow • Enhanced profitability of existing services or products • Increased revenue of existing sources • Increased value in organization stock or perceived value

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Cost-Benefit Analysis

Six Sigma Black Belt | Business Process Management | Business Results Concept: Cost-Benefit Analysis

To perform a cost-benefit analysis for the project, complete these steps: Step 1: Identify the project benefits. • Quantify the expected financial benefits assuming the project reaches the goals set for it. • Express the benefits in dollar amounts with specific time limits. For example, the project should realize an increase in sales of $156,000 per year beginning year two that should last for three years. Step 2: Identify the project costs. • Limit the project costs to those dollars expended as a result of the project. Step 3: Calculate whether benefits exceed costs.. Step 4: Determine whether the project should be implemented. • Even if the benefits do not exceed the costs, senior management may elect to complete the project. For example, improving the customer satisfaction rating of checking and savings account customers of bank is a benefit that may not exceed the cost of a project, but could impact future consumer lending relationships. If this is the case, determine what could be done to enhance the benefits and minimize the project costs. • A cost-benefit analysis may also be initiated after a project has been completed to determine whether the project should have been undertaken in the first place. The results of a cost-benefit analysis may be any of the following: • The overall benefits and costs are compared to determine whether benefits exceed costs on a straight dollar-for-dollar basis. • The benefits and costs are used within a ratio such as ROA or ROI (discussed on the following pages). These ratios can express on a relative basis the expected return for use of the assets or the investment in the project. • The information may also be used in a NPV equation if there is an issue with benefits and costs being strung out over a longer period of time.

Considering hard dollars versus soft dollars Hard dollars are those that allow companies to do the same amount of business with fewer employees (cost savings) or handle more business without adding people (cost avoidance). Soft dollars are those such as increased customer satisfaction, reduced time to market, cost avoidance, lost profit avoidance, improved employee morale, enhanced image for the organization, and other intangibles, that may result in additional savings to the organization but are harder to quantify. One should note that each organization may define hard and soft dollars differently. Soft dollars are typically high and have potential for future value, while hard dollars are low and may not even show a break-even relationship with the project costs. Soft dollars are real but are harder to quantify and forecast, and they may be viewed differently from company to company.

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Return on Assets (ROA)

Six Sigma Black Belt | Business Process Management | Business Results Concept: Return on Assets (ROA)

Return on assets (ROA) is sometimes used for Six Sigma projects to determine whether the use of organization assets is warranted based on the return realized. The formula for ROA is: ROA = Net Income/Total Assets When applied to a project: • Net income refers to expected earnings that result directly from the project’s results. • Total assets refer to the value of the assets applied to a project.

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Return on Investment (ROI)

Six Sigma Black Belt | Business Process Management | Business Results Concept: Return on Investment (ROI)

Return on investment (ROI) is also used for Six Sigma projects to determine whether the investment in the project is warranted based on the return realized. The formula for ROI is: ROI = Net Income/Investment When applied to a project: • Net income refers to expected earnings that result directly from the project’s results. • Investment refers to the value of the outlay made in the project.

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Net Present Value (NPV)

Six Sigma Black Belt | Business Process Management | Business Results Concept: Net Present Value (NPV)

A NPV allows the calculation of the current benefit of a project for each window of time and over the total duration of the project for all time periods. If the project NPV is positive, then the project is usually approved. The NPV equation is:

Where: • n = number of time periods • t = time period • r = cost of capital for a time period • CFt = cash flow in time period t Note the following regarding this equation: • CF0 is the cash flow in time period zero which is the same as the initial •

•

investment. Cash flow for a given time period is calculated by taking the cash flow for project benefits (CFB,t ) in time period t and subtracting the cash flow for project costs ( CFC,t ) in the same time period. i may be substituted for r; i represents the annual interest rate.

To convert an annual percentage rate of i to a rate r for a shorter time period with m time periods per year, use the following equation:

 

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NPV Example

Six Sigma Black Belt | Business Process Management | Business Results Concept: NPV Example

Use the information presented in the case below to calculate the NPV for the project. Then roll over Page Resources and click NPV Answer to view the solution. A project is planned to update manufacturing equipment and refine the manufacturing process in an automobile parts plant. The cost of capital is 9.5% APR. Project benefits: • Decrease rework and scrap of $700 in month 3 • Decrease rework and scrap of $500 in month 4 • Decrease rework and scrap of $450 in month 5 • Decrease rework and scrap of $450 in month 6 Project costs: • Initial process redesign and training costs $400 in month 1. • Installing new equipment costs $840 in month 2. • A second round of training costs $100 in month 6. A cash flow summary for this example: Month: Positive cash flow: Negative cash flow:

0 $0 $0

1 $0 $400

2 $0 $840

Cash Flow Analysis NPV equation:

Convert APR to monthly rate r for cost of capital:

 

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3 $700 $0

4 $500 $0

5 $450 $0

6 $450 $100

NPV Answer

Six Sigma Black Belt | Business Process Management | Business Results | NPV Example Example: NPV Answer

The APR of 9.5% is converted to a monthly rate:

The calculation for NPV is:

 

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Other Benefits

Six Sigma Black Belt | Business Process Management | Business Results Concept: Other Benefits

Although financial benefits weigh most heavily in the decision to proceed with a Six Sigma project, other benefits also accrue to the organization and may be considered in the decision-making process. Other benefits to the organization from a successful process improvement project may include: • improved market position relative to competitors. • improved ability to meet customer needs, especially enhanced service. • aligned organization behaviors with vision and values. • newly created market opportunities. • project infused spirit of continuous improvement. • improved employee morale. • improved overall productivity. • decreased cycle time. • increased simplicity.

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Lesson Summary

Six Sigma Black Belt | Business Process Management Concept: Lesson Summary

Six Sigma focuses on using a systematic approach to addressing issues with quality. In part, this is achieved through: • a thorough analysis of the business processes. • understanding who will be impacted by the Six Sigma project. • identifying all customers and deriving customer requirements from a variety of data sources. • listening to the voice of the customer. • assessing the cost of quality. • determining whether the benefits of a project outweigh the costs associated with its undertaking. Rollover Page Resources to view a summary of the metrics and a comprehensive matrix of the data analysis tools discussed in this lesson. In the next lesson, the project management methodology for Six Sigma projects is highlighted.

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Data Analysis Tools

Six Sigma Black Belt | Business Process Management | Lesson Summary Example: Data Analysis Tools

Data Analysis Tools Tool

Description

Histograms

When to Use According to The Quality Toolbox • by Nancy R. Tague, "A frequency distribution shows how often each • different value in a set of data occurs. A histogram is the most commonly used graph to show frequency distributions."

•

•

•

•

•

Line Graphs

Control Charts

According to The Quality Toolbox by Nancy R. Tague, "A line graph is the simplest kind of graph for showing how one variable, measured on the vertical y-axis, changes as another variable, on the horizontal x-axis, increases. The data points are connected with a line. The x-axis variable is called the dependent variable, because its value depends on the value of the independent variable."

•

According to The Quality Toolbox by Nancy R. Tague, "The control chart is a graph used to study how a process changes over time. Data are plotted in time order. A control chart always has a central line for the average, an upper line for the upper control limit and a lower line for the lower control limit. These lines are determined from historical data. By comparing current data to these lines, you can draw conclusions about whether the process variation is consistent (in control) or is unpredictable (out of control,

•

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•

•

When the data are numerical. When you want to see the shape of the data’s distribution, especially when determining whether the output of a process is distributed approximately normally. When analyzing whether a process can meet the customer’s requirements. When analyzing what the output from a supplier’s process looks like. When seeing whether a process change has occurred from one time period to another. When determining whether the outputs of two or more processes are different. when you wish to communicate the distribution of data quickly and easily to others. When the pairs of data are numerical When you want to show how one variable changes with another, continuous variable, usually time. Only when each independent variable is paired with only one dependent variable.

 

•

•

•

When controlling ongoing processes by finding and correcting problems as they occur. When predicting the expected range of outcomes from a process. When determining whether a process is stable (in statistical control). When analyzing patterns of process variation from special causes (non-routine events) or common causes (built into the process).

Data Analysis Tools

Six Sigma Black Belt | Business Process Management | Lesson Summary Example: Data Analysis Tools

•

When determining whether your quality improvement project should aim to prevent specific problems or to make fundamental changes to the process.

According to The Quality Toolbox • by Nancy R. Tague, "A Pareto chart is a bar graph. The lengths of the bars represent frequency or • cost (time or money), and are arranged with longest bars on the left and the shortest to the right. In this way the chart visually • depicts which situations are more significant."

When analyzing data about the frequency of problems or causes in a process. When there are many problems or causes and you want to focus on the most significant. When analyzing broad causes by looking at their specific components. When communicating with others about your data.

affected by special causes of variation)."

Pareto Analysis

• Affinity Diagram

Nominal Group Technique

According to The Quality Toolbox by Nancy R. Tague, "The affinity diagram organizes a large number of ideas into their natural relationships. This method taps a team’s creativity and intuition. It was created in the 1960s by Japanese anthropologist Jiro Kawakita."

•

• •  

According to The Quality Toolbox • by Nancy R. Tague, "Nominal group technique (NGT) is a • structured method for group brainstorming that encourages contributions from everyone. " •

•

•

•

Matrix Diagrams

According to The Quality Toolbox • by Nancy R. Tague, "The matrix diagram shows the relationship between two, three or four groups • of information. It also can give information about the relationship, such as its strength, the roles played by various individuals or measurements." •

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When you are confronted with many facts or ideas in apparent chaos When issues seem too large and complex to grasp When group consensus is necessary When some group members are much more vocal than others. When some group members think better in silence. When there is concern about some members not participating. When the group does not easily generate quantities of ideas. When all or some group members are new to the team. When the issue is controversial or there is heated conflict. An L-shaped matrix relates two groups of items to each other (or one group to itself). A T-shaped matrix relates three groups of items: groups B and C are each related to A. Groups B and C are not related to each other. A Y-shaped matrix relates three groups of items. Each group is related to the other two in a circular fashion. A C-shaped matrix relates three groups of items all

Data Analysis Tools

Six Sigma Black Belt | Business Process Management | Lesson Summary Example: Data Analysis Tools

•

•

Prioritization Matrix

A prioritization matrix is a decision making tool using a systematic process to narrow choices. It is a variation of an L-shaped matrix (discussed in Matrix Diagrams). A prioritization matrix allows raters to rank the options against pre-determined scales, weights and criteria to determine order of importance.

•

• • • •

•

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together simultaneously, in 3-D. An X-shaped matrix relates four groups of items. Each group is related to two others in a circular fashion. A roof-shaped matrix relates one group of items to itself. It is usually used along with an L- or T-shaped matrix. When prioritizing the variables with the greatest significance. When reaching consensus in small teams. When comparing a few options to specific standards. When narrowing a list of options to one choice. When making decisions based on multiple criteria (best when used for six to eight criteria). When selecting one product, approach, supplier, option or problem.

Metrics Summarized

Six Sigma Black Belt | Business Process Management | Lesson Summary Example: Metrics Summarized

Metric

Formula

Defects per Unit (DPU)

DPU = Defects / Units

Parts per Million (PPM)

PPM = DPU x 1,000,000

Defects per Million Opportunities (DPMO)

DPMO = (Defects/Total Opportunities) x 1,000,000 OR DPMO = DPO x 106

Rolled Throughput Yield (RTY) RTY = N (units entering process) – (# of reworks + # in scrap) / N (units entering process) Return on Assets (ROA)

ROA = Net Income/Total Assets

Return on Investment (ROI)

ROI = Net Income/Investment

Net Present Value (NPV)

 

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Lesson Bibliography

Six Sigma Black Belt | Business Process Management Concept: Lesson Bibliography

American Society for Quality. ASQ’s Foundations in Quality Learning Series: Certified Quality Engineer. Milwaukee, WI: ASQ, 2000. American Society for Quality. Six Sigma Green Belt Certification Preparation Course, Version 1 (web-based course). Milwaukee, WI, 2006. ASQ Statistics Division. Rudy Kittlitz, editor. Glossary and Tables for Statistical Quality Control. 4th ed. Milwaukee, WI: ASQ Quality Press, 2005. Benbow, Donald and T.M. Kubiak. The Certified Six Sigma Black Belt Handbook. Milwaukee, WI: ASQ Quality Press, 2005. Breyfogle, Forrest W. III. Implementing Six Sigma: Smarter Solutions® Using Statistical Methods. 2nd ed. Hoboken, NJ: John Wiley and Sons, Inc., 2003. Camp, Robert C. Benchmarking: The Search For Industry Best Practices That Lead to Superior Performance. Milwaukee, WI: ASQ Quality Press, 1989. Keller, Paul. Six Sigma Demystified. New York, NY: McGraw-Hill, 2005. Pries, Kim H.Six Sigma for the Next Millennium: A CSSBB Guidebook. Milwaukee, WI: ASQ Quality Press, 2006. Pyzdek, Thomas. The Six Sigma Handbook: A Complete Guide for Green Belts, Black Belts, and Managers at All Levels, Revised and Expanded, 2nd ed. New York: McGraw-Hill, 2003. Tague, Nancy R. The Quality Toolbox. 2nd ed. Milwaukee, WI: ASQ Quality Press, 2005.

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Six Sigma Black Belt Project Management

Lesson Introduction

Six Sigma Black Belt | Project Management Introduction: Lesson Introduction

Understanding project management basics is essential to successfully completing the multiple phases of a potentially large and complex project. This topic covers the fundamental tools needed to execute any successful project. To better understand this concept, the ASQ Body of Knowledge provides the following topics: Project charter and plan • Compare, select and explain elements of a project's charter and plan. • Plan the project using tools such as Gantt chart, program evaluation and review technique (PERT) chart and planning trees. • Create data-driven and fact-driven project documentation using spreadsheets, storyboards, phased reviews, management reviews and presentations to the executive team. • Create and negotiate the charter, including objectives, scope, boundaries, resources, project transition and project closure. Team leadership • Know the elements of launching a team and why they are important: clear purpose, goals, commitment, ground rules, roles and responsibilities of team members, schedules, support from management and team empowerment. • Select team members who have appropriate skills sets (e.g., self-facilitation, technical/subject-matter expertise) and create teams with appropriate numbers of members and representation. • Facilitate the stages of team evolution, including forming, storming, norming, performing, adjourning and recognition. Team dynamics and performance • Recognize and apply the basic steps in team building: goals, roles and responsibilities, introductions and both stated and hidden agendas. • Apply coaching, mentoring and facilitation techniques to guide a team and overcome problems such as overbearing, dominant or reluctant participants, the unquestioned acceptance of opinions as facts, group think, feuding, floundering, the rush to accomplishment, attribution, discounts and "plops" and digressions and tangents. • Measure team progress in relation to goals, objectives, and metrics that support team success. • Define, select and apply team tools such as nominal group technique, force field analysis, multivoting and conversion/diversion. Change agent • Understand and apply techniques for facilitating or managing organizational change through change agent methodologies. • Understand the inherent structures of an organization (e.g., its cultures and constructs) that present basic barriers to improvement; select and apply techniques to overcome them. • Define, select and apply tools such as consensus techniques, brainstorming, effort/impact and interest-based bargaining to help conflicting parties (e.g., departments, groups, leaders, staff) recognize common goals and how to work together to achieve them.

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Lesson Introduction

Six Sigma Black Belt | Project Management Introduction: Lesson Introduction

• •

Define, select and apply techniques that support and sustain team member participation and commitment. Use effective and appropriate communication techniques for different situations to overcome organizational barriers to success.

Management and planning tools • Define, select and use affinity diagrams, interrelationship digraphs, tree diagrams, prioritization matrices, matrix diagrams, process decision program (PDPC) charts and activity network diagrams.

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Lesson Overview

Six Sigma Black Belt | Project Management Introduction: Lesson Overview

The tools and objectives of the Project Management lesson are illustrated below.

   

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Six Sigma Black Belt Project Management Project Charter and Plan

Learning Objectives

Six Sigma Black Belt | Project Management | Project Charter and Plan Concept: Learning Objectives

At the end of this Project Management topic, all learners will be able to: • compare, select and explain elements of a project's charter and plan. • plan the project using tools such as Gantt chart, program evaluation and review technique (PERT) chart and planning trees. • create data-driven and fact-driven project documentation using spreadsheets, storyboards, phased reviews, management reviews and presentations to the executive team. • create and negotiate the charter, including objectives, scope, boundaries, resources, project transition and project closure.         Portions of this topic were taken from the ASQ Six Sigma Green Belt web-based Certification Preparation Course.

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Project Charter

Six Sigma Black Belt | Project Management | Project Charter and Plan Concept: Project Charter

The project charter is a written commitment approved by management stating the scope of authority for an improvement project. It is recognized by all parties involved in the project. Once published, it provides powerful communication about the project to the entire team. At the same time, a charter is a “living” document, constantly being reviewed and updated to reflect the addition of relevant data as it becomes known.  

Project Charter Purposes • • • •

Gives authority to act, gives permission to work Summarizes the project itself and its goals, boundaries and deadlines Provides a source for reference to determine which new requirements are covered under the original agreement Serves as a living document which continues to evolve as more requirements are uncovered, but also provides a central source from which to manage these changes

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Project Charter Elements

Six Sigma Black Belt | Project Management | Project Charter and Plan Task: Project Charter Elements

Listed below are project charter elements. Click each term below to learn more. To view the a charter template, roll over Page Resources and click Project Charter Template. To view a completed charter, roll over Page Resources and click Project Charter Example. Business Case The business case is a short summary of the strategic reasons for the project.  The justification for a business case would typically involve at least one of the following: • Cost per unit • Quality or defect rate • Cycle time Good business cases should: • Define one primary business metric. • Focus on a process rather that a cost account. • Quantify a financial impact. • Focus on the output (product/service) for the external customer. • Provide details regarding the baseline performance of the primary business measure to ensure that this is really a problem, not an exception. • Determine the gap between the baseline performance of the primary business measure and the business objective. Problem Statement The problem statement will detail the issue that the project team wants to improve. From the perspective of owners and relevant stakeholders, a major cause of project failure is the lack of clarity in describing the problem. Develop the problem statement as thoroughly as possible with the information you have. The problem statement is a crucial part of the charter. Problem cases include: • historical data • what areas of the business are affected • how long the problem has existed • any other symptoms of the problem The project description, along with the entire charter, should be reviewed by and with owners and appropriate stakeholders to ensure the right problem is being addressed and the anticipated solution will fix the "real" problem. Problem statements are discussed further in the Define lesson of this course. Project Scope The project scope is the specific aspect of the problem that will be addressed, and serves to specify the boundaries of the project. The project scope is discussed further in the Define lesson of this course along with tools that help determine the scope.

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Project Charter Elements

Six Sigma Black Belt | Project Management | Project Charter and Plan Task: Project Charter Elements

Goal Statement As discussed later in this lesson and in the Define lesson, the goal statement should specifically outline what you hope to achieve at the end of the project. Goals should: • Be carefully thought out and expressed. • Specify how completing the project will lead to improvements over the status quo. You should be able to clearly describe the outcomes, deliverables and benefits to stakeholders and customers. • Provide the criteria you need to evaluate the success of the project in terms of time, costs, and resources. • Be reviewed by the core team, which must reach consensus before moving to the next phase of the project. Resources In terms of the project charter, resources are the people required to complete the project. In the Team Leadership topic of this lesson, you will read more about the creation of teams and the roles and responsibilities of team members.

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Work Breakdown Structure

Six Sigma Black Belt | Project Management | Project Charter and Plan Concept: Work Breakdown Structure

The work breakdown structure (WBS) is a hierarchical chart representing all the activities that must be completed in order to finish the project. It may be completed as a tree diagram or an outline. In essence, the WBS is like an organizational chart for a project. The idea behind the WBS is to break larger tasks (or milestones) into individual components. Typically, a work breakdown structure will include three levels. However, for more complex projects, it may involve as many as five levels.

Procedure 1. 2. 3. 4. 5.

Gather input from the project team by using questionnaires, interviews, group sessions and historical data. Restate the project mission and objectives and confirm that they are correct. Define the project in terms of major elements of work, or deliverables (level 1 categories). Break each level 1 work element into detailed activities and milestones (levels 2, 3, etc.). Identify an activity owner and deliverable for each activity at the lowest WBS level.

 

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Planning Tools

Six Sigma Black Belt | Project Management | Project Charter and Plan Concept: Planning Tools

In developing the project plan, the Six Sigma leader uses a variety of tools. In the next section, we will explore and explain the following tools: • Gantt chart • Critical path analysis • PERT chart

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Gantt Chart

Six Sigma Black Belt | Project Management | Project Charter and Plan Concept: Gantt Chart

The Gantt chart was developed by Henry Gantt in the 1910s. According to The Quality Toolbox, Second Edition, Nancy Tague states, "A Gantt chart is a bar chart that shows the tasks of a project, when each must take place, and how long each will take. As the project progresses, bars are shaded to show which tasks have been completed." The Gantt chart may also be known as a "milestones chart" or "project bar chart."

Benefits • • • • • • •

Easy for people to understand Helps all parties understand the project Monitors the project's progress Manages the dependencies between tasks Displays the project schedule and status at a glance Assesses the time needed to complete the project Stimulates thinking among group members about accomplishing the goal

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Gantt Chart Cont.

Six Sigma Black Belt | Project Management | Project Charter and Plan Concept: Gantt Chart Cont.

Procedure In The Quality Toolbox, Second Edition, Tague suggests the following steps for creating a Gantt chart: 1.

Identify the following tasks needed to complete the project: a. b. c.

Key milestones (important check points) Time required for each task The sequence: i. Tasks to be finished before the next task can begin ii. Simultaneous tasks iii. Tasks to be completed before each milestone

2. 3.

Draw a horizontal time axis along the top or bottom of a page, and then mark off in an appropriate scale for the length of the tasks (days or weeks). Down the left side of the page, write each project task and milestone in order: a. b.

For each event happening at a point in time, draw a diamond (unfilled) under the time for that event. For activities occurring over a period of time, draw a bar (unfilled) spanning the appropriate times on the timeline: i. Align the left end of the bar with the time the activity begins. ii. Align the right end with the time the activity concludes. iii. Ensure that every task of the project is on the chart.

4.

5.

As events and activities take place, shade the diamonds and bars to show completion. For tasks in-progress, estimate the percentage of completion and shade the appropriate amount. Place a vertical marker to show the current date. When posting the chart on the wall, a heavy dark string hung vertically across the chart with two thumbtacks is an easy way to show the current time.

Use When Tague states that Gantt charts are used when: " • • •

scheduling and monitoring tasks within a project. communicating plans or status of a project. the steps of the project or process, their process, their sequence, and their duration are known.

"

User Tips Tague also states:

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Gantt Chart Cont.

Six Sigma Black Belt | Project Management | Project Charter and Plan Concept: Gantt Chart Cont.

" •

•

•

Sometimes Gantt charts have additional columns for showing details, such as the amount of time the tasks is expected to take, resources or skill level needed, or person responsible. Beware of identifying reviews or approvals as events unless they really will take place at a specific time, such as a meeting. Reviews and approvals often can take days or weeks. It can be useful to indicate the critical points on the chart with bold or colored outlines of the bars.

"

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Critical Path Analysis

Six Sigma Black Belt | Project Management | Project Charter and Plan Concept: Critical Path Analysis

Developed by project managers in the 1950s, critical path analysis (CPA) is one of several planning tools for demonstrating and viewing chronological tasks, identifying possible timing risks, and establishing the least amount of time for the project/process. CPA is also known as critical path method (CPM).

Benefits • • • • •

Displays a graphical model of the project Predicts the shortest time required to complete the project Emphasizes activities critical to maintaining the schedule Provides a timing reference point throughout the project Identifies interrelationships between tasks

Three paths exist in the diagram above: • 1-3-4-5-7 (8 weeks) (critical path; longest time) • 1-3-5-7 (6 weeks) • 1-2-6-7 (7 weeks)

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Critical Path Analysis Cont.

Six Sigma Black Belt | Project Management | Project Charter and Plan Concept: Critical Path Analysis Cont.

Procedure 1. 2. 3. 4. 5. 6.

Use sticky notes to individually list all tasks in the project. Underneath each task, draw a horizontal arrow pointing right. Arrange the sticky notes in the appropriate sequence (from left to right). Between each pair of tasks, draw circles to represent events and to mark the beginning or end of a task. Label all events, in sequence, with numbers. Label all tasks, in sequence, with letters. For each task, estimate the completion time. Write the time below the arrow for each task. Draw the critical path by highlighting the longest path from the beginning to the end of the project.

Use When • • • •

Developing an optimal plan for the project Identifying the most critical issues/processes that would affect the overall project time Identifying the longest path through the process causing the most risk to miss the deadline (the critical path) Determining fixed time targets

User Tips • • •

All activities begin and end at circles (nodes: a stage of completion). All activities with no predecessor branch from node 1. All activities with no successor point to the last node (the highest number).

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PERT Chart

Six Sigma Black Belt | Project Management | Project Charter and Plan Concept: PERT Chart

First developed by the Navy in the 1950s to manage complex projects, program evaluation and review technique (PERT) charts are powerful tools for reducing the time and cost for completing a project. PERT's planning technique accounts for randomness in time requirements. PERT charts fall under the category of network tools similar to the activity network diagram detailed later in this lesson under the Management and Planning Tools topic.

Benefits • • • • • • •

Provides a means of estimating the project completion time Demonstrates the probability for completing the project ahead of schedule Identifies start and end dates as well as critical path activities that affect completion time Organizes tasks in established timeframes Acts as a decision-making tool Identifies where and when parallel activities occur Serves as an evaluation tool to determine the effect of changes

Key Terms The following terms are important to keep in mind when using PERT charts: • Critical path refers to the sequence of tasks (path) that takes the longest time and determines the project’s completion date. Any delay of tasks on a critical path will delay the project completion time. • Slack time refers to the time an activity can be delayed without delaying the entire project. Tasks on the critical path have a zero slack time. Slack time is the difference between the latest allowable date and the earliest expected date. It is represented by the following nomenclature: ° T/E = The earliest time (date) on which an event can be expected to occur ° T/L = The latest time (date) on which an event can occur without extending the completion date of the project ° Slack time = T/L – T/E • An event is the starting or ending point for a group of tasks.

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PERT Chart

Six Sigma Black Belt | Project Management | Project Charter and Plan Concept: PERT Chart

•

Activity is the work required to proceed from one event or point in time to another.

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PERT Chart cont.

Six Sigma Black Belt | Project Management | Project Charter and Plan Concept: PERT Chart cont.

Procedure 1. 2. 3. 4. 5. 6. 7.

Use sticky notes to individually list all tasks in the project. Underneath each task, draw a horizontal arrow pointing right. Arrange the sticky notes in the appropriate sequence (from left to right). Between each two tasks, draw circles to represent events, to mark the beginning or end of a task. Label all events, in sequence, with numbers. Label all tasks, in sequence, with letters. For each activity, make three estimates regarding time requirements: the shortest possible time, the most likely time, and the longest time. Determine the critical path. Adjustments to the PERT Chart should be made to reflect any changes to the project along the way.

Use When • • • • • • • • •

Planning and controlling projects Determining feasibility of meeting deadlines Identifying possible bottlenecks in the project Evaluating the effects of changes in the project requirements Evaluating the effects of deviating from the schedule Evaluating the effects of diverting resources from the project, or redirecting additional resources to the project Constructing a chart showing start and finish times for each activity as well as relationships to other activities in the project Identifying critical activities to be completed on time Gathering information for improving the project schedule

User Tips • • • • •

•

Use a Pareto analysis to identify those critical elements that are most likely to lead to significant improvement in overall project completion time. Although time estimates are subjective, they are very important. Be sure to include documentation tasks because they can be time consuming. PERT is a variation on critical path that is more skeptical of the time estimates. To use the PERT chart, first estimate the following for each activity: ° Shortest possible time each activity will take ° Most likely length of time each activity will take ° Longest time possible each activity will take Calculate the time for each activity with the following formula:[(shortest time) + (4 x likely time) + (longest time)]/ 6

 

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PERT Chart Example - Table

Six Sigma Black Belt | Project Management | Project Charter and Plan Concept: PERT Chart Example - Table

Constructing a PERT network requires two inputs: events required to complete the project and the sequence of these events. The network can be created when answers are provided to the following three questions: 1.      What job immediately precedes this job? 2.      What job immediately follows this job? 3.      What jobs can run concurrently? The following table illustrates a sequence of events: Activity

Event Title/Code

A-B B-C

A: Contract signed B: Long lead procurement C: Bill of materials D: Manufacturing schedules E: Manufacturing plans F: Start-up activity

B-D C-E D-E E-F  

Immediate Predecessors A

Activity Time (Weeks) 1 5

B B

2 2

C and D

2

E

2

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PERT Chart Example - Simplified PERT Chart

Six Sigma Black Belt | Project Management | Project Charter and Plan Concept: PERT Chart Example - Simplified PERT Chart

Data from the sequence-of-events table is then converted into a PERT network. The following PERT network is based on the data presented in the table on the previous page. The bold line represents the critical path, or the longest time span through the total series of project events.

The critical path in in the above PERT chart tells management two things: • There is no slack time in any of the events on this path. Any slippage in the schedule will cause a corresponding slippage in the end date of the program, unless this slippage can be recovered on the critical path during any of the downstream events. • Because events on this path are the most critical to the success of the project (in terms of resource scheduling and allocation), management must examine these events carefully if it seeks to improve overall performance on the project.    

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PERT Chart Example - PERT Chart with Slack Time

Six Sigma Black Belt | Project Management | Project Charter and Plan Concept: PERT Chart Example - PERT Chart with Slack Time

An adaptation of a PERT network with slack time appears in the Figure 1. The event with slack time is D. On large, complex projects, PERT networks can subdivide events into subevents, as shown in Figure 2.

Figure 1 PERT Network with Slack Time

Figure 2 PERT Chart Breakout by Subevent

 

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Project Documentation

Six Sigma Black Belt | Project Management | Project Charter and Plan Task: Project Documentation

Project documentation is an important part of measuring and ensuring the success of any project. Several tools and processes for documentation exist. Regardless of the tools or processes used, it is important that all information provided be accurate, specific and detailed. Status Reports Status reports are written with a standardized format and formal tone, specific to each organization.  The report is delivered periodically to the members of the project team. Status reports provide information, such as: • Where the project is in relation to the plan • Risks or issues affecting the time, scope or cost of the project • Action plan to address the risks or issues • Requests for management assistance or intervention The status report may even include other documentation, such as: • Milestone charts • Performance reports • Budget reports To see a sample, roll over Page Resources, and click Status Report. Spreadsheets Another way to monitor the project in terms of status, deadlines and budget is to use spreadsheet applications such as MS Excel.  Spreadsheets provide an excellent visual representation of information when project management software, such as MS Project, is not available. Project Storyboards Project storyboards are useful for depicting a sequence of events or explaining a process to someone not familiar with a workflow or procedure.  Storyboards are also helpful when conveying project information involving changes that are more easily explained in a visual manner than with words. A common application for project storyboards is the use of before-and-after pictures.  Before-and-after-pictures are particularly helpful for facility or product redesign projects. Storyboards are frequently used when preparing a presentation to the executive team, and allow the team to collect their thoughts in a way conducive to soliciting support and obtaining buy-in from top management for a Six Sigma project. To see a sample, roll over Page Resources, and click Project Storyboard.

198

Project Documentation

Six Sigma Black Belt | Project Management | Project Charter and Plan Task: Project Documentation

Phased Reviews Phased reviews are also called "milestone reviews" or "tollgates". Typically there are 5 reviews in a Six Sigma project corresponding to the 5 phases of the Six Sigma DMAIC (Define-Measure-Analyze-Improve-Control) process, which will be discussed in upcoming lessons. Phased reviews offer an opportunity for the project team to assess the progress in relationship to the project’s goals. They also allow the project team to regroup and make any necessary changes or modifications to the project. Management Reviews Management reviews are meetings between the project leader (typically the Black Belt) and the management team.  They allow the project leader to update management on the status of the project in terms of financial progress. In some organizations tollgates are both an opportunity to review the project with senior management as well as an opportunity to update key stakeholders on the project’s overall progress (i.e., its current phase).

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Charter Negotiation

Six Sigma Black Belt | Project Management | Project Charter and Plan Task: Charter Negotiation

The project charter is a written commitment approved by management stating the scope of authority for an improvement project.  It is a byproduct of negotiations that have occurred based on relevant data and decisions made by the team, the Project Manager or Black Belt, and the project sponsor or champion. The charter elements were introduced earlier in this lesson and the following should be considered when making charter negotiations.  Objectives • What is the purpose of the project? • What do we hope to accomplish? Scope • What, specifically, is included in this project? • What is not included in this project? Boundaries • What areas of the company are included? • What departments are involved? • What levels within each department are involved? Resources • Who is available to work on the project? • How much of their time will be spent with project work? • What is the budget? • What software will be available? • Are special skills or certifications needed? Project Transition (hand-off) At the completion of the project, • What lessons have been learned? • What will we stop, start or continue for the next project? • Who will monitor the process from this point forward? Project Closure At the end of the project, • The Black Belt support draws to a close. • Successes are reviewed and compared with goals for process improvement and financial benefits. • The team members should be rewarded and recognized for their efforts.

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Assessment - Project Charter

Six Sigma Black Belt | Project Management | Project Charter and Plan Concept: Assessment - Project Charter

Read the following statements about project charters. Click True or False for each item. [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

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Project Charter Pyramid Game

Six Sigma Black Belt | Project Management | Project Charter and Plan Concept: Project Charter Pyramid Game

[ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

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Six Sigma Black Belt Project Management Team Leadership

Learning Objectives

Six Sigma Black Belt | Project Management | Team Leadership Concept: Learning Objectives

At the end of this Project Management topic, all learners will be able to: • know the elements of launching a team and why they are important: clear purpose, goals, commitment, ground rules, roles and responsibilities of team members, schedules, support from management and team empowerment. • select team members who have appropriate skills sets (e.g., self-facilitation, technical/subject-matter expertise), and create teams with appropriate numbers of members and representation. • facilitate the stages of team evolution, including forming, storming, norming, performing, adjourning and recognition.       Portions of this topic were taken from the ASQ Six Sigma Green Belt web-based Certification Preparation Course, the ASQ Foundations in Quality Learning Series: Certified Quality Manager and the ASQ Foundations in Quality Learning Series: Certified Quality Engineer.

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Initiating Teams

Six Sigma Black Belt | Project Management | Team Leadership Concept: Initiating Teams

A team is a group of individuals organized to work together to accomplish a specific objective.  Two or more people may be considered a team as long as they are mutually accountable for the accomplishment of a specific purpose and specific performance objectives.  Teams pool their talents, skills, and knowledge for the good of the organization.  They become the components of a system, working toward the common goal of quality and process improvement. For a project team to be productive, it is important that the team members understand what they are trying to accomplish and why. Clearly stated goals and a clear statement of purpose will direct the team and will provide each team member a sense of purpose and commitment. The team purpose should: • be specific, not vague. • be directly related to the project charter. • not be defined by the team. • be communicated to team members at the beginning of the project.

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Ground Rules

Six Sigma Black Belt | Project Management | Team Leadership Task: Ground Rules

In the initial stages, team members need basic guidelines to add predictability to their work environment and create a sense of safety around team interactions. Ground rules are group norms regarding how meetings will be run, how team members will interact, and what kind of behavior is acceptable.  Each member is expected to respect these rules during the project’s duration. Some areas to consider when establishing ground rules include: Logistics • Regular meeting time and place • Procedure for notifying members of meetings • Responsibilities for taking notes, setting up the room, etc. Attendance • Legitimate reasons for missing a meeting • Procedure for informing the team leader when a meeting will be missed • Procedure for providing updates to absent members Promptness • Acceptable definition of “on-time” • Value of promptness • Ways to encourage promptness Participation • Basic conversational courtesies (i.e., listening attentively) • Tolerable interruptions (i.e., phone calls, operational emergencies) • Confidentiality guidelines • Value of timely task completion • Voting protocol (i.e., an absent member votes with the majority)

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Roles and Responsibilities

Six Sigma Black Belt | Project Management | Team Leadership Concept: Roles and Responsibilities

It has been well documented that teams can outperform individuals. But simply pulling a group together to work on a project does not result in an effective team.  A group becomes an effective team when members learn to work together, capitalizing on their knowledge, skills, and a creativity borne of their diverse perspectives on work. Team members must fulfill their respective responsibilities. Provisions must be in place to manage a variety of group dynamics related to team agendas, operational guidelines, and how to best handle distractions and disruptive behavior. With such guidelines in place, the stage is set for individuals to realize their part in the greater whole. Teams have key players who carry out specific duties and orchestrate team activities.  These fundamental roles emerge in teams: • A team sponsor (or champion) who fulfills a guidance role and supports the team’s activities, helps secure resources, and clears a path in the organization. Generally an executive or manager in the organization. • A team leader, typically the Black Belt, who carries out the appropriate leadership functions to help the team effectively accomplish its purpose. • Team members who participate and carry out agreed-to assignments. • A facilitator who is trained in working with groups and helps keep the team on track. Organizations may use different labels for these roles, and one individual may fulfill multiple assignments.  For example, the facilitator role may be carried out by the team leader.  However, the number of key players is not important as long as the work gets done. The following pages provide a closer look at each of these four key roles.

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Team Sponsor or Champion

Six Sigma Black Belt | Project Management | Team Leadership Task: Team Sponsor or Champion

Teams need the executive support and direction from top management to achieve their best results.  An individual executive or manager may fulfill the role of team sponsor .  The sponsor generally has a stake in the outcomes of the project, has influence in the organization, and may even select the team members and team leader. A team sponsor does not serve as a member of the team. The team sponsor supports the team, offering guidance as necessary and empowering the team to take actions and accomplish results. According to The Team® Handbook, the following duties of a Sponsor or Champion occur in three phases:

Before the project • Select the project • Prepare a mission statement • Identify goals • Develop the project charter • Determine needed resources • Select the team leader • Assign a quality advisor or coach • Select the team members During the project • Orient the team • Meet regularly with the team • Develop and improves systems to enable change • Represent the team to others in the company • Eliminate obstacles to the team’s progress After the project • Oversees improvements made by the team (with the guidance and monitoring from the process owner) and ensures the solutions are implemented and followed • Assume responsibility for communicating data and lessons learned from the team for future improvements

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Team Sponsor or Champion

Six Sigma Black Belt | Project Management | Team Leadership Task: Team Sponsor or Champion

209

Team Leader

Six Sigma Black Belt | Project Management | Team Leadership Concept: Team Leader

The team leader may be selected by the sponsor and can be a supervisor, manager, or employee in the related project area. In a Six Sigma project, the team leader is the Black Belt. Team leaders use their knowledge of the project to guide the team, yet they do not dominate team meetings or force the group to self-determined conclusions. The team leader: • Creates and maintains channels within the organization that allow the team to do its work. • Facilitates communication between the team and the team sponsor. • Maintains all team records and meeting notes. • Sets the agenda and makes sure the team sticks to it. • Helps the team resolve any problems that may arise. • Leads/drives the implementation of team recommendations. To carry out their responsibilities, team leaders need to be competent at leadership, coaching and facilitation skills.

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Team Members

Six Sigma Black Belt | Project Management | Team Leadership Concept: Team Members

Teams generally have 5-8 members who are appointed by the sponsor or guidance team in consultation with the team leader and facilitator.  Depending on the nature of the project or mission, the team may consist of cross-functional or even cross-company employees. Becoming part of a team is a big responsibility.  Team members accept their positions with the knowledge that they are to contribute fully to the project—sharing their talents and abilities, participating actively in team meetings, and completing tasks to the best of their abilities.  If team members are appropriately selected based on their skill set and current jobs, team membership can be an integral part of their job responsibilities, rather than an added burden. In general, team members are responsible for: • Preparing for team meetings. • Helping to adhere to the meeting schedule and ground rules. • Participating in team activities. • Completing assignments between meetings. During team meetings, team members are responsible for: • Maintaining good body language and eye contact. • Avoiding judgment of others and suspending judgment of ideas. • Understanding what was said before responding. • Asking questions to get information and to ensure understanding. • Participating in team discussions. • Refraining from dominating team discussions.

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Facilitator

Six Sigma Black Belt | Project Management | Team Leadership Concept: Facilitator

Facilitators have special training in project management, group process, quality tools, etc. They help team members work together to execute quality processes.  The facilitator, who is typically the Black Belt, can also be a consultant to the team helping monitor team progress and making suggestions for process improvements.  The facilitator is primarily concerned with process and how decisions are made rather than what decisions are made. As a result, the facilitator must have: • Skills in interpersonal communication, meeting conduct and group process.  • Good understanding of quality tools and their use. • The ability to teach team members about necessary quality tools. In addition, the facilitator can help the team leader: • Form groups • Build teams • Give feedback • Resolve conflicts

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Team Empowerment and Management Support

Six Sigma Black Belt | Project Management | Team Leadership Task: Team Empowerment and Management Support

Empowerment occurs when employees have the authority to make decisions and take action in their work areas without prior approval.  For example, an operator can stop a production process if he or she detects a problem, and a customer service representative can send out a replacement product if a customer reports a problem with a defective one. Employee empowerment involves shifting knowledge, responsibility and authority to persons who actually operate business processes. Empowerment takes on added importance in a team setting, where employees are responsible for all work activity and performance results in their respective areas.  Click each of the topics below to learn more about the role that management can take in empowering teams. Establishing boundaries Before a project begins, the sponsor/champion should clearly define the process or problem that the team will study, identify the desired outcomes, and then give team members the authority and responsibility to achieve them.  Team members also need to understand that empowerment requires respecting individual boundaries. Providing resources and training Management is responsible for providing the equipment, supplies, technical support, personnel, and training required for a team to take meaningful action during a project. Providing support/removing barriers During the project, management can support the team’s authority by promoting its interests throughout the organization and helping team members overcome difficulties.

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Selecting Team Members

Six Sigma Black Belt | Project Management | Team Leadership Concept: Selecting Team Members

Selecting team members is typically a collaborative effort among the Champion/Sponsor, Black Belt, and Process Owner to ensure the right combination of process expertise, commitment and drive for improvement. Keep in mind organizations may handle team selection differently. According to The Team® Handbook, the following should be considered when forming a process improvement team: • Limit the team to five to eight members. • Team members should represent each area affected by the project and have a detailed understanding of the target process/function. • Sometimes, team members can represent each stage of the process under study. • Choose those whose positions and opinions are respected by their peers. • Also consider each individual’s: ° Personal experience with the process ° Interest in improvement methods and tools ° Communication skills ° Ability to think analytically ° Dedication to servicing customers ° Commitment to process improvement • •

Finally, remember to include support groups such as Human Resources, Information Technology, and Marketing, whose buy-in you may eventually need. Ensure the Finance group is involved, even if they are not among the core team members.

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Stages of Team Development

Six Sigma Black Belt | Project Management | Team Leadership Concept: Stages of Team Development

As teams are formed, they typically go through a series of stages, from formation to recognition. The first 4 stages – forming, storming, norming and performing – have historically been used in management theory to describe team behavior.  Over time a fifth stage – adjourning and recognition – was added. These stages are both normal and expected in a team’s transformation to a productive performing unit.  All are necessary for the team to grow, to face up to challenges, tackle problems, find solutions, plan work and deliver results. The following pages will describe each of the following stages of team development: • Forming: startup • Storming: conflict • Norming: cohesion • Performing: focus • Adjourning and Recognition: work ends As you learn about the different stages, keep in mind individuals, dyads, small groups, and even entire teams move back and forth among the various stages. A Performing team can slip back into major conflict (Storming) given a certain set of circumstances. Team leaders must be aware of this possibility and offer guidance as needed at any given stage.

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Forming

Six Sigma Black Belt | Project Management | Team Leadership Concept: Forming

The forming stage is synonymous with startup.  During this period, team members may not yet share a complete understanding of the group’s mission.  Emotions such as excitement, anxiety and hope take center stage.  The goal during the forming stage is for team members to get to know one another and to become familiar with the team’s mission and process.  To meet this end, creativity and innovation are essential and mistakes are welcomed as signs of learning. Team members feel: • eager with high expectations. • anxious about how they will fit in and what is expected of them. • dependent on authority to provide direction. Primary issues: • Inclusion and trust ° ° °

Willingness to involve others Desire to be included in the team’s processes Desire to feel they can trust the team leader and other team members

Task accomplishment and morale: • Task accomplishment is low to moderate • Team energy focused on defining goals, tasks and strategies for accomplishment • Morale is high

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Storming

Six Sigma Black Belt | Project Management | Team Leadership Concept: Storming

Storming is the next stage of team development.  At this point, team members may recognize that tasks are different or far more difficult than they originally thought.  This situation may induce a general sense of resentment and irritation among team members.  Conflict may arise as members argue about next steps.  Outside demands and expectations for the team’s performance create added pressure.  Competition and control take precedence over collaboration and teamwork. Although it can be contentious, the storming stage is crucial to the growth of the team.  The goal of storming is for team members to develop an understanding for other members’ interpersonal styles, to recognize the need for cohesion, and to reestablish the team’s focus. Storming can also be detrimental to a team if individuals do not find ways to overcome obstacles and work together to accomplish group goals.  Conflict resolution techniques, which are discussed later in this lesson, may be required to prevent injury to the team. Team members feel: • dissatisfied with dependency on authority. • angry and frustrated about goals and tasks. • negatively toward the formal team leader and other team members. • incompetent or confused. • competitive for power or control. Primary issues: • Power and control • May not want to follow directions • May want to influence the direction of the team Task accomplishment and morale: • Task accomplishment may be disrupted • Skill development increases as conflicts are addressed • Morale is low

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Norming

Six Sigma Black Belt | Project Management | Team Leadership Concept: Norming

Norming is considered a period of fine-tuning.  Team members reconcile competing loyalties and responsibilities and accept the team and its collective purpose.  They establish rapport and are able to express criticism constructively.  The predominant feelings are of acceptance and relief. During norming, the main goal is for team members to come together and shift their collective focus toward task completion. Team members feel: • more satisfied as they learn to work together. • better as each team member gains appreciation for the others' differences. • self-confidence regarding task accomplishment. Primary issues: • Affection and intimacy • Team members begin to open up to one another Task accomplishment and morale: • Task accomplishment increases • Positive feelings among members increase along with team results • Morale is improving

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Performing

Six Sigma Black Belt | Project Management | Team Leadership Concept: Performing

At the performing stage, team members feel relationship cohesion and recognize that individuals have differing talents.  Relationship tension has subsided, and the team can problem solve and begin to implement changes in a relatively predictable environment as a competent, cohesive unit.  The predominant feeling is a sense of pride and accomplishment.  For a performing team, the primary goal is more successful task completions.       Team members feel: • excited and eager about team activities. • capable of collaboration. • highly confident. • able to recognize and support each other. • able to communicate freely. Primary issues: • No major issues Task accomplishment and morale: • Task accomplishment optimal • Morale is high

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Adjourning

Six Sigma Black Belt | Project Management | Team Leadership Concept: Adjourning

As appropriate, teams need to disband when their work is accomplished.  Adjourning refers to breaking up the team when the job is done.  Lessons learned should be documented and successes should be recognized and celebrated.  Adjourning is an opportunity to express a willingness to work together again on future assignments. Team members feel: • sad or a sense of loss about separating from the team. • so uncomfortable that they may joke to deny feelings. • strong positive feelings about accomplishments. Primary issues: • Loss and separation • Feelings of sadness, loss and separation • Tendency to become less productive Task accomplishment and morale: • Task accomplishment decreases • Morale is stable or decreases

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Recognition

Six Sigma Black Belt | Project Management | Team Leadership Concept: Recognition

Recognition is a critical part of a project's success. Anyone who has been on a significant company project has likely received the obligatory "project shirt", pen, or paperweight, but are those gifts meaningful rewards? Meaning We recognize individuals or groups for a job well done and for the results they achieve. But do we do that for them or for ourselves? Many rewards are given out of a sincere appreciation for accomplishments, but if the person receiving the reward does not feel "lifted up", the reward can fall flat. Many people when asked to stand up in front of a group to be recognized are very uncomfortable with public recognition. Such recognition as a reward may not match their individual needs. The reward must match the person. Find out something specific that will truly make each person in the group feel special. Then present "their reward" to them in the way that feels comfortable to them. In addition, make sure you provide the specific reason for their receiving the reward. "For a good job" is much less effective than "You improved the morale of the customer service department and saved the company $250,000 a year." Value A parent would not reward high school graduation for one child with a fast food restaurant gift certificate and then bestow another child with a new car for obtaining a B+ in math. The reward you present should align with the particular results achieved. How has the achievement affected the bottom line? What was the effort involved? Rewards that match the achievement will also help people to understand that bigger rewards are based on bigger results, not any kind of favoritism.

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Assessment - Team Stages

Six Sigma Black Belt | Project Management | Team Leadership Concept: Assessment - Team Stages

Read each definition relating to team stages. Match the terms below to the corresponding definitions by dragging each term to the appropriate box. [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

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Six Sigma Black Belt Project Management Team Dynamics and Performance

Learning Objectives

Six Sigma Black Belt | Project Management | Team Dynamics and Performance Concept: Learning Objectives

At the end of this Project Management topic, all learners will be able to: • recognize and apply the basic steps in team building: goals, roles and responsibilities, introductions and both stated and hidden agendas. • apply coaching, mentoring and facilitation techniques to guide a team and overcome problems such as overbearing, dominant, or reluctant participants, the unquestioned acceptance of opinions as facts, groupthink, feuding, floundering, the rush to accomplishment, attribution, discounts and "plops" and digressions and tangents. • measure team progress in relation to goals, objectives and metrics that support team success. • define, select and apply team tools such as nominal group technique, force field analysis, multivoting and conversion/diversion.     Portions of this topic were taken from the ASQ Six Sigma Green Belt web-based Certification Preparation Course, the ASQ Foundations in Quality Learning Series: Certified Quality Manager and the ASQ Foundations in Quality Learning Series: Certified Quality Engineer.

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Team Building Techniques

Six Sigma Black Belt | Project Management | Team Dynamics and Performance Concept: Team Building Techniques

In a team’s progression through the stages of development, team building provides a framework for developing relationships and alliances among members.  Project managers who utilize team-building techniques during the early stages of team formation and continue team-building sessions throughout a project’s life cycle achieve the following benefits: • The quality of information exchange is higher. • The level of trust among team members is increased. • The process for making decisions is more effective. • There is increased commitment to individual members and to the team. • The team is focused on problem solving. • The team can develop self-enforcing, self-correcting project controls. • The need for direct supervision and coaching is minimized. • The team can operate in a self-directed mode. Some team building occurs naturally as team members work together on common tasks.  However, there are specific techniques that can be used to facilitate the process, including: • Handling team introductions in the first meeting. • Agreeing on team objectives. • Identifying and assigning specific team roles. • Establishing norms and decision-making procedures.

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Team Goals

Six Sigma Black Belt | Project Management | Team Dynamics and Performance Concept: Team Goals

Developing and agreeing upon team goals are key factors contributing to dynamic, productive teams. In the majority of situations, by the time a team convenes, the charter or purpose for the team’s formation will have been set.  The team members must ultimately have a shared vision of what will happen by the end of the project. In order to help team members understand their purpose, the following should be discussed with them: • The nature of the problem • Why this assignment is important to the organization and its customers • How the team is connected to other organizational teams and departments, customers, as well as the organization’s mission, goals, and strategies • What boundaries and constraints exist (e.g., time limits or budget) • Start and end dates, key milestones • Key measures that will define success • The team’s level of autonomy and authority in decision making Once a team convenes, members should review and discuss their charter — that is, what they are trying to accomplish and why and how the team’s purpose is aligned to organizational strategies. Goals (or objectives) are defined as quantitative statements of future expectations that include a deadline for completion.  Team objectives should be approached using the following guidelines, collectively known as "SMART":

We will discuss SMART in more detail in the Define lesson.

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Team Roles and Responsibilities

Six Sigma Black Belt | Project Management | Team Dynamics and Performance Task: Team Roles and Responsibilities

The roles of facilitator, timekeeper, note-taker and scribe should be assigned and can be rotated among team members from meeting to meeting. Facilitator The facilitator, in many cases also the team leader, is the one who assumes overall responsibility for keeping the meeting focused and tracking against the agenda.  The following activities are the responsibility of the facilitator: • Opening and closing the meeting • Facilitating discussion • Managing participation Timekeeper A timekeeper, as the name implies, keeps track of time.  This individual alerts the team when time allocations are almost up without policing the agenda or mandating that the team move on. Note-taker The note-taker ensures that meeting minutes are recorded, distributed and/or posted.  The note-taker will record the following: • Key topics • Discussion points • Action items • Future agenda items Scribe A scribe captures and posts ideas on an easel chart or whiteboard during the meetings, including those items that remain unresolved during a meeting and must be noted on the “parking lot.”

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Team Introductions

Six Sigma Black Belt | Project Management | Team Dynamics and Performance Concept: Team Introductions

Employees may arrive at the first meeting distracted, whether about their overloaded schedule for the day, personal issues, or the meeting they just attended.  In addition to these distractions, team members may approach their initial meeting with anxiety about working with one another.  Managers can help address anxiety and ease members into the meeting by conducting team introductions, or “icebreakers,” to allow for spontaneous interaction and conversation.  Several techniques, as identified in The Team® Handbook, are discussed below. Ask team members to share basic information with the group, such as: • Name and job title. • What they like best about their work. • Recent successes in their work. • What they currently find most challenging in their job. • How they came to be on the team. If the team members are comfortable, they may also want to share information about their families or interests outside of work. To view an exercise that can be used during team introductions, roll over Page Resources and click Team Activity.

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Team Activity

Six Sigma Black Belt | Project Management | Team Dynamics and Performance | Team Introductions Example: Team Activity

Paired Introductions Pair up team members who don’t know each other well and have them get acquainted by asking each other: • What is your name? • What is your job? • How long have you been at the organization? • What got you started here? • What do you like best about your job? • How did you become part of this team? • What is your favorite hobby? It is helpful if these questions are posted on and easel in the front of the room.  After the paired introductions, ask partners to introduce each other to the rest of the team.

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Stated and Hidden Agendas

Six Sigma Black Belt | Project Management | Team Dynamics and Performance Concept: Stated and Hidden Agendas

Within teams, there are two types of agendas: those that are stated and those that are hidden.

Stated Agendas A stated agenda is essential to an effective team meeting.  It helps keep team members on task by defining the meeting's purpose and identifying who will discuss what and when. Ideally, a meeting agenda is prepared and distributed to all team members before the meeting. A good agenda typically includes the following elements: • Objective of the meeting • Allocations of time for each topic • Time on the agenda to review and revise the agenda • Agenda items listed in order • Action items to be discussed from the previous meeting • Time at the end of the meeting to evaluate the meeting and summarize action items Roll over Page Resources and click Agenda to see an example.

Hidden Agendas Hidden agendas are much different than stated agendas. They typically represent individual interests that may or may not complement the team’s purpose and goals. To help surface hidden agendas for the group discussion before project work begins, managers may utilize certain discussion techniques.  To see two examples of discussion techniques that can be used to surface hidden agendas, roll over Page Resources and click Technique Examples.

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Technique Examples

Six Sigma Black Belt | Project Management | Team Dynamics and Performance | Stated and Hidden Agendas Example: Technique Examples Hopes and Concerns In this activity, team members begin by reflecting on their hopes for the team or project as well as their concerns about the outcome.  After individual reflection, paired team members share their responses with one another and then with the rest of the group as the team leader documents responses on an easel chart.  Finally, the entire group discusses what the team or organization can do to help prevent the negative from happening and to help make the hopes come true. “What I want for myself out of this.” Once team members understand the purpose of the project, this technique helps to explore what each individual would like to achieve above and beyond the team goals.  Team members begin by taking approximately five minutes to list personal goals for their team participation such as learning new skills or getting to know other people in the organization.  Then, members share their lists with the group and either discuss them or simply listen.

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Team Facilitation Techniques

Six Sigma Black Belt | Project Management | Team Dynamics and Performance Concept: Team Facilitation Techniques

Even the most well-intentioned teams can slide into dysfunctional behaviors that detract from team growth and performance.  The table below outlines some counter-productive behavioral traits along with recommended solutions. Trait

Description

Possible Solution

Overbearin Team members attempt to use influence g based on position of authority in the participant organization

Talk to the authority off-line; ask for cooperation and patience

Dominant Participants who talk too much participant

Structure meeting so that everyone is encouraged to participate (i.e. have members write down their opinions, and then discuss them one by one)

Reluctant Participants who rarely speak participant

Practice “gate keeping” by asking “John, what’s your view on this?” or dividing tasks into individual assignments and having all report

Unquestion Participants who make opinions sound like ed facts acceptance of opinions as facts

Ask the speaker to clarify whether this is an opinion or fact and/or request supporting data

Groupthink All or most of the participants coalesce in support of what they believe to be the consensus of the group but team members may actually be pressured into agreement to avoid conflict

Remain impartial. Serve as the “Devil’s Advocate.” Break the team into small groups. Have groups report their findings to the team

Feuding

Request that these types of conflicts be taken off-line.  Reinforce ground rules

Conflict involving personal matters

Flounderin Difficulty in starting or ending an activity g

Redirect team to the project plan and written statement of purpose.

Rush to Rushing to get to a solution before the Remind the group that rushing can hurt the accomplish problem-solving process is worked through quality of the team’s work ment Attribution Resolving confusion or disagreement by explaining another person’s motivations to act rather than the act itself Discounts

Identify the attribution and encourage further discussion; reaffirm the importance of supporting data

Ignoring or ridiculing another’s values or Provide training in active listening early in not acknowledging a statement made during the project. Support the discounted person or a meeting;the idea or statement just "plops" talk off-line with anyone who frequently discounts or puts down another person’s statements

Digressions Meandering and unfocused conversations and tangents

 

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Use written agenda with time estimates and continually direct the conversation back on track. Remind the team of its mission

Team Performance Evaluation

Six Sigma Black Belt | Project Management | Team Dynamics and Performance Concept: Team Performance Evaluation

When teams move from one project to the next without pause, they are missing valuable opportunities for evaluation and improvement. Teams that move too quickly on to their next project also miss their opportunity to celebrate successful outcomes with recognition and rewards. Team performance evaluations help members assess how effective their interactions are with one another and how durable their solutions are when implemented in the organization.  The data from these evaluations and assessments can help the team's processes improve further, thereby guaranteeing the team's continued success. Team performance evaluations may be carried out by team members themselves or by an outside party. The following pages describe several methods for performing team evaluations.

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Self-evaluation

Six Sigma Black Belt | Project Management | Team Dynamics and Performance Concept: Self-evaluation

A team is in a good position to self-evaluate if, at the beginning of a project, its members establish objectives against which to measure their team's performance.  Performance objectives should relate to both tasks and behaviors. Some examples are provided in the table below. Task Objectives • Reduce costs • Decrease cycle time • Increase yields • Improve customer satisfaction • Improve process efficiency

Behavior Objectives • Communicate effectively • Keep team commitments • Make constructive comments • Participate in discussions • Come prepared to team meetings

The team objectives become the evaluation criteria.  Measurement against goals and objectives can be performed at the end of each team meeting or at the conclusion of the project. A common technique for assessing behavior is to compile a short list of questions along with a rating scale and distribute it directly after a team meeting.  Roll over Page Resources and click Team Objective Evaluation to see an example. Another technique, the Team Effectiveness Profile, is one in which team members assess their effectiveness in four different areas: • Mission, planning and goal setting • Group roles • Group operating processes • Interpersonal relationships Measurement against task criteria typically requires “hard data", such as the number of dollars saved or volume per unit increased.  Figures from hard data are useful in assessing progress during a project and measuring overall success after project completion.  

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Team Objective Evaluation

Six Sigma Black Belt | Project Management | Team Dynamics and Performance | Self-evaluation Example: Team Objective Evaluation

Team Objective Evaluation Thank you for participating and being a key member on the project team! Your feedback is valued and necessary for continuous improvement. Please rank the team's performance by circling the appropriate number as it relates to the behavior objectives established at the beginning of the project using the following point/value scale: 1 = Never

2 = Rarely

3 = Sometimes

4 = Usually

5 = Always

1

2

3

4

5

  1. Team members communicated effectively. 2. Team commitments were kept.

 

1

2

3

4

5

3. Team members made constructive comments. 4. Team members participated in discussions. 5. Team members were prepared for meetings.  

1

2

3

4

5

1

2

3

4

5

1

2

3

4

5

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External Evaluation

Six Sigma Black Belt | Project Management | Team Dynamics and Performance Concept: External Evaluation

Even with well-defined evaluation criteria, any self-evaluation will be flawed by a certain degree of subjectivity; consequently an external evaluation is preferable.  External evaluation lends an objective perspective to complement and supplement team self-evaluations. External evaluations may be conducted by anyone outside the team’s immediate day-to-day activities, such as the team sponsor. External evaluations are based on the same criteria as self-evaluation but may draw upon a broader range of sources, such as internal and external customers, other teams or stakeholders, suppliers or management. Some organizations utilize evaluation data to assess team performance patterns across an organization.  For example, external evaluations may be used to calculate the percentage of teams exhibiting exemplary behavior as defined by management.  Desired behaviors may include: • Providing adequate data to back up claims. • Displaying data graphically so that patterns are clear. • Drawing conclusions warranted by the data analysis. • Analyzing causes. • Trying solutions on a small scale before going into full implementation. Evaluations of this sort of data could showcase team success throughout the organization, especially at the highest management levels, where positive results translate into continued support. In addition to demonstrating exemplary behavior, evaluations can reveal potential problem areas in team performance, such as difficulty in accessing necessary data, poor meeting attendance, or high membership turnover.  At the beginning of future projects, team leaders/facilitators can use the evaluations to learn what not to do, thereby reversing any damaging trends. Finally, it is important to ensure that team evaluations are linked to job-related performance evaluations even for team members who are not considered “full-time.”  Many team leaders/facilitators fail to follow-up on this critical aspect, but it is one of the most effective ways to ensure that all team members are engaged and actively supporting the project.

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Team Tools

Six Sigma Black Belt | Project Management | Team Dynamics and Performance Concept: Team Tools

There are a variety of tools available to assist teams in making decisions, such as: • Nominal group technique • Force field analysis • Multivoting Two types of thinking that go into each of these team tools are Diversion and Conversion.  Diversion refers to those team activities that produce many different options.  When a team needs a number of fresh ideas, diversion techniques such as brainstorming could be used to anticipate obstacles, or to recognize strengths, weaknesses, opportunities or threats. Conversion activities are used to narrow the list of options and prioritize them for action.  Examples are the nominal group technique and multivoting. These tools are discussed on the following pages.

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Nominal Group Technique

Six Sigma Black Belt | Project Management | Team Dynamics and Performance Concept: Nominal Group Technique

Nominal group technique is a consensus planning tool that helps prioritize issues and encourages participation from the entire group. The illustration below shows an example of nominal group technique using 4 items.

Procedure 1. 2.

3. 4.

5. 6. 7.

Participants are brought together for a discussion session led by a facilitator. After the topic has been presented to session participants and they have had an opportunity to ask questions or briefly discuss the scope of the topic, they are asked to take a few minutes to think about and write down their responses. The session facilitator will then ask each participant to read, and elaborate on, one of their responses. These are noted on a flipchart. Once everyone has given a response, participants will be asked for a second or third response, until all of their answers have been noted on flipchart sheets posted around the room. Once duplications are eliminated, each response is assigned a letter or number. Participants are then asked to choose up to 10 responses that they feel are the most important and rank them according to their relative importance. These rankings are collected from all participants, and then aggregated.

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Force Field Analysis

Six Sigma Black Belt | Project Management | Team Dynamics and Performance Concept: Force Field Analysis

Force field analysis is a tool that can be used when a team is identifying causes of a problem or is planning a change, such as the implementation of a solution.

Procedure 1. 2.

3.

4.

Write the desired change or problem at the top of easel. Draw a vertical line underneath. Brainstorm all the driving forces that support the change (or cause the problem to occur).  Write these on the left side of the line.  Determine how strong each force is.  In the area between the words and the centerline, draw an arrow pointing to the centerline.  The arrow’s length can be used to represent the strength of each particular driving force.  An alternative to different arrow lengths would be to assign a score (between 1 and 5) to each force. Brainstorm all the restraining forces that hinder the change (or prevent the problem from occurring).  Write these on the right side of the line.  Determine how strong each force is.  In the area between the words and the centerline, draw an arrow pointing to the centerline.  The arrow’s length can be used to represent the strength of each particular restraining force.  An alternative to different arrow lengths would be to assign a score (between 1 and 5) to each force. For a desired change, discuss various means to diminish or eliminate the restraining force.  For a problem, discuss various means to diminish or eliminate the driving forces.  Focus on the strongest forces.

Note: It is possible to have a one-to-many relationship between driving and restraining forces. For example the driving force--control rising maintenance costs could have two restraining forces--cost and disruption.  

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Multivoting

Six Sigma Black Belt | Project Management | Team Dynamics and Performance Concept: Multivoting

Multivoting is a tool used in Six Sigma to arrange, in order of importance, a list of ideas, problems, common causes, and the like. Multivoting allows team members to place “votes” on the topics most important to them.  Those items receiving the highest rankings from the group should get further attention and consideration. The graphic below displays a list of ideas for reducing absenteeism. The voting results are also shown.

Procedure 1. 2. 3.

4.

5. 6.

Add together like items if possible to decrease redundancy. Number or letter each item. Decide how many votes each team member is allowed.  Depending on the length of the list, each member will receive 5 to 10 votes. Another option is to include one-third of the total number of items (e.g., 24 items equals 8). Ask team members to vote on the list of items. Each team member has a set number of votes, and can spread them out any way they wish (i.e., if one wishes, all votes could be placed for one single item). Group and count the high scores from the voting activity. If necessary, perform a second vote on only the highly scored items from the first vote to further narrow the list.

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Assessment - Facilitation Barriers

Six Sigma Black Belt | Project Management | Team Dynamics and Performance Concept: Assessment - Facilitation Barriers

Read each definition relating to facilitation barriers. Match the terms below to the corresponding definition by dragging each term to the appropriate box. [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

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Six Sigma Black Belt Project Management Change Agent

Learning Objectives

Six Sigma Black Belt | Project Management | Change Agent Concept: Learning Objectives

At the end of this Project Management topic, all learners will be able to: • understand and apply techniques for facilitating or managing organizational change through change agent methodologies. • understand the inherent structures of an organization (e.g., cultures and constructs) that present basic barriers to improvement; select and apply techniques to overcome them. • define, select and apply tools such as consensus techniques, brainstorming, effort/impact, interest-based bargaining to help conflicting parties (e.g., departments, groups, leaders, staff) recognize common goals and how to work together to achieve them. • define, select and apply techniques that support and sustain team member participation and commitment. • use effective and appropriate communication techniques for different situations to overcome organizational barriers to success.     Portions of this topic were taken from the ASQ Six Sigma Green Belt web-based Certification Preparation Course, the ASQ Foundations in Quality Learning Series: Certified Quality Manager and the ASQ Foundations in Quality Learning Series: Certified Quality Engineer.

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Managing Change

Six Sigma Black Belt | Project Management | Change Agent Concept: Managing Change

In today’s competitive environment, change is constant.  It is a reality for every organization, from giant multinationals to the simplest enterprises.  Change can range from initiatives involving thousands of people worldwide, to one person suggesting a minor improvement that influences a limited number of employees in a small organization. Change management is the practice of planning and directing changes in an organization. Change management implies it is possible to introduce change deliberately and steer its development, rather than allow change to occur naturally and unpredictably. In the field of quality, change management typically refers to processes used to introduce and integrate new initiatives or systems into organizations.  Within this context, a change management effort involves transition planning, predicting and overcoming sources of resistance, organization-wide training and facilitating cultural change. The following pages will present ideas on change management techniques, the roles of management and change agents, pitfalls to avoid, and strategies for overcoming organizational roadblocks and process barriers.

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Change Agents

Six Sigma Black Belt | Project Management | Change Agent Concept: Change Agents

Whether an organization is facing a relatively minor change or planning for a major change initiative, there is generally one individual who masterminds the effort. Change agents fulfill this important role. A change agent is an individual from inside or outside an organization who facilitates change within that organization.  A change agent may or may not be the initiator of the change effort. There are two types of change agents: • Internal change agents are employees within the organization who are commissioned by management to facilitate the change process.  The employees may be at the operative, management or upper management level. • External change agents are people outside the organization who are hired to help facilitate the process. Recruiting the right person to support a change initiative is an important task.  The table below lists some advantages and disadvantages of internal and external change agents. Type Internal

External

Advantages • Are “a known quantity” • Typically bring a sound understanding of organizational culture, infrastructure and operations to the change process • Usually already have rapport with key players • Can help equip people with a new set of skills • Bring a natural objectivity and “political freedom” to the change process • Are able to more readily challenge the status quo or ask the tough questions

Disadvantages • May be hindered by a lack of objectivity or accessibility to the “big picture” • May be reluctant to engage certain areas of the organization because of existing working relationships (i.e., keeping friends safe)

•

• •

•

Must be carefully screened to ensure proper qualifications and the right fit with the organization Have limited organizational knowledge Must work diligently to build a relationship with the client organization and to understand its operations and culture Can take time to get up to speed

Change agents are not always deliberately commissioned.  As with organizational leaders, some employees may assume the role of change agent independently.  In addition, an organization may use change agent teams, in which both internal and external agents collaborate to draw upon their respective strengths.

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Roles and Techniques

Six Sigma Black Belt | Project Management | Change Agent Concept: Roles and Techniques

In The Change Agents’ Handbook, David Hutton describes the role of a change agent in terms of the following categories: Educate and work with upper management to initiate and sustain the transformation

•

•

•

• • Support and advise other colleagues

• • •

• •

• •

Organize a quality assessment to measure things like employee knowledge or resistance to change Propose and organize educational activities (e.g., formal workshops, guest speakers, off-site visits) Orchestrate the development of the improvement plan to meet organizational goals Ensure the integration of the improvement plan into the business plan Expedite the meeting schedule of upper management Play an active part in discussions and decision making Provide guidance to the team on technical issues Provide guidance on the selection of suitable strategies and methods, subject matter experts and other resources Help monitor the status of projects in the early stages Act as a considerate and discreet advisor on behavioral issues, relationships and personal issues Act as a coach where appropriate Challenge the top management team if commitment to change seems to waver

Manage specific projects

•

Act as a project manager or project sponsor for specific initiatives (e.g., expediting a customer satisfaction survey or deploying training throughout the organization)

Develop and manage a support network

•

Identify, train, develop and support others assigned to lead the change (in addition to top management)

 

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Organizational Roadblocks

Six Sigma Black Belt | Project Management | Change Agent Concept: Organizational Roadblocks

Barriers to organizational improvement or change, "roadblocks" are defined as anything that blocks or filters the implementation or realization of continual improvement.  The most significant barriers are often inherent in an organization’s structure and culture. Many improvement efforts flounder or fail because consideration was not given to barriers to implementation.  A critical part of any change initiative is: • identifying barriers. • evaluating their significance and risk. • planning how best to address them. Force field analysis is a tool that can be used help overcome barriers when a team is identifying causes of a problem, planning a change or implementing a solution. Note: Force field analysis is discussed in the Team Dynamics and Performance section of this lesson. Structural and cultural barriers will be discussed in the upcoming pages of this section.  

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Structural Barriers

Six Sigma Black Belt | Project Management | Change Agent Concept: Structural Barriers

Both vertical and horizontal structures have the potential to introduce structural barriers to change within an organization. An organization’s structure may foster a “silo” mentality, whereby each department focuses on its own interests, procedures and people rather than on cooperating with other groups to meet customer needs.  The resulting structural isolation may increase the efficiency of individual groups, but it ultimately detracts from the organization’s ability to meet customer commitments. Horizontal structures may produce communication barriers between management levels.  For example, potentially negative information at one level may be distorted or filtered before being passed to higher management.  Conversely, management plans may not be communicated to front-line employees. While vertical and horizontal structures may exist, one of the most effective ways to reduce the problems associated with potential barriers is to create a communication plan. It is important that every area of the organization touched by the project be well informed. The goal is to make sure each of the work areas understands why the project is important, how it is progressing, what effect it will have on their department and what their involvement might be. In essence, the goal is to answer the question, "What does this mean to me?" The illustration below shows an example of a communication plan. As seen in the chart below, some elements to be addressed in a communication plan include: • The audience • The message to be delivered (specific to each group) • How the message will be communicated • Frequency and timing of updates • Responsible person(s) or team(s) • Plan for receiving and utilizing feedback

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Cultural Barriers

Six Sigma Black Belt | Project Management | Change Agent Concept: Cultural Barriers

The cultural barriers to organizational improvement are rooted in reactionary attitudes and beliefs, such as mutual distrust and fear of change, along with strategic shortcomings, such as management’s failure to create a shared organizational vision. A basic methodology for overcoming cultural barriers includes the following steps: 1.

2. 3. 4. 5.

6. 7.

8.

Establish a sense of urgency: Examine the market to identify crises, potential crises and major opportunities. Then discuss them with the rest of the organization. Form a powerful guiding coalition: Assemble a group with enough power to lead the change effort and encourage its members to operate as a team. Create a vision or modify an existing vision: Create a vision to help direct the change effort and develop strategies for achieving that vision. Communicate the vision: Use every vehicle possible to communicate the new vision and strategies, including a guiding coalition. Empower others to adopt the vision: Remove systems or structures that seriously undermine the vision.  Encourage risk-taking and nontraditional ideas, activities and actions. Plan for and create short-term wins: Plan for visible performance improvements and recognize and reward the employees involved. Consolidate improvements and produce still more change: Use increased credibility to continue changing systems, structures, and policies that do not fit the vision.  If necessary, reinvigorate the process with new projects, themes and change agents.  As needed, hire, promote and develop employees who can implement the vision. Institutionalize new approaches: Articulate the connections between new behaviors and organizational success, while instilling the vision in the next generation of organizational leaders.

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Negotiation Techniques - Overview

Six Sigma Black Belt | Project Management | Change Agent Concept: Negotiation Techniques - Overview

Negotiation is a significant part of any group activity.  Whenever there are multiple people with multiple opinions and goals, there is strong potential for disagreement.  The key is to aim for a workable solution mutually acceptable to all parties – that is, to negotiate.   There are four primary approaches to negotiation: Approach

Basic Assumption

Win/Win

You and I can work together to ensure we both benefit from the negotiation.

Win/Lose

Only one person will come out on top of this negotiation – me.

Lose/Win

I've been set up to lose this negotiation, but I’ll go down fighting.

Lose/Lose

Neither of us will benefit from negotiating, but I’ll still put up a fight.

With the win/win approach, both sides enter negotiations seeking mutual interaction and benefit.  With the remaining three approaches, individuals compete for dominance before negotiations even begin.

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Positional Bargaining vs. Principled Negotiation

Six Sigma Black Belt | Project Management | Change Agent Concept: Positional Bargaining vs. Principled Negotiation

In positional bargaining, people approach negotiations with a win/lose, lose/win, or lose/lose mentality.  They lock themselves into predetermined positions and often lose sight of the underlying problems to be resolved.  As the name suggests, positional bargaining simply focuses on a winning position. Principled negotiation, on the other hand, is based on the win/win approach and the following principles: • Separating the people from the problem • Focusing on interests, not positions • Understanding what both sides want to achieve • Inventing options for mutual gain • Insisting on objective criteria Principled negotiation varies with the participants and issues involved, but there are some basic techniques that help managers and leaders in the majority of situations.

Negotiation techniques • • •

• • • •

Set clear objectives for every negotiation item. Establish a broad range of acceptable outcomes. Be alert to the real intentions of the other with respect to goals and priorities. Be well prepared with supporting data. Do not hurry. Confer with your associates when necessary. Stay flexible in your position.

• • • • •

• •

Save the hardest issues for last. Respect the importance of face saving for the other party. Build a reputation for being fair but firm. Avoid panic; learn to control your emotions. Measure each move against your objectives and understand how each move relates to all others. Remember, compromise is part of negotiation. Consider the impact of present negotiations on future negotiations.

Responding to common negotiation challenges Challenge

Recommendation

Handling goal conflict Find a common goal.  In most organizations, it is rare that two people or departments cannot find a goal that is acceptable to both. Broaching a difficult or sensitive subject

Rather than ignoring underlying problems or tension, bring obstacles into the open at the beginning of negotiations and discuss them frankly.

Handling varying ideas

Overcome the instinct to evaluate ideas instantly as right or wrong, perfect or useless.  Build on what is good in an idea and try to overcome its shortcomings.

Dealing with varying personalities and beliefs

Focus on the objective, not on individual differences.

 

251

Conflict Resolution

Six Sigma Black Belt | Project Management | Change Agent Concept: Conflict Resolution

Given the variety of opinions and desires within an organization, conflict is a natural part of the decision-making process.  When two or more parties are in conflict, they tend to believe what each wants is fundamentally incompatible with what the other wants.  From this belief stems a common misunderstanding: Conflict is inherently negative.  This is not necessarily the case. A certain amount of conflict can trigger significant creativity and innovation.  For example, it's Saturday evening and you and your friends are planning a night out at the movies. Imagine that, in an effort to avoid conflict, the group reluctantly agrees to your movie selection. While you may enjoy yourself, your friends' satisfaction is uncertain at best. Now imagine that you and your friends embrace the conflict. You openly discuss other people's desires to have dinner or a few drinks and ultimately decide on a cinema grill where customers can eat and drink while watching the latest movies. In this scenario, every member of the group finds a certain level of satisfaction with the evening's plan rather than one person feeling perfectly satisfied while the others are dissatisfied. Organizations increasingly view conflict as a vital, energizing force that unlocks the creativity of an organization and allows it to innovate, change and grow.  The key is to proactively manage conflict when it arises. Conflict resolution is the management of a disputed situation to arrive at a decision satisfactory to all parties.  Conflict management is achieved through win/win collaborations. As you'll see in the next section, the negotiation process most compatible with a win/win collaboration is interest-based bargaining (IBB).

252

Interest-based Bargaining

Six Sigma Black Belt | Project Management | Change Agent Concept: Interest-based Bargaining

Interest-based bargaining (IBB) assumes that understanding why negotiating parties feel the way they do helps reveal common interests and generate innovative options, resulting in more durable solutions and mutual gain.  Conceptually, IBB is similar to the four-step method of principled negotiation in helping people deal with their differences.  IBB focuses on issues rather than personalities, the present and future rather than the past, and interests underlying the issues, not just positions. Principled negotiation steps 1. Tune in to the feeling behind the other person's words. 2. Try to identify precisely what the feeling is about. 3. Try to clarify exactly why the person feels so strongly. 4. Paraphrase the speaker's thoughts to check understanding.

Interest-based bargaining steps 1. Select and focus on the issue(s). 2. Identify interests behind the positions. 3. Generate options to satisfy interests. 4. Generate options to satisfy interests. 5. Establish objective criteria to evaluate options. 6. Apply the criteria to the options. 7. Reach consensus on an overall solution. To move toward a successful solution, use IBB, which incorporates the use of several tools and techniques, including: • Brainstorming: removes some of the risk associated with suggesting new ideas. • Easel charts: allows participants to record and display ideas in a large, shared format, providing a common focus and reducing misunderstandings. • Consensus decision-making: results in a solution all negotiators can live with. • Closure tools (such as multivoting): narrows options so a solution can be selected. Tools such as brainstorming and multivoting are useful not only in relation to IBB but also in any conflict management situation.

253

Brainstorming

Six Sigma Black Belt | Project Management | Change Agent Concept: Brainstorming

Brainstorming provides a common method for teams to creatively and efficiently generate a high volume of ideas in an environment free from criticism and judgment. The basic brainstorming process includes the following steps: 1. 2. 3. 4. 5.

State the central brainstorming question or issue, determine agreement, and record the issue for the team to see. Ask each team member to give their ideas. No idea may be criticized. As ideas are generated, record each idea for the group to see. Continue steps 2 and 3 until all ideas are recorded. Review the list of ideas for clarity and to discard any duplicates.

Brainstorming allows all group members to participate equally and to expand their thinking about the problem's dimensions.  Participation and expanded thinking in turn broaden the spectrum of possible solutions.

254

Effort-Impact Technique

Six Sigma Black Belt | Project Management | Change Agent Concept: Effort-Impact Technique

The effort/impact technique is another conflict resolution and decision making tool.  It is used to prioritize proposed activities.  Each activity is placed in one of four categories, as seen in the following illustration:

255

Motivation Techniques

Six Sigma Black Belt | Project Management | Change Agent Concept: Motivation Techniques

People are the key to quality, but no two people are alike in their ability, motivation and persistence to perform.  Quality professionals can provide the systems, tools, and methods for quality improvement, but all employees must get on board for a quality improvement effort to be successful. Motivation can be defined as an emotion or desire within a person causing that person to act.  Managers need to understand employee motivation and needs to build and sustain employee enthusiasm.  If different or opposing outlooks surface, management must know how to help employees recognize common goals and work together to achieve them. To better understand employee motives, needs and goals, examine a few of the landmark motivational theories and studies.  Each of the studies and theories discussed in this section presents a slightly different perspective of human needs and how they collectively influence an employee's level, direction and persistence.

256

The Hawthorne Experiments

Six Sigma Black Belt | Project Management | Change Agent Concept: The Hawthorne Experiments

The roots of industrial motivational research in America date back to the period of 1924 to 1932.  During this time, experiments were conducted at the Western Electric Company Hawthorne plant in Cicero, a manufacturing division of AT&T. Management and behavioral scientists collaborated during the experiments to study the effects of various working conditions on productivity and quality.  Environmental lighting, the number of rest periods, the length of the workday and the time of day were some of the variables examined. The studies also included some unusual tactics, such as: • Conducting experiments with small groups of workers in simulated shop-floor conditions (rather than the entire population). • Discussing changes in advance with study participants. • Encouraging workers (relay assemblers) to work at a comfortable pace. Results of the Hawthorne experiments found that productivity increased and rejects decreased as favorable conditions were introduced (e.g., better lighting and shorter workdays).  But interestingly, the quality and productivity gains were sustained even after the workplace conditions returned to initial levels. Thus a classic finding of the Hawthorne experiments is that relay assemblers’ productivity increased under good conditions or poor.  The studies concluded that these gains were sustained regardless of the conditions because: • The individual worker’s needs were considered. • Workers were treated with dignity. The Hawthorne experiments demonstrated the benefits of an improved human relations atmosphere and management involvement in productivity and quality.

257

Abraham Maslow - Hierarchy of Needs

Six Sigma Black Belt | Project Management | Change Agent Concept: Abraham Maslow - Hierarchy of Needs

Abraham Maslow’s hierarchy of needs is one of the most widely cited theories of human motivation.  A pyramid configuration represents human needs, progressing from the most basic physiological needs to a stage Maslow calls self-actualization. Needs must be satisfied in order of priority, progressing from Stage One through Stage Five.  Physiological needs must be satisfied first, before the next level becomes dominant. As each level of need is satisfied, it loses its motivating power and the next higher level’s needs take precedence.  The highest level, self-actualization, is an exception to this process.  This need is considered insatiable, so it continues to be a motivator. Maslow believed that managers are responsible for creating a work environment in which employees can perform at the highest level. [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

258

David McClelland - Acquired Needs Theory

Six Sigma Black Belt | Project Management | Change Agent Concept: David McClelland - Acquired Needs Theory

David McClelland and colleagues identified three underlying needs believed to be important in understanding individual behavior. • Need for achievement: the desire to excel, solve problems and master complex tasks • Need for affiliation: the desire for harmonious relationships with other people • Need for power: the desire to control and influence other people to achieve individual goals or to achieve higher goals (for the greater good) McClelland maintained that these needs are acquired over time, based on life experiences.  For every person, one of these needs tends to be more dominant than the other two and thus has a greater effect on individual behavior. • Achievers prefer individual responsibilities and challenges.  They also appreciate feedback on their work and recognition of goal achievement. • Affiliation seekers are drawn to interpersonal relationships and opportunities for communication.  They tend to conform, shy away from standing out and seek approval rather than recognition of goal achievement. • Power seekers want agreement and compliance.  Attention, recognition and approval from others are secondary. McClelland’s theory is useful in linking individual needs to work tasks and preferences.  Additionally, success factors for various types of jobs can be identified and individuals can strive to acquire them.

259

Communication

Six Sigma Black Belt | Project Management | Change Agent Concept: Communication

Communication is the exchange of thoughts, messages or information by speech, signals or writing.  It has been described as the glue that holds an organization together.  Ongoing, reliable communication is essential for organizations.  Employees throughout the organization need the skills to communicate effectively in meetings and in one-on-one discussions. There are, however, many barriers to effective communication, including: • Frame of reference: Different individuals can interpret the same communication differently depending on previous experiences. • Selective listening: Individuals tend to block out new information especially if it conflicts with existing beliefs. • Value judgments: Individuals assign an overall worth to a message prior to receiving the entire message. • Source credibility: Individuals weigh the actions and words of the communicator based on the amount of trust, confidence and faith they have in that person. • Language and dialects: The same word may mean entirely different things to different people. • Filtering: Information is manipulated so that the receiver perceives it as positive (a common occurrence in upward communication). • Cultural differences: Different perspectives may lead to misperception and miscommunication. Questioning techniques and listening strategies are two powerful tools in overcoming communication barriers.

260

Questioning Techniques

Six Sigma Black Belt | Project Management | Change Agent Concept: Questioning Techniques

When you have determined the kind of information desired, the next step is deciding on the most appropriate questioning format.  The questioning format can be either open- or closed-ended, as described below: Type Open-ended questions

Closed-ended questions

Description • Ask for general information. • Find out what a person needs to know to begin formulating solutions. • Begin with words like how, why, or what. • Enhance communication and in the process: ° Save time. ° Reduce errors. ° Involve others in creating solutions or innovations. ° Strengthen relationships by demonstrating interest in resolving concerns. • Provide opportunities to meet and exceed expectations. • Have two purposes: to obtain specific information and to uncover needs. • Ask questions that can generally be answered with a yes, no or very brief response. • Are a preferred format for mail and convenience surveys.

Examples • How can I help you? • Why do you feel this would be the best approach? • What seems to be the source of the problem?

•

•

•

Have you experienced this problem before? Is this a training issue or a management issue? Please list the three factors with the greatest impact.

When considering a questioning technique, it is often more effective to begin with open-ended questions to get a “broad brush” understanding and then switch to closed-ended questions to target specific information.  This approach helps develop trust and reduce misgivings.

261

Listening Strategies

Six Sigma Black Belt | Project Management | Change Agent Concept: Listening Strategies

When you have asked a question, it is imperative that you listen carefully to the answer.  If the speaker gets the impression you’re not listening, it can compromise your credibility and cause your information source to become uncooperative. Listening behaviors can be one of two types: passive or active.

Passive listening Passive listening does not really qualify as listening.  Although the listener appears to be listening, in reality their attention is focused elsewhere. Unfortunately, with so many distractions at home and work, passive listening seems more the norm than active listening. As illustrated below, it takes concentration and discipline to focus on someone else’s communication needs. Here are typical barriers to active listening: • Presuming: The listener assumes they know what the speaker will say next and believes it is unnecessary to continue listening. • Distractions: The listener’s environment or inner thoughts prevent them from concentrating on the speaker’s message. • Rushing: The listener is in a hurry and does not want to take the time to listen to the speaker. • Interrupting: The listener continually interrupts the speaker and will not let the speaker continue with their line of thought. • Faking: The listener wants to maintain the outward appearance of listening and holds eye contact to be polite, but they are not focused on the speaker’s message. • Planning ahead: The listener gets interested in something in the first part of the message and stops listening to plan a response to that point. • Daydreaming: Weariness or preoccupation with other thoughts keep the listener from hearing the speaker’s message.

262

Listening Strategies Cont.

Six Sigma Black Belt | Project Management | Change Agent Concept: Listening Strategies Cont.

Active Listening Active listening means the listener is concentrating on the speaker’s message and attempting to understand what the speaker has to say.  This proves that the listener is dedicated to understanding the speaker's needs.  It also encourages the speaker to examine their needs and explain their thoughts.  Active listening has the following outcomes: • Saves time: Rather than trying to collect information through trial and error, the speaker can ask good questions, listen carefully to the response and get the necessary information efficiently. • Reduces misunderstandings: Misunderstandings occur because there is a breakdown somewhere in communication.  Active listening enhances communication and reduces misunderstandings. • Creates a climate of cooperation and trust: The speaker senses the listener's genuine interest in the situation and trusts the listener to help. Active listening is a powerful tool when used consistently.  Following a few simple guidelines will help you become a better listener and a more quality-focused professional: • Strive to understand the speaker before offering input. • Avoid barriers to active listening. • Demonstrate listening with verbal clues and eye contact. • Verify understanding by paraphrasing, clarifying or summarizing.

263

Assessment - Negotiation Techniques

Six Sigma Black Belt | Project Management | Change Agent Concept: Assessment - Negotiation Techniques

Read the following statements about negotiation techniques. Click True or False for each item. [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

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Six Sigma Black Belt Project Management Management and Planning Tools

Learning Objectives

Six Sigma Black Belt | Project Management | Management and Planning Tools Concept: Learning Objectives

At the end of this Project Management topic, all learners will be able to define, select and use management planning tools such as: • affinity diagrams. • interrelationship digraphs. • tree diagrams. • prioritization matrices. • matrix diagrams. • process decision program (PDPC) charts. • activity network diagrams (AND).       Portions of this topic were taken from the ASQ Six Sigma Green Belt web-based Certification Preparation Course.

266

Introduction

Six Sigma Black Belt | Project Management | Management and Planning Tools Concept: Introduction

In the 1970s, a Japanese team developed new tools in response to changes in quality technology. Known as "the 7M tools", these instruments are used by leading organizations throughout the world to improve decision making, communication, planning and implementation. As with any methodology, a tool's name varies from organization to organization. Some of these tools are new while others are refinements of predecessors. The 7M tools are: • Affinity diagrams • Interrelationship digraphs • Tree diagrams • Matrix diagrams • Prioritization matrices • Process decision program (PDPC) charts • Activity network diagrams While these tools help teams respond effectively to issues, do not expect to use all the tools in all projects. In addition, although these tools may be used during the planning stage of a Six Sigma project, it is recommended they be implemented whenever needed throughout the entire DMAIC process. Roll over Page Resources, click Flow of Management and Planning Tools to view a "typical" flow of the 7M tools from The Memory Jogger Plus+® Featuring the Seven Management and Planning Tools by Michael Brassard.

267

Affinity Diagrams

Six Sigma Black Belt | Project Management | Management and Planning Tools Concept: Affinity Diagrams

Developed by Dr. Kawakita Jiro in the 1960s to discover meaningful groups, the affinity diagram clarifies data by categorizing a large number of ideas based on their natural relationships.

Benefits • • • • • • •

Is a good tool for organizing information into categories Provides creative process and display Links ideas Adds structure to a complicated topic Stimulates critical thinking Helps organize unfamiliar ideas or problems Helps in the Six Sigma problem definition phase to scope the project objective

The following example of an affinity diagram refers to the process of making coffee.

268

Affinity Diagrams Cont.

Six Sigma Black Belt | Project Management | Management and Planning Tools Concept: Affinity Diagrams Cont.

Procedure 1. 2. 3. 4.

State the problem (issue). Brainstorm. Everyone records their ideas on sticky notes or cards. Gather all notes. Move notes into related ideas.  Loners may exist. • If a topic fits into two groups, make an extra copy. • Look to see if small sets should belong in a larger group. • Look to see if a larger group needs to be subdivided with cards for each.

5.

Sort the brainstormed list. Move ideas from the brainstormed list into affinity sets and create groups of related ideas. Determine headings for each group and write the header.

6.

Use When •

• • •

Confronting many disparate facts or ideas. Affinity diagrams are especially useful for organizing qualitative comments, such as those collected during the “Voice of the Customer” process Attempting to grasp a large, complex issue Refining brainstorm results into coherent outcomes Seeking group consensus

User Tips • •

Affinity diagrams are not necessary when the problem is simple.

•

Avoid list:2 ° Do not place the notes in any order. ° Do not determine categories or headings in advance. ° Do not talk during the writing phase and the first sorting phase. (This is hard for some people!) ° Do not have more than eight people working on an affinity diagram.

Do list:1 ° Write clearly. ° Wait until everyone is ready. ° Allow plenty of time for initial idea development. ° Use markers because regular pens are harder to read. ° If possible, post the randomly arranged notes in a public place and allow grouping to happen over several days.

_____ 1 Tague, The Quality Toolbox, 99. 2 Ibid.

269

Interrelationship Digraphs

Six Sigma Black Belt | Project Management | Management and Planning Tools Concept: Interrelationship Digraphs

As one of the 7M tools identified by Dr. Shigeru Mizuno, interrelationship digraphs show cause-and-effect relationships between factors, areas or processes. One item connects to other items to illustrate the effect of each on the other.

Benefits • • • • • •

Displays a goal divided into different levels. Maps interactions between ideas and factors. Encourages team members to think in multiple directions. Depicts a hierarchy of tasks and subtasks. Creates an analysis of natural links. Helps identify root causes.

270

Interrelationship Digraphs Cont.

Six Sigma Black Belt | Project Management | Management and Planning Tools Concept: Interrelationship Digraphs Cont.

Procedure 1. 2. 3. 4. 5.

Write a statement or issue to explore. Brainstorm ideas about the issue (write each idea on a card or note). Individually determine a relationship for each idea. Draw arrows showing influences (from the idea to its causes and influences). Analyze the diagram.  Count the arrows to and from each idea. a. b. c. d. e. f.

Write the total counts at the bottom of each idea. Key ideas are the ones with the most arrows. Note which ideas have primarily outgoing (from) arrows. These are causes. Note which ideas have primarily incoming (to) arrows. These are effects. Be sure to check whether ideas with fewer arrows are also key ideas. Draw bold lines around the key ideas.

Use When • •

• • • • •

Organizing related ideas. Attempting to understand links between ideas and cause-and-effect relationships. For example, a digraph can be useful when trying to identify the area of greatest impact for improvement.1 Analyzing a complex issue for causes.2 Problem-solving a complex situation. Linking intertwined causal relationships. Determining a final solution. Evaluating the relationship between ideas.

User Tips • • • • • • •

Affinity diagrams arrange ideas into groups; interrelationship digraphs attempt to define influences on each group. Group titles should be brought from the affinity diagram to the interrelationship digraph. Directional arrows should be used to encourage critical thinking. If in a large group, sticky notes or cards, a large paper surface, marking pens and tape should be used. A high number of outgoing arrows indicates a root cause, while a high number of incoming arrows indicates outcomes or results. The number of arrows is only an indicator, not an absolute rule. Interrelationship digraphs can be used to supplement cause-and-effect or fishbone diagrams.

_____ 1 Tague, The Quality Toolbox, 444. 2 Ibid.

271

Tree Diagrams

Six Sigma Black Belt | Project Management | Management and Planning Tools Concept: Tree Diagrams

Resembling a trunk with branches, tree diagrams are ordered structures for organizing information by importance and details. With the larger idea broken down into smaller components, the idea is easier to understand.

Benefits • • • • • • •

Provides a simple, highly effective method. Promotes step-by-step thinking. Graphically displays information. Helps members find information easily. Displays different levels of details. Allows members to expand their thinking and see links between concepts. Reveals the real level of complexity.

272

Tree Diagrams Cont.

Six Sigma Black Belt | Project Management | Management and Planning Tools Concept: Tree Diagrams Cont.

Procedure The following list is derived from The Quality Toolbox by Nancy R. Tague: 1. 2. 3. 4. 5. 6. 7.

Develop a statement of the goal, project, plan or problem being studied. Ask a question leading to the next level of detail. If dealing with a goal, identify the needs and tasks necessary to accomplish the goal. If dealing with a problem, identify the causes of or reasons for the problem. Brainstorm all possible answers. Check to see if all items are necessary. Make sure that the final list contains everything needed to accomplish the goal.

Use When* • • • • • • • • •

Moving an idea from broad generalities to specific details Developing an action plan to implement a solution Analyzing processes in detail Probing for the root cause of a problem Evaluating implementation issues Communicating information Examining key issues after using an affinity diagram or interrelationship digraph Serving as a problem-solving aid Showing a goal and what is needed to accomplish it

User Tips • • • • •

Before starting the tree, brainstorm. Orient the tree from left to right. Do not draw lines until the list of ideas is completed. Use information from a previously created affinity diagram or fishbone diagram to help complete the tree. Use the tree to develop goals, objectives and action plans.

* The above list is derived from The Quality Toolbox by Nancy R. Tague.

273

Prioritization Matrices

Six Sigma Black Belt | Project Management | Management and Planning Tools Concept: Prioritization Matrices

A prioritization matrix is a decision making tool using a systematic process to narrow choices. It is also one of the 7M tools for quality and a variation of an L-shaped matrix (discussed in Matrix Diagrams). A prioritization matrix allows raters to rank the options against pre-determined scales, weights and criteria to determine order of importance. A prioritization matrix is also known as a decision grid, selection matrix or grid, problem matrix, problem selection matrix, opportunity analysis, solution matrix, criteria rating form or criteria-based matrix.  

Benefits • • • •

Is simple to use. Forces analyzing. Displays information in a table format. Connects multiple ideas and causes.

274

Prioritization Matrices Cont.

Six Sigma Black Belt | Project Management | Management and Planning Tools Concept: Prioritization Matrices Cont.

Procedure 1. 2. 3. 4. 5. 6. 7. 8.

Generate the criteria for making the decision. Determine the weight of each criterion. Create an L-shaped matrix (discussed next in the Matrix Diagrams section) and list the choices by rows. Label the matrix column headings with the criteria and their relative weights. Have each member order the options according to each criterion. Ask each member to multiply their ranking by the criterion weight. For each option, have individuals add the option's score. Have the team leader add up the individual scores into a group score.

Use When • • • • • •

Prioritizing the variables with the greatest significance. Reaching consensus in small teams. Comparing a few options to specific standards. Narrowing a list of options to one choice. Making decisions based on multiple criteria (best when used for six to eight criteria). Selecting one product, approach, supplier, option or problem.

User Tips • • • •

Utilize prioritization matrices after reducing the options to a manageable number. Prioritization matrices can be applied in conjunction with a tree diagram. The higher the weight, the more important the criterion. The higher the total score, the more important the criterion.

275

Matrix Diagram

Six Sigma Black Belt | Project Management | Management and Planning Tools Concept: Matrix Diagram

By showing the relationship between two, three or four groups of information, matrix diagrams can reveal intelligence about the relationship, such as its strength, the roles played by various individuals or measurements.

Benefits • • • •

Is simple to use. Arranges information in a table format for easy use and display. Displays multiple connections and causes. Forces analysis.

The following is an example of an L-shaped matrix. Additional types of matrix diagrams are shown on the next page.

 

276

Matrix Diagram Cont.

Six Sigma Black Belt | Project Management | Management and Planning Tools Concept: Matrix Diagram Cont.

The illustration below provides a brief summary of when to use the different matrix diagrams, as determined by the number of groups and the type of relationships. Click See Example next to each diagram type to see an illustration and brief description of each. [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

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Matrix Diagram Cont.

Six Sigma Black Belt | Project Management | Management and Planning Tools Concept: Matrix Diagram Cont.

Procedure 1. 2. 3. 4. 5. 6.

Define the purpose of the diagram. Identify what sets of elements need to be included to meet the objective of the diagram. Assemble the best team to connect all the elements of the matrix. Select the matrix format. Choose and define the relationship symbols. Complete the diagram.

Use When • • • • • • • •

Exploring possible causes for a problem. Identifying who needs to be involved in a project. Prioritizing various problems. Identifying and analyzing the presence and strength of relationships. Explaining customer defects or complaints. Combining two tree diagrams into a single matrix. Selecting an option to pursue. Comparing the results of implementing a new process to the customer's stated needs.

User Tips • • • •

An L-shaped matrix is the most commonly used diagram. Matrix diagrams are good for selecting numerical weighting from provided options. Prioritization matrices follow the L-shaped format. Use matrix diagrams in conjunction with tree diagrams.

278

Process Decision Program Charts

Six Sigma Black Belt | Project Management | Management and Planning Tools Concept: Process Decision Program Charts

The process decision program chart (PDPC) is a diagram display for identifying risks and countermeasures. You can use the PDPC to anticipate what might go wrong and to develop countermeasures to offset those problems. The PDPC is therefore useful in steering events toward your desired goals.

Benefits • •

Helps quantify alternatives. Clarifies implications of alternatives.

279

Process Decision Program Charts Cont.

Six Sigma Black Belt | Project Management | Management and Planning Tools Concept: Process Decision Program Charts Cont.

Procedure The following list is derived from The Quality Toolbox by Nancy R. Tague: 1. 2.

Determine the activity flow for the plan. Construct a tree diagram by placing prerequisite activities in a time sequence: • Objective (first level) • Main activities (second level)

3. 4.

For each task, brainstorm what could go wrong (third level). Review all potential problems and eliminate any that are improbable or those with an insignificant consequence (fourth level). For each remaining potential problem, brainstorm possible countermeasures for either preventing the problem or applying a remedy after its occurrence (fifth level, as clouds or jagged lines). Discuss to decide the practicality of each countermeasure: • Criteria: cost, time required, ease of implementation, effectiveness • Mark impractical countermeasures with an X • Mark practical countermeasures with an O

5.

6.

Use When* • • • •

Implementing a complex plan or any new plan. Exploring the possible contingencies. A high price for failure exists. Implementing a plan with a time constraint.

User Tips • • •

Select team members close to the process or product. Use sticky notes on a large surface when mapping the flow of activities. Use a flip chart when brainstorming potential problems and countermeasures, then create a final PDPC.

* The above list is derived from The Quality Toolbox by Nancy R. Tague.

280

Activity Network Diagram

Six Sigma Black Belt | Project Management | Management and Planning Tools Concept: Activity Network Diagram

As introduced in the Planning Tools section of this lesson, activity network diagrams show the required order of tasks in a project or process, their interconnectivity, the best schedule for the entire project and any potential scheduling and resource problems with their solutions.

Benefits •

Displays: ° Total amount of time needed to complete the project ° Task sequence ° Concurrent tasks ° Critical tasks to monitor ° Task dependencies

•

Aids in determining the critical path method (CPM)

In the example above, the shaded boxes with dotted lines represent tasks that may not be required depending on the outcome of other tasks but still need to be planned. For example, based on the results of the software testing, modifications of software may or may not be required.

281

Activity Network Diagram Cont.

Six Sigma Black Belt | Project Management | Management and Planning Tools Concept: Activity Network Diagram Cont.

Procedure The following list is derived from The Quality Toolbox by Nancy R. Tague: 1. 2. 3.

List all the necessary tasks in the project or process. Determine the first task and place it on the left side. Determine the correct sequence of the tasks: • Which tasks must happen before this one can begin? • Which tasks can be done at the same time as this one? (Place these cards vertically above or below the first job card.) • Which tasks should happen immediately after this one? (Place the card to the right of the first card.) ° Note: It can be useful to create a table with four columns: prior task(s), this task, simultaneous task(s), and following tasks.

4. 5.

Identify the next task and place the card to the right of the first card. Determine the tasks that can be done at the same time as this task and place the cards vertically above or below. Repeat this procedure until all the cards are in sequence or parallel. Diagram the network of tasks by arranging the cards in sequence on a large piece of paper. • Time should flow from left to right and concurrent tasks should align vertically. • Leave space between the cards.

6. 7.

8.

Between each task, draw circles for "events." An event marks the beginning or end of a task. Thus, events are the nodes that separate tasks.

Use When* • • •

Scheduling, assigning and monitoring tasks within a complex project or process. A project schedule is critical, with serious consequences for completing the project late or significant advantages of completing the project early. You know the steps of the project or process, their sequence and how long each step takes.

User Tips • •

Use sticky notes or cards on a large surface. Draw extra events to separate tasks that stop and start with the same event.

* The above list is derived from The Quality Toolbox by Nancy R. Tague.

282

Planning Tools Pyramid Game

Six Sigma Black Belt | Project Management | Management and Planning Tools Concept: Planning Tools Pyramid Game

[ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

283

Lesson Summary

Six Sigma Black Belt | Project Management Concept: Lesson Summary

Project management is a crucial part of the DMAIC process. Many tools, techniques and concepts were introduced in this lesson. Although project planning is primarily the focus at the beginning of the DMAIC process, the elements of the project management discipline can be practiced to some extent in each of the phases to keep the project moving. Proper planning and management is the foundation that will support the project through to completion. Project charter The project charter is a written commitment approved by management, stating the scope of authority for an improvement project.  It is recognized by all parties involved in the project. Once published, it provides powerful communication about the project to the entire team. At the same time, a charter is a “living” document, constantly being reviewed and updated to reflect additional relevant data as it becomes known. Team leadership Effective team leadership involves initiating teams and clearly defining purpose, goals, ground rules, roles and responsibilities. Selecting the right people for the team is also very important; make sure the team is composed of the right combination of process expertise, commitment and motivation for improvement.  Team dynamics and performance It is essential to understand team dynamics and performance. There are many techniques for building and maintaining a strong, productive team. Being able to facilitate valuable discussion is crucial. Providing the team with the tools to make decisions is also important. Change agent A change agent is an individual from inside or outside an organization who facilitates change within the organization.  Change agents must be proactive by anticipating roadblocks. They must prepare for such roadblocks by setting up proper communication plans and helping the organization see why change is necessary. Change agents must also be skilled in negotiation, conflict resolution and motivation techniques to keep the team on track. Management and planning tools Selecting the appropriate management and planning tools during the planning process and using them throughout the DMAIC process is also very important to ensure the success of the Six Sigma project. Roll over Page Resources to view a comprehensive matrix of the planning and estimation tools discussed in this lesson. Again, keep in mind that project management is not only vital in the beginning of a project but throughout the project life cycle as well.

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Planning and Estimation Tools Matrix

Six Sigma Black Belt | Project Management | Lesson Summary Example: Planning and Estimation Tools Matrix

Planning Tools Tool Gantt

Advantages

Disadvantages • • •

•

• Simple to understand Easy to modify The least complex means of • portraying progress (or lack of it) Easily expanded to identify specific elements that are either behind or ahead of • schedule

 

•

CPM

•

•

•

•

PERT

•

•

•

Interdependencies and problem areas that might not be obvious by other planning methods are revealed Project managers can determine the probability of meeting specified deadlines through the development of alternative plan Project managers can evaluate the effect of changes in the program A large amount of sophisticated data can be presented in a well-organized diagram from which the project team and the customer can make joint decisions Determine where the greatest effort should be made for a project to stay on schedule Allows project managers to determine the probability of meeting specified deadlines by development of alternative plans Evaluates the effect of deviations in project resources, performance

285

  • •

•

•

•

• •

•

Provide only vague descriptions of how projects function or react as a system Do not show interdependencies of project activities; therefore, they do not represent a network of activities Cannot show the results of either an early or a late start in project activities; therefore the project team has no idea what the impact of slippage in one element of the project has on another or how that slippage affects the project completion date Do not show any uncertainty involved in the performance of project activities; that is, what is the longest, shortest, or average time required to complete the activity These techniques are timeand labor-intensive Even when using available software packages, these techniques can be complicated to implement These techniques are expensive to set up and maintain because there are so many data requirements. They may require and consequently display more detail than is necessary or desirable.

The complexity adds to project implementation problems and increases overall data requirements Time- and labor-intensive effort is required Upper-level management decision-making ability is reduced There exists a lack of functional ownership in estimates

Planning and Estimation Tools Matrix

Six Sigma Black Belt | Project Management | Lesson Summary Example: Planning and Estimation Tools Matrix

•

Activity Network Diagram

•

•

• expectations, and required time Allows data to be presented in a well-organized diagram • from which both the contractor and customer can • make joint decisions

There exists a lack of historical data for time-cost estimates The assumption of unlimited resources may be inappropriate There may exist the need for too much detail

Allows users to transform a • complex planning task into a simplified schedule for fulfilling a plan or tracking results Useful when planning a complex project or process with interrelated tasks and resources

The user must know the steps of a project or process, the sequence, and how long each step takes

286

Lesson Bibliography

Six Sigma Black Belt | Project Management Concept: Lesson Bibliography

American Society for Quality. ASQ's Foundations in Quality Learning Series: Certified Quality Engineer. Milwaukee, WI: ASQ, 2000. American Society for Quality. ASQ’s Foundations in Quality Learning Series: Certified Manager of Quality/Organizational Excellence. Milwaukee, WI: ASQ, 2005. American Society for Quality. Six Sigma Green Belt Certification Preparation Course, Version 1 (web-based course). Milwaukee, WI, 2006. Benbow, Donald W. and T.M. Kubiak. The Certified Six Sigma Black Belt Handbook. Milwaukee, WI: ASQ Quality Press, 2005. Brassard, Michael. The Memory Jogger Plus+®: Featuring the Seven Management and Planning Tools. rev. ed. Salem, NH: GOAL/QPC, 1996. Hutton, David W. The Change Agents' Handbook. Milwaukee, WI: ASQ Quality Press, 1994. Pries, Kim H.Six Sigma for the Next Millennium: A CSSBB Guidebook. Milwaukee, WI: ASQ Quality Press, 2006. Scholtes, Peter R., Brian L. Joiner, and Barbara J. Streibel. The Team Handbook. 3rd ed. Madison, WI: Oriel Incorporated, 2003. Tague, Nancy R. The Quality Toolbox. 2nd ed. Milwaukee, WI: ASQ Quality Press, 2005.

287

Six Sigma Black Belt Define

Lesson Introduction

Six Sigma Black Belt | Define Introduction: Lesson Introduction

The purpose of the Define phase of the DMAIC methodology is to identify an improvement project that is valuable enough to dedicate time, money, and resources to accomplish. Once this phase is completed, the value has been established, the project is defined and the resources can be allocated. Significant time and effort must be placed on the Define phase. Teams have been known to fail, stall, or cycle back to Define because they were not diligent in this phase. To better understand this concept, the ASQ Body of Knowledge provides the following topics: Project scope • Determine project definition/scope using Pareto charts and top-level (macro) process maps. Metrics • Establish primary and consequential metrics (e.g., quality, cycle time, cost). Problem Statement • Develop a problem statement, including baseline and improvement goals.  

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Lesson Overview

Six Sigma Black Belt | Define Introduction: Lesson Overview

The tools and objectives of the Define phase are illustrated below.

 

290

Six Sigma Black Belt Define Project Scope

Learning Objectives

Six Sigma Black Belt | Define | Project Scope Concept: Learning Objectives

At the end of this Define topic, all learners will be able to determine project definition/scope using Pareto charts and top-level (macro) process maps.               Portions of this topic were taken from the ASQ Six Sigma Green Belt web-based Certification Preparation Course.

292

Introduction

Six Sigma Black Belt | Define | Project Scope Concept: Introduction

As introduced in the Project Management lesson, the project scope defines the specific aspects of the problem that will be addressed. Project scope is another component of the project charter. To develop the project scope, various tools are used. This lesson will concentrate on two of these tools: Pareto charts and process mapping. A third tool, "in scope/out of scope" will also be demonstrated.

293

Pareto Charts

Six Sigma Black Belt | Define | Project Scope Concept: Pareto Charts

Created by Vilfredo Pareto, an Italian economist, Pareto charts graphically display how different categories of failure contribute to an issue. Later popularized by Dr. Joseph Juran, Pareto's principle and chart are used to depict the concepts of "the vital few" and the "trivial many."

Concept The Pareto principle states that 80% of the problems come from 20% of the causes (the 80/20 rule). The Pareto chart visually depicts the most significant of these situations: • 80% of interruptions come from the same 20% of the people. • 80% of staff problems come from 20% of the staff. • 80% of a nurse's time is spent with 20% of the patients.

Features • •

Bar graphs display frequency or cost with bars arranged from high (longest) on the left to low (shortest) on the right. Line graphs display the cumulative percentage of individual issues from the highest to the lowest.

Benefits • • •

Focuses on the highest impact causes Displays relative significance Breaks the problem into identifiable components

294

Pareto Charts Cont.

Six Sigma Black Belt | Define | Project Scope Concept: Pareto Charts Cont.

Procedure 1.

2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

Decide the categories, measurements and time period involved. Note: Pareto categories must be unambiguous or mutually exclusive. An item can only fit into one category or else the Pareto becomes invalid. Collect the data. Order the data (high to low). Label the left vertical axis for the frequency or cost. Plot and label the bars (tallest on the left, shortest on the right). Label the right vertical axis as percentage. Calculate the percentage for each category (the category total divided by the total for all categories, multiplied by 100). Calculate the cumulative percentage. Start with the highest, then add the second bar's percentage (record), then the third (record), and so on. Plot the first point (highest percentage). Plot the appropriate cumulative percentage above each of the corresponding bars. Continue the process for all bars. Connect the dots to form a line graph. Add a title, legend, and date.

Use When • • • • •

Analyzing the causes or frequency of problems in a process. Focusing on the most significant critical issue(s). Prioritizing problems. Analyzing the before and after impact of changes (by comparing before and after Pareto charts). Communicating data to others.

295

Pareto Charts Cont.

Six Sigma Black Belt | Define | Project Scope Concept: Pareto Charts Cont.

User Tips • • • •

Look for the point where the line's slope begins to flatten. Factors under the steepest curve are the most important. If the change in the slope is not clear, identify the factors making up at least 60% of the problem. If the bars are all similar sizes or when more than half of the categories are needed to reach the necessary 60%, try breaking the categories down differently.

As previously covered, Pareto charts help identify the most critical issues to study. By relying on the Pareto principle's guideline of 80% of the problems coming from 20% of the causes, you will be able to differentiates the vital few from the trivial many. Often it is more cost effective to take the biggest problem (largest Pareto bar) as a top priority project and dissect it into smaller projects than it is to generate several projects out of the lesser prioritized problems (smaller Pareto bars).

296

Nested Pareto Charts

Six Sigma Black Belt | Define | Project Scope Concept: Nested Pareto Charts

Once the initial Pareto chart has been completed, it is sometimes useful to create a secondary or nested Pareto chart to further analyze the data that make up the top categories. As demonstrated by the chart above, the biggest complaints stem from quality certificate errors. To analyze this further and narrow the project's scope, a nested (or secondary) Pareto chart could be created. In this case, the specific types of quality certificate errors would be gathered and charted as shown in the graphic below.  

297

Nested Pareto Charts

Six Sigma Black Belt | Define | Project Scope Concept: Nested Pareto Charts

 

298

Weighted Pareto Charts

Six Sigma Black Belt | Define | Project Scope Concept: Weighted Pareto Charts

According to The Quality Toolbox, Second Edition by Nancy R. Tague, "In a weighted Pareto chart, each category is assigned a weight, which lengthens or shortens the bars. This reflects the relative importance or cost of each category." Tague states that weighted Pareto charts are used when: " • • • "

A Pareto analysis is appropriate The categories do not result in equal cost or pain to the organization There are more opportunities for one category to occur than another

Before creating a weighted Pareto chart, each category must be given a weight of importance. Using the example from the previous page, it was determined that legal issues are of greatest concern, therefore recall notification errors should be weighted the highest. This category, along with the others, was given the appropriate weight then multiplied by the number of occurrences to determine the final weighted value. Type of Certificate Error

Weight

# of Occurrences

Weighted Value

Recall Notification Errors

5

2

10

Incorrect Product Number

2

4

8

Incorrect Model Number

3

2

6

Incorrect Warranty Expiration Date

1

1

1

Incorrect Customer Information

0.5

9

4.5

Once the weighted value have been calculated, use the procedures for creating a Pareto chart as shown in the graphic below:

Roll over Page Resources for an opportunity to practice creating Pareto charts.

299

Pareto Chart Practice

Six Sigma Black Belt | Define | Project Scope | Weighted Pareto Charts Example: Pareto Chart Practice

Materials Needed • graph paper • calculator Description RF Toys produces a toy dart gun. Concerned about the number of products returned to various stores, the quality improvement specialist gathers the following data about customer returns: Gun won't cock

4

Missing pieces

7

Split dart

8

Tip off the dart

27

Trigger won't release

4

Task Draw a Pareto chart displaying this data. When completed, roll over Page Resources at the bottom of the screen and click Pareto Answer to see if you are correct.

300

Pareto Answer

Six Sigma Black Belt | Define | Project Scope | Weighted Pareto Charts Example: Pareto Answer

 

301

Top-Level Process Maps

Six Sigma Black Belt | Define | Project Scope Concept: Top-Level Process Maps

As you will learn in the Measure lesson, process maps display the separate steps of any series of activities that produce an outcome. Steps are in sequential order and include inputs and outputs, required decisions, people involved, time at each step and other measurements. Detailed process maps are useful when analyzing potential causes of problems and preparing action plans to improve existing processes or develop new processes. In contrast, the top-level process map (sometimes referred to as "the 30,000-foot overview") shows only the major steps of the process. The top-level process map is useful in scoping process improvement projects and establishing boundaries. Top-level process maps are also referred to as a high-level flow chart or macro process map.

Benefits • • • •

Visually represents how the process works Improves process understanding Identifies process boundaries Allows all team members to view the process in the same light

302

Top-Level Process Maps Cont.

Six Sigma Black Belt | Define | Project Scope Concept: Top-Level Process Maps Cont.

Procedure 1. 2. 3. 4.

Define (identify) the process. List 6 to 8 major activities involved in the process. Arrange activities in the proper sequence. Draw arrows to show the flow.

Use When • •

Communicating or trying to understand the major steps in a process (the "big-picture"). Preparing to draw a more detailed flowchart.

User Tips • •

If there are more than 8 steps, there is the danger of including too much detail for a broad overview. Decisions, delays and recycle loops are details usually not shown on a top-level process map.

   

303

SIPOC

Six Sigma Black Belt | Define | Project Scope Concept: SIPOC

Often, project teams will complete a SIPOC (Suppliers, Inputs, Process, Outputs and Customers) diagram in conjunction with a top-level process map. A SIPOC diagram identifies the process activities, key inputs, outputs, customers and stakeholders. As mentioned earlier, when mapping the process, only the 6 to 8 major steps should be shown at this stage. Here is an example of a SIPOC diagram:

304

In Scope - Out of Scope Tool

Six Sigma Black Belt | Define | Project Scope Concept: In Scope - Out of Scope Tool

Another tool that can be used to determine project scope is the in scope/out of scope tool. Based on the outcome of other tools used, team members can brainstorm possible ways to help narrow the scope.

Procedure 1. 2. 3. 4. 5.

Have team members brainstorm specific items to include or not include in the overall project scope. Have team members write the items on sticky notes. Team members discuss the items and determine whether each is in or out of scope. Using a template, team members place sticky notes in appropriate categories. Add the resulting in scope items to the project charter.

[ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

305

Six Sigma Black Belt Define Metrics

Learning Objectives

Six Sigma Black Belt | Define | Metrics Concept: Learning Objectives

At the end of this Define topic, all learners will be able to establish primary and consequential metrics (e.g., quality, cycle time, cost).

307

Primary and Consequential Metrics

Six Sigma Black Belt | Define | Metrics Concept: Primary and Consequential Metrics

Once the top-level process map or SIPOC has been completed, the next step is to determine the outputs or elements of the processes that are most important to the customer and which would have the biggest impact if improved. At this stage, primary and consequential metrics should be defined and later calculated within the Measure phase. Primary metrics, also called "process metrics," are the metrics Six Sigma practitioners can most influence. Primary metrics are: • almost always the direct output characteristic of a process. • a measure of a process outcome, but not a financial goal or business objective. • frequently focused on quality, cycle time and cost. • derived from the project stakeholders, including internal customers, external customers and suppliers. Consequential metrics, also called "secondary metrics," can be either business or process metrics, and are derived from or are a result of the primary metric. In any given project, there may be one primary metric or multiple consequential metrics for improving one process. Where there is one primary metric, secondary or consequential metrics are needed to assure that improving the primary metric does not degrade other critical metrics (e.g., reducing a primary metric of cost but at the consequence of degrading secondary metrics of quality or cycle time).

308

Examples

Six Sigma Black Belt | Define | Metrics Concept: Examples

Using the SIPOC diagram from earlier in the lesson, our primary metrics might include: • accuracy of the order (quality). • timeliness of order processing (cycle time). • accuracy and timeliness of inventory database (quality and cycle time). • cost of reworking the order (cost). • cost of IT having to update database (cost). • cost of customer canceling order (cost). Consequential metrics might include: • return on sales as represented by a change in the volume of customer orders. • overall number and level of customer complaints.

As metrics are defined, always look back to the Voice of the Customer (VOC) determinations (discussed in the Business Process Management lesson) to ensure you are selecting measurements that will have an impact on quality and are meaningful to the customer.

309

Six Sigma Black Belt Define Problem Statement

Learning Objectives

Six Sigma Black Belt | Define | Problem Statement Concept: Learning Objectives

At the end of this Define topic, all learners will be able to develop a problem statement, including baseline and improvement goals.                 Portions of this topic were taken from the ASQ Six Sigma Green Belt web-based Certification Preparation Course.

311

Problem Statement

Six Sigma Black Belt | Define | Problem Statement Concept: Problem Statement

A problem statement details the issue the project team wants to improve. The problem statement should be specific and based on data that describes the issue's current state. The problem statement should not include the proposed solution.

Purpose • •

Problem statements focus the team on a process deficiency, thus controlling the scope of the project. Problem statements also communicates the significance of the process deficiency to others.

  Poorly-Written Problem Statements

Well-Written Problem Statements

There are too many customer returns. The housewares department return rate is 17%.

In 2005, the big ticket return rate was 17%, representing $15 million in returns. This was 7% higher than the target objective or goal for the division.

There are too many incorrect customer invoices. We must reduce incorrect invoices by 15%.

In the 4th quarter, 20% of all customer invoices were incorrect. This was an increase of 5% from 3 rd quarter.

 

312

Problem Statement Practice

Six Sigma Black Belt | Define | Problem Statement Concept: Problem Statement Practice

For each of the problem statements below, determine whether they are poorly-written or well-written. Please select "good" for well-written statements, and "bad" for poorly-written statements. [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

313

Goal Setting

Six Sigma Black Belt | Define | Problem Statement Concept: Goal Setting

As first introduced in the Project Management lesson, the Goal statement should specifically outline what you hope to achieve at the end of the project. Setting goals is an important part of the Define stage that must be completed before moving on to the Measure phase. Goals should: • Be carefully thought out and expressed. • Specify how completing the project will lead to improvements over the status quo. You should be able to clearly describe the outcomes, deliverables and benefits to stakeholders and customers. • Provide the criteria you need to evaluate the success of the project in terms of time, costs, and resources. • Be reviewed by the core team, which must reach consensus before moving to the next phase of the project. The acronym frequently used to assess whether a project's goals are "good" is SMART: Specific, Measurable, Attainable, Relevant, Time-Bound. These concepts are illustrated below:

Poorly-Written Goal

Well-Written Goal

Our goal is to reduce complaints by 50%.

Within the next six months, our goal is to reduce customer complaints due to invoicing errors by 25% in order to meet customer satisfaction goals.

314

Goal Setting Practice

Six Sigma Black Belt | Define | Problem Statement Concept: Goal Setting Practice

Use the SMART criteria to identify which element(s), if any, are missing from the following goal statements. When complete, roll over Page Resources, and click SMART Answers to view the missing SMART elements. 1. 2. 3. 4. 5. 6.

Reduce credit card resolution time by 75% in 2 weeks. Improve the meeting room scheduling process. Reduce failed installations by 30%. Improve profitability. Reduce late and early appliance deliveries within 6 months of the project kick off date. Decrease costs by end of year.

315

SMART Answers

Six Sigma Black Belt | Define | Problem Statement | Goal Setting Practice Example: SMART Answers

Goal Setting Answers 1. 2. 3. 4. 5. 6.

Reduce credit card resolution time by 75% in 2 weeks. (not attainable) Improve the meeting room scheduling process. (not relevant) Reduce failed installs by 30% (not time bound) Improve profitability. (not specific, not time bound, don't know if it's attainable because we don't have enough info) Reduce late and early appliance deliveries within 6 months of the project kick off date. (not measurable, by what percent?) Decrease costs by end of year. (not specific)

316

Define Review

Six Sigma Black Belt | Define Summary: Define Review

[ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

317

Lesson Summary

Six Sigma Black Belt | Define Summary: Lesson Summary

The purpose of the Define phase is to: • establish the specific Six Sigma project scope and boundaries. • define the specific business problem. • describe the business process needing improvement. • state the goals to be achieved. As introduced in the Project Management lesson, these goals are largely accomplished through the writing of the project charter.  The charter contains the problem statement, all team members' responsibilities and the scope of the project. As you complete the Define phase, you will use tools such as Pareto charts, top-level process mapping, SIPOC, and the in scope/out of scope tool. Additionally, you will determine primary and consequential metrics, learn how to correctly define the problem statement and create goals using the SMART elements. The second phase of the DMAIC process is Measure. The Measure lesson will further explain how to apply tools described in the Define phase, along with how to calculate statistical measures.

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Lesson Bibliography

Six Sigma Black Belt | Define Concept: Lesson Bibliography

American Society for Quality. Six Sigma Green Belt Certification Preparation Course, Version 1 (web-based course). Milwaukee, WI, 2006. Tague, Nancy R. The Quality Toolbox, 2nd ed. Milwaukee, WI: ASQ Quality Press, 2005.

319

Six Sigma Black Belt Measure

Lesson Introduction

Six Sigma Black Belt | Measure Introduction: Lesson Introduction

According to the ASQ Glossary, measure is the criteria, metric or means to which a comparison is made with output. Measure is the phase that quantifies the levels of quality desired and currently produced within the selected process. The Measure phase is typically characterized by the development of a detailed process map that clearly defines the interrelated work activities subject to the improvement effort. These work activities are characterized by a set of specific inputs and value-added tasks that comprise a procedure. To better understand this concept, the ASQ Body of Knowledge provides the following topics: Process analysis and documentation • Develop and review process maps, written procedures, work instructions and flowcharts. • Identify process input variables and process output variables, and document their relationships through cause and effect diagrams and relational matrices. Probability and statistics • Distinguish between enumerative (descriptive) and analytical (inferential) studies, and distinguish between a population parameter and a sample statistic. • Define the central limit theorem and understand its significance in the application of inferential statistics for confidence intervals and control charts. • Describe and apply concepts such as independence, mutually exclusive, multiplication rules, complementary probability and joint occurrence of events. Collecting and summarizing data • Identify, define, classify and compare continuous (variables) and discrete (attributes) data and recognize.opportunities to convert attributes data to variables measures. • Define and apply nominal, ordinal, interval and ratio measurement scales. • Define and apply methods for collecting data such as check sheets, coding data and automatic gauging. • Define and apply techniques for assuring data accuracy and integrity such as random sampling, stratified sampling and sample homogeneity. • Define, compute and interpret measures of dispersion and central tendency, and construct and interpret frequency distributions and cumulative frequency distributions. • Depict relationships by constructing, applying and interpreting diagrams and charts such as stem-and-leaf plots, box-and-whisker plots, run charts and scatter diagrams. Depict distributions by constructing, applying and interpreting diagrams such as histograms, normal probability plots and Weibull plots. Properties and applications of probability distributions • Describe and apply the following distributions commonly used by Black Belts: binomial, Poisson, normal, chi-square, Student's t and F distributions. • Recognize when and how to use the following, less frequently used distributions: hypergeometric, bivariate, exponential, lognormal and Weibull. Measurement systems • Describe and review measurement methods such as attribute screens, gauge blocks, calipers, micrometers, optical comparators, tensile strength and titration.

321

Lesson Introduction

Six Sigma Black Belt | Measure Introduction: Lesson Introduction

•

•

Calculate, analyze and interpret measurement system capability using repeatability and reproducibility, measurement correlation, bias, linearity, percent agreement, precision/tolerance (P/T), precision/total variation (P/TV), and use both ANOVA and control chart methods for non-destructive, destructive and attribute systems. Understand traceability to calibration standards, measurement error, calibration systems, control and integrity of standards and measurement devices.

Analyzing process capability • Identify, describe and apply the elements of designing and conducting process capability studies, including identifying characteristics, identifying specifications and tolerances, developing sampling plans, and verifying stability and normality. • Distinguish between natural process limits and specification limits, and calculate process performance metrics such as percent defective. • Define, select and calculate Cp and Cpk, and assess process capability. • Define, select, and calculate Pp, Ppk, Cpm, and assess process performance. •

• •

Understand the assumptions and conventions appropriate when only short-term data are collected and when only attributes data are available; understand the changes in relationships that occur when long-term data are used; interpret relationships between long-term and short-term capability as it relates to technology and/or control problems. Understand the cause of non-normal data and determine when it is appropriate to transform. Compute sigma level and understand its relationship to Ppk.

322

Lesson Overview

Six Sigma Black Belt | Measure Introduction: Lesson Overview

The tools and objectives of the Measure phase are illustrated below.

 

323

Six Sigma Black Belt Measure Process Analysis and Documentation

Learning Objectives

Six Sigma Black Belt | Measure | Process Analysis and Documentation Concept: Learning Objectives

At the end of this Measure topic, all learners will be able to: • develop and review: ° ° ° ° • •

process maps. written procedures. work instructions. flowcharts.

identify process input variables and process output variables. document input and output relationships through cause-and-effect diagrams and relational matrices.

325

Introduction to Documentation

Six Sigma Black Belt | Measure | Process Analysis and Documentation Concept: Introduction to Documentation

One of the first steps in analyzing a process is to determine the current process. Start by reviewing all supporting documentation and examining the various levels of documentation available as part of process analysis. The need for a quality documentation system spans a variety of applications such as but not limited to: • Assurance of quality in products shipped to customers • Fulfillment of contractual and regulatory requirements • Adequate defense in liability cases • Benchmark data • Data to ensure that the organization is properly responsive to needed improvements • Product performance data • Documentation of quality costs Organizations need to approach the mass of quality data from a systems perspective. A typical hierarchy of quality system documentation is shown below. [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

326

Process Analysis Using Documentation

Six Sigma Black Belt | Measure | Process Analysis and Documentation Concept: Process Analysis Using Documentation

The project team should review documentation including any flowcharts, specs, standards and guidelines that describe the process under consideration. Although sometimes lacking specific details, flowcharts describe the process at a general level. These flowcharts may conceptualize the entire operation and the individual steps within the operation. On the other hand, written procedures and task instructions provide step-by-step details helpful in analyzing the process. Examining written documentation helps clarify the current condition and may provide clues to possible quality issues. To start process analysis using written documentation: 1. 2. 3. 4.

Obtain a copy of the written procedures, task instructions or flowcharts. Study the written procedures. Construct a basic process map to display the actions. Use this information as you continue process analysis.

 

327

Process Map

Six Sigma Black Belt | Measure | Process Analysis and Documentation Concept: Process Map

A process map uses a flowchart as a graphical means of depicting process structure, visually defining the separate steps of any process. Steps are in sequential order and typically include inputs and outputs, required decisions, the people involved, time at each step, and/or measurements. The process map might document a combination of looking at current operating procedures, analysis on these, and developing new processes. And if available, they should be mapped to current document procedures. The image below represents a simple process map.  

328

Process Maps and Flowcharts

Six Sigma Black Belt | Measure | Process Analysis and Documentation Concept: Process Maps and Flowcharts

Symbols are used to define certain types of steps in a flowchart: rectangles for most steps and diamonds for decisions. Roll over the Page Resources link at the bottom of the page for a list of flowchart symbols. A sample process flowchart is shown below. Each symbol on the map can have additional information added to it such as inputs and outputs. To see an example of the inputs and outputs of a step in the process flowchart, roll over the step indicated in the image below. [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

329

Flowchart Symbols

Six Sigma Black Belt | Measure | Process Analysis and Documentation | Process Maps and Flowcharts Example: Flowchart Symbols

 

330

Benefits of a Process Map

Six Sigma Black Belt | Measure | Process Analysis and Documentation Concept: Benefits of a Process Map

A well-developed process map yields several benefits: • Visually represents how the process works • Supports the identification of disconnects and non-value-added steps • Helps the team better understand the process • Enables the discovery of problems or miscommunications • Helps define the boundaries of the process • Identifies process inputs and outputs • Assists in recognition of process bottlenecks and opportunities for improvement Process maps also serve functions in other phases of DMAIC: • Improve: Define and communicate the proposed changes to the process • Control: Document the revised process

331

Creating Process Maps

Six Sigma Black Belt | Measure | Process Analysis and Documentation Concept: Creating Process Maps

Procedure Materials needed: yellow sticky notes, notecards or flipchart paper; marking pens 1. 2. 3. 4. 5. 6.

Define (identify) the process. Brainstorm the activities involved in the process. Arrange the activities in proper sequence. Determine inputs and outputs. Identify time lags and non-value-added steps. Once the sequence is agreed upon, draw arrows to show the flow.

Use When • • • •

Developing an understanding of the steps in a process. Studying a process for improvement. Communicating how the process works. Documenting a process.

User Tips • • • •

Focus on identifying the process before worrying about correctly drawing the process map. Focus on those areas that appear complex with an excessive number of potential decision points or delays. Look for duplication, redundancy, complexity or too many “handoffs” in the process. Ask the following types of questions: ° Why are we performing the task in this manner? ° Does the current process deviate from the designed process? Why? ° What are the value-added activities? ° What are the non-value-added activities? ° How much time, money or work hours are required for each task? These may be the outputs (Ys) of the steps in the process.  

332

Inputs and Outputs

Six Sigma Black Belt | Measure | Process Analysis and Documentation Concept: Inputs and Outputs

Inputs (Xs) are causes (independent variables) that contribute to specific outputs (Ys) or effects (dependent variables). Not only are inputs and outputs important to sequential processes in an operation, they are also important to consider from a supplier-to-customer perspective. • Do I know the external customer requirements for this process? • Do I know the internal customer requirements if they, in fact, exist? If the process map is expanded beyond inputs-process-outputs, then the supplier and customer perspectives can be added forming the acronym SIPOC. SIPOC (Suppliers, Inputs, Process, Outputs, Customers) assists in capturing key links between suppliers, inputs, the process, outputs and customers, as discussed in the Define lesson of this course. Gathering measurable data from all parts of the chain allows an organization to provide feedback for process improvement. Roll over Page Resources and click SIPOC Diagram to view an example.

333

SIPOC Diagram

Six Sigma Black Belt | Measure | Process Analysis and Documentation | Inputs and Outputs Example: SIPOC Diagram

Purpose SIPOC (suppliers, inputs, process, outputs, customers) is a tool for identifying all elements involved in a process improvement project.

Procedure 1. 2. 3. 4. 5.

Identify the steps. Identify the outputs of the process. Identify the customers who will receive the outputs of the process. Identify the inputs needed by the process. Identify the supplies of the required inputs.

   

334

Working with Inputs and Outputs

Six Sigma Black Belt | Measure | Process Analysis and Documentation Concept: Working with Inputs and Outputs

All work is a process and everyone is someone's supplier and someone's customer. Once a process map has been defined with inputs (Xs) and outputs (Ys), be sure to: 1.

2.

identify all Xs and ensure that none were missed. A cause-and-effect diagram will help identify what else needs to be included. This tool is covered later in this lesson. include all the Xs at this point in your project. Relational matrices, covered later in this lesson, are tools we use to help identify which Xs are vital by numerical assessment ranking.

Every process consists of inputs and outputs. All inputs and outputs have a measurable value. Generally, inputs follow the "6 Ms": Methods, Machines, Manpower, Materials, Measurement and Mother Nature. Note: The "6 Ms" are discussed in more detail later in this lesson.

335

Cause-and-Effect Diagram

Six Sigma Black Belt | Measure | Process Analysis and Documentation Concept: Cause-and-Effect Diagram

Created by Kaoru Ishikawa, cause-and-effect or fishbone diagrams are problem-analysis tools for identifying, sorting and displaying as many causes as possible for an effect or problem. To this end, a cause-and-effect diagram may be used to identify additional inputs for a process. The fishbone diagram is sometimes referred to as the Ishikawa diagram

Benefits • • • • •

Sorts the ideas into useful categories. Breaks down ideas into smaller chunks. Shows the interaction between various causes. Encourages group participation. Helps identify areas to collect data for further study.

 

336

Using Cause-and-Effect Diagrams

Six Sigma Black Belt | Measure | Process Analysis and Documentation Concept: Using Cause-and-Effect Diagrams

Choosing Categories Categories will differ based on the project and the type of process or process step under consideration. The categories shown below are starting points to initiate the thinking process. Each team will develop its own categories based on the needs of the project. • "6 Ms" – used commonly in manufacturing: ° ° ° ° ° °

Methods (process, documentation, and procedures) Machines (equipment) Manpower (people or management) Materials Measurement Mother Nature (environment)

•

"The 5 Ps + E" – used commonly in service industries: ° Place ° Process ° Procedure ° People ° Policies ° Environment

•

"The Right Stuff" ° tools ° materials ° instructions ° supervision ° feedback

Procedure 1. 2. 3. 4. 5. 6. 7.

Develop a problem statement by identifying the effect or symptom. Write the categories of causes as branches from the main arrow. Identify the potential causes (inputs) using brainstorming techniques. Continue to ask "Why?" for each cause and record each as a sub-cause that branches off. When the group runs out of ideas, focus attention on places on the chart where ideas are fewer. Return to each cause to prioritize the list. After the completion of the diagram, begin to collect data to support the hypothesized causes.

Use When • • •

Process mapping, to identify additional inputs (or causes). Organizing thoughts after a brainstorming session. Identifying the root cause.

337

Using Cause-and-Effect Diagrams

Six Sigma Black Belt | Measure | Process Analysis and Documentation Concept: Using Cause-and-Effect Diagrams

•

Determining additional areas for data collection.

User Tips • • • • • •

Before starting, gain consensus on the problem statement/effect. Pursue each cause to its root cause. Be specific. The diagram organizes thoughts, not solutions. The diagram does not rank items according to importance, however, the data collection should start with the top three to five most likely root causes. When process mapping, the head of the "fish" is the name of the process (if looking at high level inputs) or of a step within the process (if looking at low level inputs).

338

Relational Matrices

Six Sigma Black Belt | Measure | Process Analysis and Documentation Concept: Relational Matrices

A relational matrix is a tool used to assess the effect of each input (X) against its output (Y) in a process. See also: xy matrix, process to product, cause/effect matrix, prioritization matrix

Benefits • • • • •

The process helps team members to identify and agree upon outputs critical to the product and/or customer. Levels of importance are assigned to each output variable (using a numerical rating). The effect of each input (X) on each output (Y) is determined and assigned a numerical value. The relationship between inputs and outputs [Y=f(x)] is determined. For process maps, the relative importance of inputs is determined. Importance Scale

Association Scale

5 = High Importance

9 = Strong Relationship

4 = Above Average Importance

3 = Moderate Relationship

3 = Average Importance

1 = Weak Relationship

2 = Some Importance

0 = No Relationship

 

1 = Low Importance

  Typical examples of scales  

339

Creating Relational Matrices

Six Sigma Black Belt | Measure | Process Analysis and Documentation Concept: Creating Relational Matrices

Procedure 1. 2. 3. 4. 5.

6. 7.

Review the process map. The group should consider involving the customer when defining and rating the Ys. List the output variables (Ys) along the horizontal axis. Rate each output in terms of its overall importance. In this example, a scale of 1 (low importance) to 5 (high importance) is used. Other scales may also be used. Identify potential inputs (Xs) that can impact the various outputs (Ys). List them on the vertical axis. The Xs should come directly from the process map. Rate the effect of each X on each Y. In the example below, a scale of 0 (no relationship), 1 (weak relationship), 3 (moderate relationship) or 9 (strong relationship) is used. The rating is based on how much effect that particular input has on the quality of its corresponding output. Other scales may also be used. The customer importance rating (Y) serves as a weighted response that is multiplied by the association rating (X) for each relationship. The weighted ratings are then added together to comprise a weighted total, the importance score. This score is ranked from highest score to lowest, focusing on the top three to five in the project. Use the results to analyze and align future team activities, prioritizing where the team can begin its focus.

 

340

Six Sigma Black Belt Measure Probability and Statistics

Learning Objectives

Six Sigma Black Belt | Measure | Probability and Statistics Concept: Learning Objectives

At the end of this Measure topic, all learners will be able to: • distinguish between enumerative (descriptive) and analytical (inferential) studies, and between a population parameter and a sample statistic. • define the central limit theorem and understand its significance in the application of inferential statistics for confidence intervals and control charts. • describe and apply concepts such as independence, mutually exclusive, multiplication rules, complementary probability and joint occurrence of events.         Portions of this topic were taken from the ASQ Six Sigma Green Belt web-based Certification Preparation Course and the ASQ Foundations in Quality Learning Series: Certified Quality Engineer.

342

Introduction to Enumerative and Analytical Studies

Six Sigma Black Belt | Measure | Probability and Statistics Concept: Introduction to Enumerative and Analytical Studies

Dr. W. Edwards Deming discussed the importance of the difference between enumerative and analytic studies. In general, the basic difference is this: • Enumerative or descriptive studies describe data using math and graphs and focus on the current situation. • Analytic or inferential studies use sample data to predict or estimate what a population will do in the future. It may be helpful to consider these two examples: • A tailor takes a measurement (waist, chest, inseam, etc.) from a customer who purchases a new suit. The tailor is taking a measurement to obtain quantifiable information – an enumerative approach. • A doctor takes a measurement (temperature, blood pressure, heart beat, etc.) from a patient who feels ill. The doctor is taking a measurement to obtain a causal explanation for some observed phenomenon – an analytic approach.

343

Enumerative (Descriptive) Studies

Six Sigma Black Belt | Measure | Probability and Statistics Concept: Enumerative (Descriptive) Studies

Use enumerative (descriptive) statistics to explain data, usually sample data: • Central tendency - median, mean and mode • Variation - range and variance • Graphs of data like histograms, box plots and dot plots When these measures describe a population, they are referred to as parameters.

344

Analytic (Inferential) Studies

Six Sigma Black Belt | Measure | Probability and Statistics Concept: Analytic (Inferential) Studies

Use analytic (inferential) statistics to draw conclusions from a sample about a population. Methods include: • Testing hypotheses to determine the differences in population means, medians or variances between two or more groups of data and a standard • Calculating confidence intervals or prediction intervals

345

Population Parameters and Sample Statistics

Six Sigma Black Belt | Measure | Probability and Statistics Concept: Population Parameters and Sample Statistics

A statistic is a quantity derived from a sample of data that assists in forming an opinion of a specified parameter of a target population. A sample is frequently used because data on every member of a population is often impossible or too costly. A population is an entire group of objects that have been made, or will be made, containing a characteristic of interest. A population parameter is a constant or coefficient that describes some characteristic of a target population. An example of a population parameter is the mean or variance. Frequently used symbols: • N = Population • n = Sample • µ = Population Mean • σ2 = Population Variance • •

X = Sample Mean s2 = Sample Variance

346

Central Limit Theorem

Six Sigma Black Belt | Measure | Probability and Statistics Concept: Central Limit Theorem

According to Pyzdek, " The central limit theorem can be stated as follows: Irrespective of the shape of the distribution of the population or universe, the distribution of average values of samples drawn from that universe will tend toward a norm distribution as the sample size grows without bound. " The central limit theorem is the theoretical foundation for many statistical procedures. The theorem states that a plot of the sampled mean values from a population tends to be normally distributed.

Key Points of the Central Limit Theorem and Six Sigma •

Using ± 3 sigma control limits, the central limit theorem is the basis of the prediction that, if the process has not changed, a sample mean falls outside the control limits an average of only 0.27% of the time.

• • •

Most points on the chart tend to be near the average. The curve's shape tends to be bell-shaped and the sides tend to be symmetrical. The theorem allows the use of smaller sample averages to evaluate any process because distributions of sample means tend to form a normal distribution. The theorem appears when the process is in control (predictable). The theorem leaves variations from common causes to chance (thus distributing according to the central limit theorem). The theorem identifies and removes variations from special causes.

• • •  

347

Demonstrating Central Limit Theorem

Six Sigma Black Belt | Measure | Probability and Statistics Concept: Demonstrating Central Limit Theorem

The graphs below demonstrate the central limit theorem using dice-rolling experiments. An "experiment" consists of rolling a certain number of dice and graphing the results. This experiment is performed repeatedly, keeping track of the number of times each outcome is observed. These outcomes are plotted in the form of a histogram. According to the central limit theorem, if the number of dice rolled is not too small, the histogram's shape should resemble that of the "bell-shaped curve" when the experiment is repeated many times.  

348

Basic Probability Concepts

Six Sigma Black Belt | Measure | Probability and Statistics Task: Basic Probability Concepts

As mentioned earlier in this section, probability is the chance that something will occur, and it is expressed as a decimal fraction or a percentage. Click each of the key terms below to learn more. Probability The chance that something will occur is probability. It is expressed as a decimal fraction or a percentage. The probability of drawing an ace from a deck of 52 cards is: 4 (aces in the deck) / 52 = .0769 Probability then can be the number of successes divided by the total number of possible occurrences. Sample Space The sample space is the set of possible outcomes of an experiment or the set of conditions. The sample space is often denoted by the capital letter S. Sample space outcomes are denoted using lower-case letters (a, b, c . . .) or the actual values if given. Example: Using this notation, we can show an example of the events in a sample space. An experiment run at random can result in one of the outcomes a, b, c, d, or e. The sample space for this experiment is S = {a, b, c, d, e}. Event An event is a subset of a sample space. It is denoted by a capital letter such as A, B, C, etc. Events have outcomes, which are denoted by lower-case letters (a, b, c . . .) or the actual values if given. Example: Let’s continue with the above example, in which the experiment had a sample space of S = {a, b, c, d, e}. Let A be the event in which either outcome c, d, or e occurs. This event is given as A = {c, d, e}. Let B be the event in which either a or c occurs. This event is given as B = {a, c}. Let C be the event in which either b, d, or e occurs. This event is given as C = {b, d, e}. Union The union of two events is that event consisting of all outcomes contained in either of the two events. The union is denoted by the symbol υ placed between the letters indicating the two events. Example. In our previous example, A = {c, d, e} and B = {a, c}. The event A union B is denoted as A υ B = {a, c, d, e}. (Note that duplicated outcomes are written only once.)

349

Basic Probability Concepts

Six Sigma Black Belt | Measure | Probability and Statistics Task: Basic Probability Concepts

Intersection The intersection of two events is that event consisting of all outcomes that the two events have in common. The intersection is denoted by the symbol ∩ placed between the letters indicating the two events. Example: If A = {c, d, e} and C = {b, d, e}, the event A intersect C is denoted as A ∩ C = {d, e}. The intersection of two events can also be referred to as the joint occurrence of events. Complement The complement of an event is the set of outcomes in the sample space that are not in the event itself. The complement is shown by the symbol ( ′ ) placed after the letter indicating the event. Example: If S = {a, b, c, d, e} and A = {c, d, e}, the complement of A is A′ = {a, b}. Mutually Exclusive Mutually exclusive events have no outcomes in common. It should be noted that the intersection of an event and its complement contains no outcomes—it is the empty set, Ø . These events are mutually exclusive. Example: If B = {a, c} and C = {b, d, e}, the event B intersect C is given by B ∩ C = Ø , and B and C are mutually exclusive.

350

Probability Examples

Six Sigma Black Belt | Measure | Probability and Statistics Concept: Probability Examples

The following example will summarize the use of the terms: • sample space • event • union • intersection • complement • mutually exclusive Samples of semiconductors from two suppliers are classified for conformance to specifications. The results from 50 samples are summarized in the table below: Semiconductor Sample Results  

Conforms

 

Yes

No

Supplier 1

28

2

Supplier 2

17

3

  Let A be the event in which the sample is from Supplier 1. Let B denote the event in which the sample conforms to specifications. The number of samples in event A is 28 + 2 = 30, as shown below. There are 30 total samples from Supplier 1 (regardless of whether they conform or not). Semiconductor Sample Results, Event A  

Conforms

 

Yes

No

Supplier 1

28

2

Supplier 2

17

3

  The number of samples in event B is 28 + 17 = 45, as shown below. There are 45 total samples that conform to specifications (regardless of supplier). Semiconductor Sample Results, Event B  

Conforms

 

Yes

No

Supplier 1

28

2

Supplier 2

17

3

  The number of samples in event A′ is 17 + 3 = 20, as shown below. There are 20 total samples that do not come from Supplier 1. You can interpret A′ as the event that a sample comes from Supplier 2. Semiconductor Sample Results, Event A′  

Conforms

 

Yes

No

Supplier 1

28

2

Supplier 2

17

3

351

Probability Examples

Six Sigma Black Belt | Measure | Probability and Statistics Concept: Probability Examples

  The number of samples in the event A′ ∩ B is 17, as shown below. There are 17 total samples that come from Supplier 2 (A′) and conform to specifications (B). You can interpret A′ ∩ B as the event that a sample comes from Supplier 2 and conforms to specifications. Semiconductor Sample Results, Event A′ ∩ B  

Conforms

 

Yes

No

Supplier 1

28

2

Supplier 2

17

3

   

352

Equally Likely Outcomes

Six Sigma Black Belt | Measure | Probability and Statistics Concept: Equally Likely Outcomes

When a sample space consists of N possible outcomes, all equally likely to occur, then the probability of each outcome is 1/N.

Example Consider the sample space representing all the possible outcomes of rolling a fair die (i.e., all outcomes are equally likely): S = {1, 2, 3, 4, 5, 6} Since there are six possible outcomes, all equally likely, each outcome has a probability of 1/6 of occurring. Let A be the event of getting a 3, 4, or 6 on one roll of the die: A = {3, 4, 6} The probability of event A occurring (that is, of getting a 3, 4, or 6) is: P(A) = P(3) + P(4) + P(6) = 1/6 + 1/6 + 1/6 = 3/6 or 1/2 The sample space, S, has a probability of 1 of occurring, as seen from: P(S) = P(1) + P(2) + P(3) + P(4) + P(5) + P(6) = 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 =1

353

Probabilities for Independent Events

Six Sigma Black Belt | Measure | Probability and Statistics Concept: Probabilities for Independent Events

Events are independent if the occurrence of one event does not depend on the occurrence or lack of occurrence of another (or preceding) event. If two events, A and B, are independent of one another, then the probability of both event A and event B occurring is: P(A ∩ B) = P(A)P(B) For more than two independent events, the independence rule can be extended: P(A∩B∩C∩. . .) = P(A)P(B)P(C) . . . This rule can also be referred to as the multiplication rule.

Example Assume that the probability that a lab specimen contains high levels of contamination is 0.15. Three samples are checked and are independent. The probability that all three specimens contain high levels of contamination is: P(A∩B∩C∩. . .) = P(A)P(B)P(C) . . . = P(all contaminated) = P(1st cont.∩2nd cont.∩3rd cont.) = P(1st cont.)P(2nd cont.)P(3rd cont.) = (0.15)(0.15)(0.15) = 0.003375        

354

Probabilities for Mutually Exclusive Events

Six Sigma Black Belt | Measure | Probability and Statistics Concept: Probabilities for Mutually Exclusive Events

Mutually exclusive events do not occur at the same time or in the same sample space and do not have any outcomes in common. Given two mutually exclusive events, A and B, the event A∩B = Ø, and the probability of events A and B occurring is zero, that is: P(A∩B) = 0

Addition Rule For events A and B, the probabilities of either or both of the events occurring is: P(AυB) = P(A) + P(B) – P(A∩B)

Example Let P(A) = 0.2, P(B) = 0.4, and P(A∩B) = 0.5. Then: P(A′) = 1 - P(A) = 1 - 0.2 = 0.8 P(AυB) = P(A) + P(B) - P(A∩B) = 0.2 + 0.4 - 0.5 = 0.1 Events A and B are not independent. If events A and B were independent, then P(A∩B) = P(A)P(B), and this is not the case: 0.5 ≠ (0.2)(0.4) If the events are mutually exclusive, the term P(A∩B) drops out of the addition rule, because A and B cannot occur at the same time. The addition rule becomes: P(A∩B) = P(A) + P(B) If more than two events are mutually exclusive, then the addition rule can be extended: P(AυBυCυ. . .) = P(A) + P(B) + P(C) + . . .

355

Conditional Probability

Six Sigma Black Belt | Measure | Probability and Statistics Concept: Conditional Probability

Conditional probability is the result of an event depending on the sample space or another event. The conditional probability of an event (the probability of event A occurring given that event B has already occurred) can be found by the following relationship:

Example Let’s return to our example in which samples of semiconductors from two suppliers are classified for conformance to specifications. The results from 50 samples are summarized in the table below. Let A denote the event in which the sample does not conform to specifications, and let B be the event in which the sample is from Supplier 1. Semiconductor Sample Results  

Conforms

 

Yes

No

Supplier 1

28

2

Supplier 2

17

3

  The probability that the sample does not conform to specifications given that the sample came from Supplier 1 is given by P(A|B). A∩B is the event in which the sample does not conform to specifications and comes from Supplier 1. The number of samples for this event is 2. Therefore, the probability of this event, P(A∩B), is 2/50. (Remember that there are a total of 50 samples.) B is the event in which the sample comes from Supplier 1. The number of samples for this event is 30. Therefore, P(B) = 30/50. Finally, the probability of interest can be found as:

This probability could also have been found directly from the table above. The total number of samples from Supplier 1 was 28 + 2 = 30, and the number that are nonconforming is 2. Therefore, the probability is 2/30 or 1/15.

356

Probability Problems

Six Sigma Black Belt | Measure | Probability and Statistics Concept: Probability Problems

Think about each of the following questions: • When flipping a coin, what is the chance of landing on heads? • When flipping the same coin a second time, what is the chance of landing on heads? • When flipping the same coin a third time, what is the chance of landing on heads? • On the other hand, before individually flipping 3 coins, what is the chance they all will land on heads? When flipping a coin, a 50-50 chance (0.5 probability) of landing on heads exists. When flipping the coin a second, third or fourth time, the same 50-50 chance still holds. Assuming each flip is without bias, the previous event does not influence any following event.   What is the probability of flipping three heads in a row? Answer: P(3H) = 1/2 x 1/2 x 1/2 = 1/8   Roll over Page Resources for additional problems and their subsequent answers.

357

Probability Problems

Six Sigma Black Belt | Measure | Probability and Statistics | Probability Problems Example: Probability Problems

Probability Problems 1. 2. 3.

What is the probability of drawing three aces in a row from a deck of cards if the cards are replaced and reshuffled after each draw? Given one standard deck of 52 playing cards. What is the probability of drawing a spade? Given 2 people, what is the probability of Person 1 drawing a spade (without replacing and reshuffling) and Person 2 drawing a spade from the same deck?

To check your answers, roll over Page Resources and click Probability Answers.

358

Probability Answers

Six Sigma Black Belt | Measure | Probability and Statistics | Probability Problems Example: Probability Answers

Probability Answers 1. 2. 3.

P(3 aces replacement) 4/52 x 4/52 x 4/52 = .0004552 = .05% Given one standard deck of 52 playing cards, the probability for Person 1 drawing a spade is 13 of 52 = 0.25 = 25%. The probability of Person 1 drawing a spade is 13/52 or .25 and the probability of Person 2 then drawing a spade from the same deck is 12/51 or .235. The conditional probability of Person 2 drawing a spade after Person 1 draws a spade is .25 x .235 = .0588.

359

Six Sigma Black Belt Measure Collecting and Summarizing Data

Learning Objectives

Six Sigma Black Belt | Measure | Collecting and Summarizing Data Concept: Learning Objectives

At the end of this Measure topic, all learners will be able to: • identify, define, classify and compare continuous (variables) and discrete (attributes) data and recognize opportunities to convert attributes data to variables measures. • define and apply nominal, ordinal, interval and ratio measurement scales. • define and apply methods for collecting data such as check sheets, coding data and automatic gauging. • define and apply techniques for assuring data accuracy and integrity such as random sampling, stratified sampling and sample homogeneity. • define, compute and interpret measures of dispersion and central tendency and construct and interpret frequency distributions and cumulative frequency distributions. • depict relationships by constructing, applying and interpreting diagrams and charts such as stem-and-leaf plots, box-and-whisker plots, run charts and scatter diagrams. • depict distributions by constructing, applying and interpreting diagrams such as histograms, normal probability plots and Weibull plots.   Portions of this topic were taken from the ASQ Six Sigma Green Belt web-based Certification Preparation Course and the ASQ Foundations in Quality Learning Series: Certified Quality Engineer.

361

Need for Measurement

Six Sigma Black Belt | Measure | Collecting and Summarizing Data Concept: Need for Measurement

"Measure what is measurable, and make measurable what is not so." - Galileo Galilei Why do we need metrics? In order to improve a process, it must be measurable. Measurements must provide an organization with information, knowledge and value. Frequently, organizations either lack formal data collection methods or implement complicated data collection efforts without understanding whether the data produced ties back to the organization's strategic goals. As Jack F. Welch, Jr., former G.E. Chairman and CEO, stated: "Too often we measure everything and understand nothing." Individuals within an organization must see the value in the metrics used and the data collected. Successful data collection and metrics should exhibit: • Purpose • Validity • Accuracy • Reliability • Sensitivity Along with the above-mentioned data and metrics, asking the question, "What do I need to know?" is critical before implementing a data collection effort.

362

Attribute Data

Six Sigma Black Belt | Measure | Collecting and Summarizing Data Concept: Attribute Data

Data is information that is objective. There are two primary categories of data: • Attribute data • Variable or continuous data  Attribute data is also referred to as "discrete data." Discrete data are based on counting things such as the number of statement processing errors, the number of loan documentation errors or the number of customer call-back complaints. Discrete data values can only be non-negative integers such as 1, 2, 3,... For that reason, attribute/discrete data is also referred to as "count data." However, discrete data are commonly expressed as a proportion or percent (e.g., percent of x, percent good, percent bad). Discrete data can typically answer such questions as: • How many defects occur on the production line? • How many trucks deliver to the docks each day? • How many waves hit the shoreline each hour?  

363

Continuous Data

Six Sigma Black Belt | Measure | Collecting and Summarizing Data Concept: Continuous Data

Variable or continuous data are measured on a continuum or scale. Data values for continuous data can be any real number: 2, 3.4691, -14.21, etc. Continuous data can be recorded at many different points and are typically physical measurements (e.g., volume, length, size, width, time, temperature, cost, etc.). In general, measured data are more powerful than attribute, or count data. The data are normally more precise due to the existence of decimal places that indicate higher levels of accuracy and specificity. The following is an example of run chart tracking continuous data. In the example provided, the run chart illustrates the fluctuation in temperature over time for a hospital patient.

 

364

Attribute versus Continuous Data

Six Sigma Black Belt | Measure | Collecting and Summarizing Data Concept: Attribute versus Continuous Data

  A manufacturer of sporting goods produces a line of "official" footballs. To be within league specifications, the footballs must be at least 11.25 inches in length, but not greater than 11.5 inches. If a quality control specialist measures the footballs as they come off the production line and records whether the footballs pass or fail the specifications, then the numerical data collected are attribute or discrete data.       However, if the quality control specialist records the length of each football coming off the production line with some sort of measuring device, then the measurements collected are variable or continuous data.    

365

Converting Data Types

Six Sigma Black Belt | Measure | Collecting and Summarizing Data Concept: Converting Data Types

Continuous data, by their very nature, tend to be more precise; they often use decimal places to be as precise as possible. However, it is sometimes desirable to convert continuous data into discrete data. Continuous data contain more information than discrete data. And while continuous data can be converted to discrete data, discrete data cannot be converted to continuous data. Instead of measuring how much deviation from a standard exists (as in our football example with measuring the lengths of footballs for continuous data), we may choose to convert that data to discrete data because discrete data can be easier or quicker to use. We might, for example, categorize the various lengths into groups to generate a histogram. How many footballs fall between 11.25 inches and 11.30 inches? How many footballs fall between 11.31 inches and 11.35 inches? Converting variable data to attribute data may assist in a quicker assessment, but the risk is that information will be lost when the conversion is made.  

366

Measurement Scales

Six Sigma Black Belt | Measure | Collecting and Summarizing Data Concept: Measurement Scales

Scales of Measurement are commonly divided into four types as this table indicates:   Data Type Meas urem ent Princ iple

Nominal Discrete

Indicate the presence or absence of some attribute qualitative rather than quantitative measure Scale Gender, Exa Ethnicity, mple Pass/Fail s Arith Counting metic Oper ation s Asso Mode ciate d Stati stics

Ordinal Discrete

Interval Continuous

Ratio Continuous

Indicate the presence of an attribute to a greater, lesser or same degree as others higher numbers represent higher values and scale points are not necessarily equal distance apart Movie Ratings, Wine Tasting, Horse Race Order of Finish (without times)

Defined scale with equal distance between two points but no absolute zero point Temperature (degrees F), Date on Calendar Addition/Subt raction of Values

Indicate the relationship between two values and have a defined absolute zero point Temperature (degrees K), Age, Weight

Mean, Standard Deviation

Geometric Mean

Greater than/less than

Median

Measurement Scales  

367

Multiplication/ Division of Values

Data Collection Methods

Six Sigma Black Belt | Measure | Collecting and Summarizing Data Concept: Data Collection Methods

Data collection for the project is based on three important questions: • What do we want to know? • From whom do we want to know it? • What will we do with the data? To help insure the data are relevant to the problem statement and project objective, consider these key factors when choosing a data collection method(s): • Length of time (per hour, day, shift, batch, etc.) • Type (cost, errors, ratings, etc.) • Source (reports, observations, surveys, etc.) • Cost (internally and externally) • Collector (team member, associate, subject matter expert, etc.) Understanding how the data relates to the process parameters is the beginning of data-based decision-making. There are many types of data collection methods available to the Six Sigma Black Belt. In this lesson, we will concentrate on: • Check sheets • Coded data • Automatic gaging and other gaging Check sheets and coded data could also be seen as a form of "gage" as well. The most common of all measurements are ones taken with various types of non-automatic “gages” for continuous and discrete data that are not automatic. For example, a person physically makes a measurement, such as taking a temperature reading, taking a blood pressure reading, timing an operation or running a chemical test.

368

Check Sheets

Six Sigma Black Belt | Measure | Collecting and Summarizing Data Concept: Check Sheets

A check sheet is a structured, prepared form for collecting and analyzing data. Check sheets are usually comprised of a list or lists of items and some indication of how often each item occurs. There are several types of check sheets, including the following: • Confirmation check sheets focus on confirming whether all steps in a process have been completed. • Process check sheets record the frequency of observations with a range of measurement. • Defect check sheets record the observed frequency of defects. • Stratified check sheets record observed frequency of defects by defect type and one other criterion. Ishikawa (1985) estimated that between 80% and 90% of all workplace problems could be identified using the simplest quality methods – a check sheet and a histogram. 

Benefits • • •

Easy to use Provides a choice of observations Good for determining frequency over time

The following is an example of a mutually exclusive stratified check sheet:

 

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Using Check Sheets

Six Sigma Black Belt | Measure | Collecting and Summarizing Data Concept: Using Check Sheets

 Procedure 1. 2. 3. 4. 5. 6. 7. 8.

Decide the event (problem) to be observed. Develop operational definitions (descriptions or categories) for the observations. Decide when the data will be collected and for how long. Design the check sheet form to gather and organize the data. Record by making check marks, Xs, tally marks or other similar symbols so that data do not have to be recopied for analysis. Label all spaces on the form. Test the check sheet for a short trial period for appropriateness and ease of use. Each time the targeted event or problem occurs, record the data on the check sheet.

Use When • • • •

Collecting observable data. Collection is managed by the same person or at the same location. Collecting from a frequency or patterns of events, problems, defects, defect location, defect causes, etc. Collecting from a process.

 User Tips • • •

Carefully plan the sheet for easy use. Be sure the observer knows what to observe. Be sure the observer knows the definitions of categories used.

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Coded Data

Six Sigma Black Belt | Measure | Collecting and Summarizing Data Concept: Coded Data

Use When • • • • •

too many digits are listed into small blocks on a check sheet form. errors increase when data-entry clerks try to read and enter large sequences of digits from a single observation. insensitivity of analytic results arise due to rounding of large sequence of digits. attribute data such as yes, no, good or bad are collected and ‘coded’ into numbers such as 'yes = 1', 'no = 2', etc.  data quantity is not enough for a statistical significance in the sample size - data sets can be grouped together and coded to have enough of a sample size.

Examples of Data Coding •

•

•

•

Truncation coding: Measurements such as 1.0003, 1.0002, and 1.0009 in which the digits “1.000” repeat in all observations can record the last digit expressed as an integer (e.g. 3, 2, and 9 respectively). Substitution coding: Product length is measured in sixteenths of an inch (1/16 of one inch). All products’ length should be close to 24 7/16”. A recorded observation might use an integer that expresses the number of sixteenth increments. So 24 7/16” is recorded as “7.” 24 12/16” is recorded as “12.” Category coding: Use a code, like "S" for scratch, "D" for dent, “W” for warped, etc. This method is used often for coding of discrete data on a form or for collection/analysis of categories of data. Also, it is possible an item may have multiple codings. Adding/subtracting a constant or multiplying/dividing by a factor: Let X represent raw data, XC a coded statistic, C as a constant, and f as a factor. The chart below illustrates the mathematical model to use when coding and decoding the data. Note that when decoding the data, the arithmetic mean must be computed and the original mathematical operation is reversed. Also, for addition and subtraction, note that the arithmetic mean of the raw data will be the same as the arithmetic mean of the coded data.

Another common example of coding is the translation of a normally distributed random variable into the standardized normal. The normal distribution will be described in the Distribution section of this lesson.

 

371

Gauging - Automatic and Other

Six Sigma Black Belt | Measure | Collecting and Summarizing Data Concept: Gauging - Automatic and Other

Automatic gauging refers to a process that a computer or piece of equipment performs when it has the ability to gather data without the necessity of human intervention. An example of automatic gauging would be a computer that detects the level of impurities in water and automatically records data levels for those impurities. An electronic thermometer that records the temperature of a liquid and maintains that data also uses automatic gauging. However, a regular thermometer that provides access to data (a temperature) but does not record the data would not be an example of using automatic gauging. Automatic gauging includes such examples as: • Flow meters • Thermisters to monitor temperature (for use in chemical processes, soldering baths, heat treatments, etc.) • Methods to measure thickness of material being processed in sheets like plastic, cloth, paper or non-wovens (e.g., Kevlar, disposable hospital gowns) • Methods to measure thickness of material being processed in coils (e.g., coils of steel, aluminum, or wire) These automatic gauges actively monitor what is happening during the process and are used to evaluate the product and to control or adjust the process. Other types of gauges also exist to assist with measurement. Physical gauging for measurement - for example, the use of calipers or micrometers - are very typical for dimensional measurements. Stop watches are a type of gauge for measuring time segments. Various forms of laboratory equipment are used to measure density, particle size, pH, etc. Thermometers and thermisters are used to measure temperature “by hand” on a sampling basis. Blood pressure cuffs that are used manually measure blood pressure. Even a stethoscope measures the quantity per time segment of heartbeats. These are all examples of gauges used everyday that are not automatic, but gather important data.  

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Assuring Data Accuracy and Integrity

Six Sigma Black Belt | Measure | Collecting and Summarizing Data Concept: Assuring Data Accuracy and Integrity

Data integrity and accuracy both play an important role in understanding whether the data collection process is yielding usable data. • Data integrity determines whether the information being measured truly represents the desired attribute. • Data accuracy determines the degree to which individual or average measurements agree with an accepted standard or reference value. Examples of a lack of data integrity: • A shipping company wants an accurate time for each truck departure, but the computer in which the times are logged is located inside the production facility, minutes away and inconvenient for recording of accurate data. In this example, we think we are getting good data on departure times but the process is inhibiting the collection of data with good integrity. • A manufacturing company points to distributors' sales reports to obtain data about growing customer demand for a new product line. In reality, various distributors use different definitions for their sales reports. Some reports record direct sales to customers at the point of sale, while other reports record sales to large distribution centers that indicate the number of units in stock at warehouses. Both numbers reflect sales but may yield very different information about customer demands for a product. In this example, the data does not have integrity since it does not measure what the manufacturing company needs to be measuring. Examples of a lack of data accuracy: • An electronic warehouse scale receives a short one night due to an electrical thunderstorm. The weight data it yields subsequent to the electrical short does not conform to the established standards for weights and measures. • An outdated gauge that measures the exhaust content from catalytic converters no longer conforms to the standards of the Environmental Protection Agency for the accuracy of its readings.  

373

Sampling Strategies

Six Sigma Black Belt | Measure | Collecting and Summarizing Data Concept: Sampling Strategies

In an ideal situation, we can measure every item in a population. Since that is not always possible, we use sampling to obtain a representative group of items to measure. Sampling strategies include the following: Samplin Definition g Strategy Random Select sample units so that all units have the same probability of being selected. Every unit (n) has an equal chance of being selected for the sample. Systema Every nth record is selected from a list of the population. As long as the list does not tic contain any hidden order, this strategy is just as random as random sampling.

Exa mple s • • •

• Stratifie If the population has identifiable categories, or strata, that have a common • d characteristic, random sampling is used to select a sufficient number of units from each strata. Stratified sampling is often used to reduce sampling error.

Note: Random sampling may give each unit an equal chance at being selected, but it can still be biased if it does not represent the population. Although "random" sampling is used so the data will be representative, non-representative data can still be collected, and other sampling strategies may be used instead. A random number table is a tool that may be used to select sample data on a random basis. Roll over Page Resources to view a random number table and instructions for use.

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Sample Homogeneity

Six Sigma Black Belt | Measure | Collecting and Summarizing Data Concept: Sample Homogeneity

Sample homogeneity occurs when the data chosen for a sample are similar or maintain similar characteristics. Whereas stratified sampling ensures that data are obtained from multiple strata of data within a population for the best possible results, sample homogeneity looks at how alike the data are in a given sample. If data are obtained from a variety of sources, such as several production streams or several geographical areas (from different processes that may look the same but are different), results will reflect these combined sources. The objective is to have data that are homogeneous and reflect a single source to the degree possible. Otherwise, it will be difficult to evaluate and determine the influence of the “X,” or input, of concern. Data that are not homogeneous result in errors. For example, when production results from a lab are inspected only at the end of the line or service, results are reviewed at a national level and variation in all the sources of the product/service become part of the results. To get to the root cause, drill down to the various sources. In other words, you need to evaluate groups or sub-populations that can be analyzed by production line, by geographic or economic group, or method of service delivery. You need to address these sources of variation should be addressed at the source, not at the end of a process. Lack of homogeneity in data will mask the sources and make root cause analysis difficult, if not impossible.  

375

Central Tendencies

Six Sigma Black Belt | Measure | Collecting and Summarizing Data Concept: Central Tendencies

Central tendency is a measure that characterizes the central value of a collection of data that tends to cluster somewhere between the high and low values in the data. Central tendency refers to a variety of key measurements like mean (the most common), median, and mode. Mean • Gives the distribution's arithmetic average (center) • Provides a reference point for relating all other data points • Typically used with normal data Median • The distribution's center point (middle value) • An equal number of data points occur on either side of the median • Useful when the data set has extreme high or low values • Typically used with non-normal data Mode • Represents the value with the highest frequency of occurrence (the most often repeated value) • Typically used with non-normal data

376

Central Tendency Challenge

Six Sigma Black Belt | Measure | Collecting and Summarizing Data Concept: Central Tendency Challenge

Exercise For the following data sets, calculate the mean, median and mode. When you have completed the exercise, roll over Page Resources and click Central Tendency Answer to check your calculations. Point A B C D E F G H I J K

Data Set 1 3 3 6 7 4 7 5 5 4 6 5

Data Set 2 4 3 5 4 16 4 3 4 3 6 3

Data Sets  

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Data Set 3 10 1 7 1 10 6 1 8 1 1 9

Central Tendency Answer

Six Sigma Black Belt | Measure | Collecting and Summarizing Data | Central Tendency Challenge Example: Central Tendency Answer

Answer: Statistic Data Set 1 Data Set 2 Data Set 3 Mean 5 5 5 Median 5 4 6 Mode 5 3 and 4 (Bimodal) 1 Notice that data set 2 has a bimodal distribution in which two values (3 and 4) occur more frequently in the data set than the rest of the values.

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Measures of Dispersion

Six Sigma Black Belt | Measure | Collecting and Summarizing Data Concept: Measures of Dispersion

Dispersion, also referred to as spread, is another important parameter used to describe a data set. Review the table below to understand these measures.

 

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Frequency Distributions

Six Sigma Black Belt | Measure | Collecting and Summarizing Data Concept: Frequency Distributions

A distribution is the amount of potential variation in the outputs of a process, typically expressed by its shape, mean or variance. The shape is often thought of in terms of how closely it resembles the well-known "bell curve" shape or whether it is flatter or skewed to the right or left. The frequency distribution's centrality illustrates the degree to which the data center on a specific value. The distribution also expresses the amount of variation in range or variance from the center. A frequency distribution groups data into certain categories, each category representing a subset of the total range of the data population or sample. Frequency distributions are most often displayed in a histogram (shown later in this topic). Data are sometimes displayed in other ways such as dot-plots, or box plots – also called box-and-whisker plots or stem-and-leaf plots – as part of analysis steps. Size is shown on the horizontal axis (x-axis) and the frequency of each size is shown on the vertical axis (y-axis) as a bar graph. The length of the bars is proportional to the relative frequencies of the data falling into each category, and the width is the range of the category.

Purpose •

A frequency distribution graphically summarizes and displays the distribution of a process data set.

 

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Frequency Distributions Procedure

Six Sigma Black Belt | Measure | Collecting and Summarizing Data Concept: Frequency Distributions Procedure

As stated previously, the frequency distribution is most often represented by a histogram. To develop a histogram, complete these steps:

Procedure 1.

Segment the range of the data into equal sized bars (also called bins, segments, groups, categories or cells) with no overlaps. Looking at the example below, the bars are: 0 - 1.1; 1.11 - 1.2; 1.21 - 1.3, etc. A general rule-of-thumb for determining the number of bars in a histogram can be found in the following table: Number of Data Points 50     100   150   200  

2.

3.

Number of Bars 7 8 9 10 11 12 13 14  

Label the vertical axis ‘Frequency’ (the number of counts for each bar), and label the horizontal axis of the histogram with the range of the response variable. For this example the horizontal axis is labeled ‘Queue Time (Minutes).’ Determine the number of data points that reside within each bar and construct the histogram.

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Frequency Distributions Procedure

Six Sigma Black Belt | Measure | Collecting and Summarizing Data Concept: Frequency Distributions Procedure

Use When •

Ascertaining information about data (e.g., most common data point, distribution type of the data, outliers).

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Frequency Distribution Table

Six Sigma Black Belt | Measure | Collecting and Summarizing Data Concept: Frequency Distribution Table

Another way to display frequency data is to use a frequency distribution table. This is a compact way of displaying a set of measurements compared to listing all the numbers.

Purpose Gives direct information about how many data points are at each value

Example Temperature 43 44 45 46 47 48 49 50 51

Frequency 3 3 4 3 3 0 6 4 4  

 

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Cumulative Frequency Distribution

Six Sigma Black Belt | Measure | Collecting and Summarizing Data Concept: Cumulative Frequency Distribution

A cumulative frequency distribution is created from a frequency distribution by adding an additional column to the table called 'Cumulative Frequency.' For each value, the cumulative frequency for that value is the frequency up to and including the frequency for that value.

Purpose To show the number of data at or below a particular variable

Example For data point 45, add the cumulative frequency for the previous data point 44 (6), plus the frequency for data point 45 (4). This gives you a cumulative frequency of 10 for data point 45. Finally, notice that the cumulative frequency for the highest data point 51 is 30, the same as the total of the frequency column. Temperature 43 44 45 46 47 48 49 50 51  

Frequency 3 3 4 3 3 0 6 4 4 N=

Cumulative Frequency 3 6 10 13 16 16 22 26 30 30

 

384

Graphical Methods

Six Sigma Black Belt | Measure | Collecting and Summarizing Data Concept: Graphical Methods

One of the most effective tools for the visual evaluation of data is a graph showing the relationship between variables. In Six Sigma, graphical methods provide a visual image of the data, and include stem-and-leaf plots, box-and-whisker plots, run charts, scatter diagrams, histograms, normal probability plots and Weibull plots. Graphical methods are used as a complement to numerical methods because graphs are sometimes better suited than numerical methods for identifying patterns in the data.

 

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Stem-and-Leaf Plots

Six Sigma Black Belt | Measure | Collecting and Summarizing Data Concept: Stem-and-Leaf Plots

Designed by John Tukey (1977), a stem-and-leaf plot separates each number into a stem (all numbers but the last digit) and a leaf (the last digit). As an example, for the numbers 95, 99, 100 and 110, the stems are 9, 9, 10 and 11, while the leaves are 5, 9, 0 and 0.

Benefits • • • • • •

Easy and quick to construct Shows shape and distribution Visually compact Convenient Displays both variable and categorical data sets Data may be read directly from the diagram. With a histogram the individual data values may be lost as frequencies within a category

Example The results of 24 students' spelling tests (with a best possible score of 50) are recorded below: 8, 12, 16, 26, 28, 28, 29, 32, 34, 36, 38, 38, 39, 40, 42, 42, 44, 46, 46, 47, 47, 48, 48, 50 The stem-and-leaf-plot looks like this: Stem 0 1 2 3 4 5

Leaf 8 26 6889 246889 0224667788 0 Spelling scores of 24 students

  The stem-and-leaf plot reveals that most students scored in the interval between 40 and 49.

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Using Stem-and-Leaf Plots

Six Sigma Black Belt | Measure | Collecting and Summarizing Data Concept: Using Stem-and-Leaf Plots

Procedure 1. 2. 3. 4.

Some find it helpful to first write (sort) the data in numerical (ranking) order. Separate the numbers into stems and leaves. Group the numbers with the same stems. Prepare an appropriate title and legend for the plot.

Use When • •

Classifying data. Organizing data as it is collected.

User Tips • • •

All numbers should have similar structure such as all whole numbers, all with one decimal, etc. (e.g., [10, 15, 18] or [2.5, 3.8, 6.7]). To find the median, count to half the total number of leaves. Use good judgment when determining what to do with outliers because they can either be significant pieces of information or poor information due to an error or misinformation.

Roll over Page Resources and click Stem-and-Leaf Activity to practice a stem-and-leaf plot.

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Stem-and-Leaf Activity

Six Sigma Black Belt | Measure | Collecting and Summarizing Data | Using Stem-and-Leaf Plots Example: Stem-and-Leaf Activity

Offline Activity Materials needed: pencil, paper   Scenario Create a stem-and-leaf plot for the following situation and identify the median: The collected data tracked the number of emails sent by company staff between October 3 and November 11. 506, 511, 482, 494, 453, 499, 509, 547, 501, 474, 490, 483, 504, 517, 488, 497, 502, 512, 513, 507, 480, 474, 495, 509, 498, 479, 505, 492, 480, 504   When complete, roll over Page Resources and then click Stem-and-Leaf Answer to see the correct response.

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Stem-and-Leaf Answer

Six Sigma Black Belt | Measure | Collecting and Summarizing Data | Using Stem-and-Leaf Plots Example: Stem-and-Leaf Answer

 

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Box-and-Whisker Plots

Six Sigma Black Belt | Measure | Collecting and Summarizing Data Concept: Box-and-Whisker Plots

Credited to John Tukey (1977), box-and-whisker plots use five key data points to graphically depict all data in the sample or population: • The upper and lower quartiles of the data form the ends of the box. • The median forms the centerline within the box. • The minimum and maximum data points serve as end points to lines that extend from the box (the whiskers). • Outlier data are represented by asterisks or diamonds outside of the minimum or maximum points. • The box-and-whisker plot is also called a box plot or a five-number summary.

Benefits • • • • • •

Shows outliers Useful with a large number of data sets Provides a graphic summary of a data set Visually represents the center, the spread, and the overall range Indicates whether the distribution is skewed and possible unusual observations Explores data and draws informal conclusions when two or more variables are present

390

Using Box-and-Whisker Plots

Six Sigma Black Belt | Measure | Collecting and Summarizing Data Concept: Using Box-and-Whisker Plots

Procedure 1. 2. 3. 4. 5. 6. 7. 8. 9.

Write the data in rank (numerical) order. Calculate the median. Identify the lower quartile (values below the median) and calculate the median for that group. Identify the upper quartile (values above the median) and calculate the median for that group. Calculate the interquartile range by subtracting the medians of the upper and lower quartiles. Plot the three medians, the lowest value and the highest value (the 5-points) to a number line. Draw a box through the points of the upper and lower quartiles. Draw a vertical line through the box at the median point. Draw the whiskers from each end of the box to the smallest and largest values.

Use When • •

Comparing two or more sets of data. Determining significance of an apparent difference.

User Tips • • •

Box-and-whisker plots are good in the early stages of data analysis. A simple rule is that a whisker longer than three times the length of the box probably indicates an outlier. There are several ways to describe the distribution: ° The 5-number summary ° Using the mean and standard deviation to interpret the spread. • •

•

Best used with symmetrical data and no outliers or high skew. Better measures of center and spread.

Notes about the semi-quartile range: ° Rarely used to measure spread. ° Less subject to fluctuation samples in highly skewed spreads.

 

391

Run Charts

Six Sigma Black Belt | Measure | Collecting and Summarizing Data Concept: Run Charts

A predecessor of control charts, a run chart displays how a process performs over time. With data points plotted in chronological order and connected as a line graph, run charts may detect special causes of variation. Since shifts have an assignable special cause, run charts provide a signal that leads to the cause. Run charts are also called trend charts (variations on a control chart, but without the limits)

Benefits • • • • •

Recognizes problem trends or patterns Displays sequential data Serves as a visual aid in spotting patterns and abnormalities Monitors and communicates process performance Presents information around a middle value (centerline)

 

392

Using Run Charts

Six Sigma Black Belt | Measure | Collecting and Summarizing Data Concept: Using Run Charts

Procedure 1. 2. 3. 4. 5. 6. 7. 8.

List the collected data in the sequence in which it occurred. Order the data (lowest to highest) and determine the range. Calculate the median. Construct the Y-axis and make the scale 1.5 to 2 times the range. Construct the X-axis and make it 2 to 3 times as long as the Y-axis. Draw a dotted line to illustrate the median. Plot the points and connect them to form a line graph. Label each axis with units and title the chart to identify the investigation.

Use When • •

Displaying performance/process data over time. Displaying tabulations or lists of numbers.

User Tips • • •

•

Trends that are observable on the run chart may or may not indicate variation that is beyond normal limits. If 25 or more points of data exist, then a run chart may be used to determine if a special cause exists that is causing variation in the process. In this situation, three types of data patterns may indicate variation due to special causes: ° Trend: Six or more data points moving in one direction indicate a special cause is influencing the process; flat line segments do not count toward the trend or to reverse it. ° Shift: Eight or more points on one side of the centerline indicate a special cause acting on the process. ° Cycle: A repeated pattern that occurs eight or more times may also be an indication of a special cause. As a general guideline, statistical control requires a minimum of 100 observations without one of the above patterns occurring.

393

Scatter Diagrams

Six Sigma Black Belt | Measure | Collecting and Summarizing Data Concept: Scatter Diagrams

Scatter diagrams graph pairs of continuous data, with one variable on each axis, to examine the relationship between them. Scatter diagrams may show what happens to one variable when the other variable changes. This is particularly true when one of the two variables is independent and one is dependent. The dependent variable is normally charted along the vertical (Y) axis and the independent variable along the horizontal (X) axis. If the relationship between the two variables is understood, then the dependent variable may be controlled. The relationship between the two variables may illustrate: • Correlation: A correlation suggests there is a relationship between the two variables. A correlation does not necessarily mean that a cause and effect relationship exists. A third characteristic (or more) might be the cause of both the variables behaving as they do. A correlation may be: ° Positive: as one variable moves in one direction, the second variable moves in the same direction. ° Negative: as one variable moves in one direction, the second variable moves in the opposite direction. • No correlation exists. Scatter diagrams are also called scatter plots, X-Y graphs or correlation charts

Benefits •

Enhances cause-effect relationships

394

Using Scatter Diagrams

Six Sigma Black Belt | Measure | Collecting and Summarizing Data Concept: Using Scatter Diagrams

Procedure 1. 2. 3.

4.

Collect pairs of data for both variables. Draw a graph with the independent variable on the horizontal axis (x) and the dependent variable on the vertical axis (y). For each pair of data, plot a dot (or symbol) where the x-axis value intersects the y-axis value. (If two dots fall together, put them side by side, touching, so that you can see both.) If correlated, "eyeball" a line of best fit.

Use When • • • • •

Acting on a hunch that two variables are related. Evaluating paired continuous data. Attempting to identify potential root causes of a problem by relating two variables. Following a brainstorming session to create a fishbone diagram. Testing for autocorrelation before developing a control chart.

User Tips •

The more the data resemble a straight line, the stronger the relationship (see examples, below). ° The tighter the data points along the line, the stronger the relationship. ° Direction of the line indicates whether the relationship is positive or negative. ° If the line was hard to draw or see, and if the points show no significant clustering, there is probably no correlation.

•

Do not assume that a relationship means that one variable caused the other because another factor may influence both measured factors. To determine the degree of association between the two variables, calculate the correlation coefficient.

•

Examples of Scatter Diagrams  

 

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Using Scatter Diagrams

Six Sigma Black Belt | Measure | Collecting and Summarizing Data Concept: Using Scatter Diagrams

 

396

Normal Probability Plots

Six Sigma Black Belt | Measure | Collecting and Summarizing Data Concept: Normal Probability Plots

Normality probability plots, also called normal test plots, are used to investigate whether process data exhibit the standard normal bell curve or Gaussian distribution. The plot is defined by two parameters: mean and variance. For normally distributed data, the mean and median are very close and may be identical. The normal probability plot shows whether or not the data are distributed as a standard normal distribution. Normal distributions will follow a linear pattern. In other words, if the data plot along a straight line, then the plot is normally distributed. The following is an example of a normal probability plot:

 

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Using Normal Probability Plots

Six Sigma Black Belt | Measure | Collecting and Summarizing Data Concept: Using Normal Probability Plots

Use When • • •

predicting and making decisions based on the data distribution. differentiating when it is equally likely that readings will fall above or below the average. testing the assumption of normality.

User Tips • • •

Most of the data concentrate at, or near, the centerline. The centerline divides the curve into two equal halves. Fewer of the data points approach the minimum and maximum values.

   

398

Weibull Plots

Six Sigma Black Belt | Measure | Collecting and Summarizing Data Concept: Weibull Plots

Another form of plot is the Weibull plot. Weibull plots are often used to estimate the cumulative probability that a given sample will fail under certain conditions. The data can be used to determine a point at which a certain number of samples will fail. Once known, this information can help design a process such that no part of the sample approaches the stress limitations. The Weibull plot has special scales designed so that the data points will be almost linear if they follow a Weibull distribution. The Weibull distribution has three parameters but can use only two if the third is assumed: • α is the shape parameter • θ is the scale parameter • γ is the location parameter

Life Analysis Data Weibull plots are used to chart data about the life of a product or process. This plot helps determine the parameters for use with Weibull distributions. Product lifetimes can be measured in hours, miles, or any other metric that describes the time-to-failure. • For complete data, the exact time-to-failure is known (e.g., the unit failed after 400 hours of operation). • For suspended or "right censored" data, the unit operates successfully for a known period of time and could have continued for an additional period of time that is not known. • For interval or "left censored" data, the time-to failure is known but only within a certain range of time (e.g., the unit failed between 400 and 450 hours of operation).

Weibull Plot Example

    When a Weibull plot is graphed, it resembles the example of a Weibull distribution seen below.

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Weibull Plots

Six Sigma Black Belt | Measure | Collecting and Summarizing Data Concept: Weibull Plots

 

400

Six Sigma Black Belt Measure Properties and Applications of Prob. Distributions

Learning Objectives

Six Sigma Black Belt | Measure | Properties and Applications of Prob. Distributions Concept: Learning Objectives

At the end of this Measure topic, all learners will be able to: • describe and apply the following distributions commonly used by black belts: binomial, Poisson, normal, chi-square, Student's t and F distributions. • recognize when and how to use the following, less frequently used distributions: hypergeometric, bivariate, exponential, lognormal and Weibull.    

Portions of this topic were taken from the ASQ Six Sigma Green Belt web-based Certification Preparation Course and the ASQ Foundations in Quality Learning Series: Certified Quality Engineer.

402

Introduction to Probability Distributions

Six Sigma Black Belt | Measure | Properties and Applications of Prob. Distributions Concept: Introduction to Probability Distributions

Fitting data to distributions (e.g., normal, binomial, or Poisson) is helpful for purposes of prediction and decision-making. A probability distribution is a tool that may help identify whether a value will occur within a given range. Distributions help to answer questions such as: • What is the probability that x will occur? • What is the probability that a value that is lesser or greater than x will occur? • What is the probability that a value between x and y will occur? According to the ASQ Glossary, "a distribution is the amount of variation in the outputs of a process, typically expressed by its shape, average, or standard deviation. A distribution's shape may often be described by symmetry, skewness, and kurtosis." • For distributions that are symmetrical, the mean provides a good description of the central tendency of the data. • For distributions that are skewed, the median is usually a better indicator of central tendency. • Standard deviation provides a measure of variation from the mean. • Skewness provides a measure of the location of the mode relative to the mean. If the mode, which is the highest point of the distribution, is to the mean's left, then the skewness is negative. If the mode is to the right, then skewness is positive. If the distribution is perfectly symmetrical, then skewness is equal to zero. • Kurtosis measures the peakness or relative flatness of the distribution. If the distribution has a higher and narrower peak, then the kurtosis is higher. If the distribution’s peak is flatter and wider, then the kurtosis is lower.  

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Probability Distributions for Different Data Types

Six Sigma Black Belt | Measure | Properties and Applications of Prob. Distributions Concept: Probability Distributions for Different Data Types

A probability distribution is a mathematical formula relating the values of a characteristic with their probability of occurrence in the population. Probability distributions fall into two basic groups: those that address discrete (counting) data and those that address continuous (variable) data. • Probability distributions for discrete data describe a finite set of possible occurrences for the data in question. An example is rolling a die. The probability distribution is discrete because the random variable representing the number of possibilities can only be a 1, 2, 3, 4, 5 or 6. • Probability distributions for continuous data describe a continuum of possible occurrences that is unbroken. For example, the distribution of body weight is a random variable with an almost infinite number of possible data points.

404

Probability Density Functions

Six Sigma Black Belt | Measure | Properties and Applications of Prob. Distributions Concept: Probability Density Functions

Probability distributions for continuous variables use probability density functions (also referred to as PDF), which are mathematical functions modeling the probability density reflected in a histogram. Those distributions for discrete variables do not have a probability density function. Instead, they have a probability mass function. The probability density function models the probability density for continuous random variables reflected in a histogram. As part of the equation, a probability density function uses integrals – the summation of area between two points. If a histogram depicts the relative frequencies of a series of output ranges for a random variable, then this histogram should resemble the shape of the probability density of the random variable. For that reason, the shape that results from the probability density function is sometimes described as the shape of the distribution. For example, a real estate office manager’s survey reveals the following data for the age of a rented house in a particular neighborhood. Age of House (yrs) – x axis

0-1.0

1.1-2.0

2.1-3.0

3.1-4.0

4.1-5.0

5.1-6.0

6.1+

Probability – y axis

.20

.28

.20

.15

.10

.05

.02

These data are represented by a histogram that looks like the graph on the bottom left of the page. If points are plotted along the top of each vertical bar in the histogram, the histogram suggests a curve similar to that seen in the graph on the right. The probability density function would resemble the same shape. Using the example above, if the real estate office manager wants to know the probability that a rental house is between 0 and 4 years of age, the PDF may be written in equation form for this problem: P(0 ≤ x ≤ 4) = 0.20 + 0.28 + 0.20 + 0.15 = 0.83

This is true when f(x) is greater than or equal to zero for all values of x and the total area under the graph is 1.

405

Probability Distribution Types

Six Sigma Black Belt | Measure | Properties and Applications of Prob. Distributions Concept: Probability Distribution Types

View an introduction to the more common probability distributions used by Six Sigma Black Belts in the table below. Detailed information will be provided for each distribution type later in the lesson. Distribution Type Binomial

Poisson

Normal

Chi-square

Student's t

F

Hypergeometric

Typical Application

Approximate Distributions (if any) Used in finite sampling Can approximate the problems when each Poisson or Normal observation has only one of distributions under certain two possible outcomes, conditions. such as pass/fail. Used for situations when an   attribute possibility is that each sample can have multiple defects or failures. Characterized by the   traditional "bell-shaped" curve, the normal distribution is applied to many situations with continuous data that is roughly symmetrical around the mean. Used in many situations   when an inference is drawn on a single variance or when testing for goodness of fit or independence. Examples of use of this distribution include determining the confidence interval for the standard deviation of a population or comparing the frequency of variables. Used in many situations   when inferences are drawn without a variance known in the case of a single mean or the comparison of two means. Used in situations when   inferences are drawn from two variances such as whether two population variances are different in magnitude. This is the "true" The binomial distribution distribution. Used in a approximates the

406

Probability Distribution Types

Six Sigma Black Belt | Measure | Properties and Applications of Prob. Distributions Concept: Probability Distribution Types

Bivariate

Exponential

Lognormal

Weibull

similar manner to the binomial distribution except that the sample size is larger relative to the population. This distribution should be considered whenever the sample size is larger than 10% of the population. The hypergeometric distribution is the appropriate probability model for selecting a random sample of n items from a population without replacement and is useful in the design of acceptance-sampling plans. Created with the joint frequency distributions of modeled variables. Used for instances of examining the time between failures. Used when raw data is skewed and the log of the data follows a normal distribution. This distribution is often used for understanding failure rates or repair times. Used when modeling failure rates particularly when the response of interest is percent of failures as a function of usage (time).

Probability Distributions  

407

hypergeometric distribution.

 

 

 

 

Binomial Distribution

Six Sigma Black Belt | Measure | Properties and Applications of Prob. Distributions Concept: Binomial Distribution

A binomial distribution is typically used to model discrete data (also referred to as "attribute" or "counting" data) having only two possible outcomes (e.g., pass or fail, yes or no). In a situation where there are exactly two mutually exclusive outcomes (e.g., pass or fail) of a trial, the binomial distribution may be used to find the proportion of defective units produced by a process.  The binomial distribution is best used when: • Population is large – when N > 50 • Sample size is small compared to the population, ideally when sample size (n) is less than 10% of the population (N) – also written as n < 0.1N The necessary conditions for a random variable to follow the binomial distribution are as follows: • There are a fixed number of observations, n. • The n observations are all independent. Choosing one item does not affect the probability that another item will be chosen. • Each trial results in one of two possible outcomes, success or failure. • The probability of a success can be denoted by p; the probability of a failure can be denoted by 1 - p. The binomial probability distribution equation will show the probability of getting x defectives in a sample of n units:

Where: • n = sample size • x = number of defectives or occurrences • p = probability or the proportion defective • 1 – p = probability of the defect not occurring The binomial probability distribution may also be used as an approximation to the hypergeometric distribution when the sample size is less than ten percent of the population. Conversely, the hypergeometric distribution is preferred when the sample size is greater than 10% of the population. Refer to the page on hypergeometric distributions to learn more.  

408

Binomial Distribution Individual Example

Six Sigma Black Belt | Measure | Properties and Applications of Prob. Distributions Concept: Binomial Distribution Individual Example

The binomial distribution could be used in situations such as these: • Determine the number of defective products when the product either passes or fails a given test • Determine the proportion of people who respond positively to a survey when the responses are either yes or no • Determine the number of errors on a form when the form is either completed correctly or incorrectly • The appearance of a candy product is either acceptable or unacceptable when the candy has an established appearance standard that is either acceptable or unacceptable

Example The Sweet Shoppe produces many types of candy. Traditionally, their Pecan Caramel Delites have a 1% defect rate. If we test a sample of ten candy units from the process, what is the probability that there will be 0 defective candies? Using the information outlined above: • n = 10 • x = 0 (n units taken x at a time) • p = .01 Placing these values in the binomial distribution equation, the correct answer of 90.4% is the probability of having 0 defective candies.

 

409

Binomial Cumulative Distribution Example

Six Sigma Black Belt | Measure | Properties and Applications of Prob. Distributions Concept: Binomial Cumulative Distribution Example

The binomial cumulative distribution is the probability of exactly (x) or fewer successes in (n) trials with a probability of success equal to (p) on each trial.

Example A manufacturing process is performing at a 5% nonconforming rate. What is the probability that less than two units will be nonconforming for the sample taken from the lot received? The necessary values in this case are: • n = 10 • p = 0.05 • x = 0, 1 P(X = x) =nCxpx(1 - p)n-x Where: • P(X = x) = the format used to denote probability • X = number of trials in an experiment that are successes • nCx = the number of ways of getting (x) successes on (n) trials: ° °

10C0

is the combination of 10 units taken 0 at a time

10C1

is the combination of 10 units taken 1 at a time

The probability of interest is given by p(x < 2) = p(x = 0) + p(x = 1): P(X < 2) = P(X = 0) + P(X = 1) =10C0(0.05)0(1 - 0.05)10-0+10C1(0.05)1(1 - 0.05)10-1 = 1(1)(0.95)10 + 10(0.05)(0.95)9 = 0.5987 + 0.3151 = 0.9138 The probability of selecting less than two nonconforming units out of the 10 possible is 0.9138.

410

Poisson Distribution

Six Sigma Black Belt | Measure | Properties and Applications of Prob. Distributions Concept: Poisson Distribution

The Poisson distribution is used to estimate the number of instances a condition of interest occurs in a process or population. Most frequently, this distribution is used when the condition may occur multiple times in one sample unit and you are interested in knowing the number of individual characteristics found. For example: • A manufactured part has a number of critical attributes. These attributes are measured in a random sampling of the production process. The number of non-conforming conditions is recorded for each sample. The collective number of failures from the sampling may be modeled using the Poisson distribution. • A company records the number and types of industrial accidents that occur at various plant locations across North America. The Poisson distribution could be used to help project the number of industrial accidents for the following year and their probable locations. • An auto body shop tracks the number of dents, paint drips, scratches, pinholes, etc. on a car. There might be any number or all of these characteristics on a single car or a sample of (n) cars. The necessary conditions for a random variable to follow a Poisson distribution are as follows: • The probability that a count occurs in an interval is the same for all intervals. • Counts are independent of each other. The Poisson distribution equation is:  

Where:             • f(x) = probability of x occurrences in the sample/interval • λ = mean number of counts in an interval (where λ > 0) • x = number of defects/counts in the sample/interval • e = a constant approximately equal to 2.71828

411

Poisson Distribution Examples

Six Sigma Black Belt | Measure | Properties and Applications of Prob. Distributions Concept: Poisson Distribution Examples

Example The serious accident rate in a large manufacturing plant is 3 per month. What is the probability in August there will be 1 serious accident at the plant? For this example, λ = 3 and x = 1. The probability of interest is given as x = 1:

The probability that exactly 1 serious accident will occur in August is approximately 0.15. Cumulative Now let us determine the probability that there will be at most 1 serious accident in the month of September at this large manufacturing plant. The probability of interest is:

The probability at most 1 serious accident will occur in September is approximately 0.2. Note: Not all 'averages' of Poisson are whole numbers. For the above example, the accident rate could have been 34 accidents in the past 12 months. In this case the average is 2.83 accidents per month.  

412

Poisson Approximation to the Binomial

Six Sigma Black Belt | Measure | Properties and Applications of Prob. Distributions Concept: Poisson Approximation to the Binomial

The Poisson distribution can also be used to approximate the binomial if n ≥ 100 and np < 10. As n gets larger, the Poisson distribution and the binomial distributions are approximately equal, resulting in λ = np.

Example In manufacturing automobiles, a company has been experiencing a defect (nonconformity) rate of 7 per 100 autos. What is the probability of finding 5 or fewer nonconforming autos in a sample of 100 autos taken from the next day's production? This is a binomial problem, since there are two possible outcomes: conformity/nonconformity. In this example, nonconformity is considered a "success" because we are "successful" in observing an outcome of interest - in this case an auto that does not conform to all requirements. The probability of a success is p = 7/100 = 0.07. The sample size of interest is n = 100. The probability of interest is p(x ≤ 5). Either the binomial distribution or Poisson distribution may be used, since n ≥ 100 and np < 10. Using the Poisson distribution as an approximation to the binomial, the necessary formulation is:

Note: A Poisson distribution table could have been used here to find the solution to the example above. Roll over Page Resources at the bottom of the screen and click Poisson Distribution Table to view and/or print for use as a job-aid. Note: In this example we are interested in the number of nonconforming products, not number of defects causing the nonconforming product. A ‘nonconforming auto’ is defined as one that does not ‘conform’ in every way, (i.e, it may have one or more defects).

413

Normal Distributions

Six Sigma Black Belt | Measure | Properties and Applications of Prob. Distributions Concept: Normal Distributions

The most recognizable continuous distribution is the normal distribution:

According to the ASQ Glossary, the normal distribution charts a data set of which most of the data points are concentrated around the average (mean) in a symmetrical manner, thus forming a bell-shaped curve. The normal distribution’s shape is unique in that the most frequently occurring value is in the middle of the range and other probabilities tail off symmetrically in both directions. The normal distribution is used for continuous (measurement) data that is symmetric about the mean. The graph of the normal distribution depends on two factors - the mean and the variance. When the variance is large, the curve is short and wide; when the variance is small, the curve is tall and narrow. Assume both graphs below have the same scale. The curve on the left is wider than the curve on the right because the curve on the left has a larger variance.

 

414

Standard Normal Distribution

Six Sigma Black Belt | Measure | Properties and Applications of Prob. Distributions Concept: Standard Normal Distribution

A standard normal distribution (also referred to as a "Gaussian" or "standard bell" curve) may be viewed in the chart below. Note that the population mean μ is zero and that the population variance σ2 equals one.

 

415

Normal Dist. Single Observation Example

Six Sigma Black Belt | Measure | Properties and Applications of Prob. Distributions Concept: Normal Dist. Single Observation Example

In the following equation, the random variable X follows a normal distribution with mean μ and variance σ2. The random variable Z can be computed as:

The random variable Z also follows a normal distribution but with mean μ = 0 and σ2 = 1.

Example The life of an automotive battery manufactured from a certain process is normally distributed with mean life of μ = 800 days and a variance of σ2 = 225. What is the probability that a randomly selected battery will have a life of less than 760 days? Roll over Page Resources at the bottom of the screen and click Z Table to find the Z value for the corresponding calculation.

The probability that a randomly selected battery will have a life of less than 760 days is 0.00379.  

416

Normal Dist. Sample Mean Example

Six Sigma Black Belt | Measure | Properties and Applications of Prob. Distributions Concept: Normal Dist. Sample Mean Example

To find probabilities involving the sample average X, some information about the distribution must be obtained. If the random variable X follows a normal distribution with mean μ and variance σ2, then the sample mean X for a sample of size n also follows a normal distribution with mean μ and with variance σ2 / n. The standard deviation, or "standard error of the mean," is:

If X for a sample of size n follows a normal distribution with mean μ and with variance σ2 / n, then the random variable Z can be computed as:

The random variable Z also follows a normal distribution with mean μ = 0 and σ2 = 1. If the population variance σ2 is not given or known, use the sample variance s2 as an estimate for σ2. Example Returning to the example of automotive batteries with a mean life of μ = 800 days and a variance of σ2 = 225, what is the probability that a random sample of 9 batteries will have an average life of less than 750 days? Roll over Page Resources at the bottom of the screen and click Z Table to find the Z value for the corresponding calculation.

Note: A Z of -4.99 (calculated value = -10) or less on the Z Table will result in a probability of 0. The probability that the average life of 9 randomly sampled batteries will be less than 750 days is 0.

417

Chi-Square Distribution

Six Sigma Black Belt | Measure | Properties and Applications of Prob. Distributions Concept: Chi-Square Distribution

The chi-square (χ2 ) distribution is used when testing a population variance against a known or assumed value of the population variance. It is skewed to the right (i.e., it has a long tail toward the large values of the distribution). The overall shape of the distribution will depend on the number of degrees of freedom in a given problem. The degrees of freedom are 1 less than the sample size (i.e., if the sample size is n, the degrees of freedom necessary for a particular problem are n - 1). An example of a χ2 distribution with 6 degrees of freedom is shown below.

There is a distribution curve for each degree of freedom, n – 1, from 1 to 30 in most probability tables.

418

Student t Distribution

Six Sigma Black Belt | Measure | Properties and Applications of Prob. Distributions Concept: Student t Distribution

The Student's t distribution was developed by W.S. Gosset (Student 1908) through his work at the Guinness brewery. Since Guinness at that time did not allow its staff to publish, Gosset used the pseudonym of “Student.” The t distribution is commonly used to determine the confidence interval of the population mean and confidence statistics when you are comparing the means of sample populations. To use the t distribution, we must know the degrees of freedom for the problem. The degrees of freedom are 1 less than the sample size (i.e., if the sample size is n, the degrees of freedom necessary for a particular problem are n - 1). The student’s t distribution is a symmetrical continuous distribution. It is similar to the normal distribution, but the extreme tail probabilities are larger than for the normal distribution for sample sizes of less than 31. The shape and area of the t distribution approach that of the normal distribution as the sample size increases. The t distribution can be used whenever samples are drawn from populations possessing a normal, bell-shaped distribution. There is a family of curves, one for each sample size from n = 2 to n = 31, in most tables given in standard statistics texts.

 

419

F Distribution

Six Sigma Black Belt | Measure | Properties and Applications of Prob. Distributions Concept: F Distribution

The F distribution (F-test) is a tool used for assessing the ratio of independent variances (equality of variances). The F distribution is particularly important in the Analysis of Variance (ANOVA) - a technique frequently used in the Design of Experiments (DOE) to test for significant differences in variance within and between test runs. ANOVA will be discussed along with examples in the Analyze lesson of this course. The F-distribution is represented by:

Where: • s12 is the variance of the first sample (n1 - 1 degrees of freedom in the numerator) • s 2 is the variance of the second sample (n - 1 degrees of freedom in the 2

2

denominator) Given two random samples drawn from a normal distribution. The shape of the F distribution is non-symmetrical and will depend on the number of degrees of freedom associated with s12 and s22 . The distribution for the ratio of sample variances is skewed to the right (the large values).

420

Hypergeometric Distribution

Six Sigma Black Belt | Measure | Properties and Applications of Prob. Distributions Concept: Hypergeometric Distribution

The hypergeometric distribution is used when items are drawn from a population without replacement. That is, the items are not returned to the population before the next item is drawn out. The items must fall into one of two categories, such as good/bad or conforming/nonconforming. The hypergeometric distribution is similar in nature to the binomial distribution, except the sample size is large compared to the population. The hypergeometric distribution is appropriate whenever the sample size is greater than 10% of the population (n > 0.1N). The hypergeometric distribution determines the probability of exactly x number of defects when n items are samples from a population of N items containing D defects. The equation is:

Where: • x = number of nonconforming units in the sample (r is sometimes used here if dealing with occurrences) • D = number of nonconforming units in the population • N = finite population size • n = sample size  

421

Hypergeometric Distribution Example

Six Sigma Black Belt | Measure | Properties and Applications of Prob. Distributions Concept: Hypergeometric Distribution Example

A group of 12 cellular telephones is being shipped to a local retailer. While the phones are much in demand, the manufacturer has been having some problems with phones being shipped with the wrong type of battery. Because the phones are in demand, the retailer agrees to accept the shipment of 12 phones, but only if the shipment has fewer than 3 defective phones. Because time is of the essence, the manager decides to only inspect 4 phones (meaning the manager should find 1 or fewer defective phones). Checking the sample of 4, the manager finds one phone with the wrong battery. Should the remainder of the shipment be rejected? Given the information provided above: • N = population of 12 • D = number of defectives allowed at 3 • n = sample size of 4 • x = number of defectives in the sample of n • f(x) = probability of getting x defectives in the sample For this example, it is necessary to solve the equation for both probability of 0 and 1 since the shipment would be accepted if it also had no defectives.

f(1 or less) = f(0) + f(1) = .764 of accepting a “bad quality” shipment. For most retailers, this risk level would be unacceptable.

422

Bivariate Distribution

Six Sigma Black Belt | Measure | Properties and Applications of Prob. Distributions Concept: Bivariate Distribution

When two variables are distributed jointly the resulting distribution is a bivariate distribution. Bivariate distributions may be used with either discrete or continuous data. The variables may be completely independent or a covariance may exist between them. The bivariate normal distribution - a commonly used version of the bivariate distribution - may be used when there are two random variables. This equation was developed by Freund in 1962:

Where: • -∞ < x < ∞ • -∞ < y < ∞ • -∞ < μ1< ∞ • • • • •

-∞ < μ2< ∞ σx > 0, σx > 0 μ1 and μ2 = the two population means σ21 and σ22 = the two variances ρ = correlation coefficient of the random variables

Typically, you will use a statistical software package for calculating bivariate distribution are calculated using a statistical software package.

423

Exponential Distribution

Six Sigma Black Belt | Measure | Properties and Applications of Prob. Distributions Concept: Exponential Distribution

Exponential distributions are frequently used to analyze reliability, and are often used to model items with a constant failure rate. The exponential distribution is closely related to the Poisson distribution and used to determine the average time between failures or average time between a number of occurrences. For example, if there is an average of 0.50 failures per hour (discrete data - Poisson distribution), then the mean time between failure (MTBF) is 1 / 0.50 = 2 hours (continuous data - exponential distribution). If a random variable x is distributed exponentially, then its reciprocal y = 1/x follows a Poisson distribution. The opposite is also true. If x follows a Poisson distribution, then the reciprocal y =1/x is exponentially distributed. The exponential distribution equation is:

Where: • μ = the mean (also sometimes referred to as θ) • λ = failure rate which is the same as 1/μ • x = x-axis values When this equation is integrated, it yields the following equation that gives the cumulative probabilities without the need for a table:

 

424

Exponential Distribution Example

Six Sigma Black Belt | Measure | Properties and Applications of Prob. Distributions Concept: Exponential Distribution Example

A Florida electric company experiences an average of 500 electrical outages each year due to storms and hurricanes. What is the probability that the weekend crews, who work from 6:00 PM on Friday evening to 6:00 AM on Monday morning, will not receive a call? Data summary: • μ = 500 electrical outages each year • Since there are 365 days in each year and 24 hours per day, then there are 8760 hours each year. • The time between each outage is 8760/500 = 17.52 hours between each outage • The weekend shift works 60 hours (1800 Friday through 0600 Monday); therefore x = 60. Using the equation from the previous page:

The chance that the weekend crew will not get a call is 3.3%, since 96.7% of the time a call will be received during the 60 hours.

425

Lognormal Distribution

Six Sigma Black Belt | Measure | Properties and Applications of Prob. Distributions Concept: Lognormal Distribution

The lognormal distribution can be used to model various situations such as response time, time-to-failure data, and time-to-repair data. Lognormal distribution is a skewed-right distribution (with most data in the left tail), and consists of the distribution of the random variable whose logarithm follows the normal distribution. The lognormal distribution assumes only positive values. When the data follows a lognormal distribution, a transformation of data can be done to make the data follow a normal distribution. Then probabilities can be found, confidence intervals can be constructed, and tests of hypothesis can be conducted (all of which depend on the assumption that the data follows a normal distribution). The first column of the following table contains data that is lognormally distributed. The second column contains the natural logarithm of the first column. The second column is normally distributed. X (original data following a lognormal distribution) 1.6423 0.2374 5.3658 1.2848 2.0202 1.3601 1.2172 0.7089 1.3868 35.0451 1.1417 4.4567 0.4446 1.3431 1.0166

ln(X) (natural logarithm of the original data, following a normal distribution) 0.49610 -1.43817 1.68005 0.25063 0.70321 0.30759 0.19658 -0.34405 0.32699 3.55664 0.13247 1.49441 -0.81066 0.29497 0.01642

   

426

Lognormal Distribution Data Plots

Six Sigma Black Belt | Measure | Properties and Applications of Prob. Distributions Concept: Lognormal Distribution Data Plots

The data plotted in the histogram below follows a lognormal distribution. The lognormal distribution is skewed, with most of the data in the left tail area and very little data in the right tail area.

If the natural logarithm of each data point is taken and then plotted on the histogram, the shape follows a normal distribution, as shown in the histogram below.

 

427

Lognormal Distribution Example

Six Sigma Black Belt | Measure | Properties and Applications of Prob. Distributions Concept: Lognormal Distribution Example

Using the logarithm of the data instead of the original data, we can now use the normal distribution to find probabilities associated with the data. X follows a lognormal distribution with the following mean and variance:

Given the following properties: • X is a random variable that could be any positive real number • Y = ln(X) (where ln is the natural logarithm) • Y follows a normal distribution with mean μ and variance σ2 Y

Y

Let Y = ln(X), where Y is normally distributed with mean μY = 7.5 and variance σ2Y = 4. Thus, X has the following mean and variance:

The probability that X will be less than 13,000 is found using the relationship Y=ln(X). Two transformations will occur in this example. The first is the change from lognormal to normal and the second is from normal to standard normal. (Use this transformation since Y is normally distributed and X is not; only then can the standard normal distribution apply to find probabilities.) Using the standard normal distribution discussed earlier, what is the probability that X is less than 13,000? Roll over Page Resources at the bottom of the screen and click Z Table to find the Z value for the corresponding calculation.

428

Lognormal Distribution Example

Six Sigma Black Belt | Measure | Properties and Applications of Prob. Distributions Concept: Lognormal Distribution Example

The probability that the lognormal random variable X could be less than 13,000 is approximately 0.84.

429

Weibull Distribution

Six Sigma Black Belt | Measure | Properties and Applications of Prob. Distributions Concept: Weibull Distribution

The Weibull distribution is a widely used distribution for understanding reliability and is similar in appearance to the lognormal. For example, it can be used to measure time to fail, time to repair, and material strength. The shape and dispersion of the Weibull distribution depends on two parameters: • β is the shape parameter. • θ is the scale parameter. Both parameters are greater than zero. In general, the probabilities from a Weibull distribution can be found from the cumulative Weibull function:

Where: • X is a random variable • x is an actual observation The shape parameter (β) provides the Weibull distribution with its flexibility. • If β = 1, the Weibull distribution is identical to the exponential distribution and used to describe the bathtub curve. • If β = 2, the Weibull distribution is identical to the Rayleigh distribution (beyond the scope of this course). • If 3 < β < 4, then the Weibull distribution approximates a normal distribution.

430

Weibull Distribution Plot

Six Sigma Black Belt | Measure | Properties and Applications of Prob. Distributions Concept: Weibull Distribution Plot

As can be seen in the Weibull distribution chart below, the distribution can take on many shapes and can be used to describe many types of data. • The shape parameter (β) defines the probability distribution function (PDF) shape. • The scale parameter (θ) describes the magnitude of the x-axis.

 

431

Weibull Distribution Example

Six Sigma Black Belt | Measure | Properties and Applications of Prob. Distributions Concept: Weibull Distribution Example

The length of the life of a particular type of battery is known to follow a Weibull distribution with shape parameter β = 2 and scale parameter θ = 4 (measured in years). It is important to know the probability that a battery of this type lasts less than the advertised lifetime of 2 years, P(X < 2). Let X represent the life of the battery. What is the probability the battery will last less than 2 years?

There is approximately a 22% chance that the battery will last less than 2 years. Cumulative Example The time to failure in hours of an electrical circuit that is exposed to extremely high temperatures has a Weibull distribution with shape parameter β = 0.6 and scale parameter θ = 2(measured in hours). It is important to find the probability that the time to failure of the circuit is at least 4 hours,P(X ≥ 4). Let X represent the time to failure. What is the probability the time to failure of the circuit is at least 4 hours?

The probability the circuit will fail after 4 hours is 0.21965.  

432

Six Sigma Black Belt Measure Measurement Systems

Learning Objectives

Six Sigma Black Belt | Measure | Measurement Systems Concept: Learning Objectives

At the end of this Measure topic, all learners will be able to: • describe and review measurement methods such as attribute screens, gauge blocks, calipers, micrometers, optical comparators, tensile strength and titration. • calculate, analyze and interpret measurement system capability using repeatability and reproducibility, measurement correlation, bias, linearity, percent agreement, precision/tolerance (P/T) and precision/total variation (P/TV). • use both ANOVA and control chart methods for non-destructive, destructive and attribute systems. • understand traceability to calibration standards, measurement error, calibration systems, control and integrity of standards and measurement devices.     Portions of this topic were taken from the ASQ Six Sigma Green Belt web-based Certification Preparation Course and the ASQ Foundations in Quality Learning Series: Certified Quality Engineer.

434

Introduction to Measurement Methods

Six Sigma Black Belt | Measure | Measurement Systems Task: Introduction to Measurement Methods

One of the important parts of the Measure phase is gathering the data to be used in the project. Fortunately, there are numerous measurement methods available to help obtain useful data. Click the measurement method below to view a description of each. Attribute Screens Attribute screens use two categories for determining data outcomes: acceptable or not acceptable, go or no go, pass or fail. This screen is typically used when the percentage of nonconforming material is high or not known. A screen should evaluate the attributes that are most helpful in identifying major problems with a product or process.

  Gauge Blocks Gauge blocks are used in manufacturing to set a length dimension for transfer or for tool calibration. Sets of these blocks usually come in groups of eight to eighty-one. Gauge blocks are accurate to within a few millionths of an inch.

 

435

Introduction to Measurement Methods

Six Sigma Black Belt | Measure | Measurement Systems Task: Introduction to Measurement Methods

Calipers Calipers measure distance, depth, height, or length from either an inside or outside perspective. Most calipers are tools that capture physical measurements and then transfer them to a scale to determine the data.

Calipers come in several types: spring calipers, vernier calipers, dial calipers, and digital calipers. Spring calipers – named for the type of joint that connects the two sides – measure difficult to reach areas and are accurate to about a tenth of an inch. A steel ruler is used for the transfer process of the measurement. Vernier calipers use a vernier scale and are accurate to one thousandth of an inch. Vernier calipers are being replaced by dial and digital calipers. Digital calipers, as the name implies, use an electronic readout and are accurate to five thousandths of an inch.   Optical Comparators An optical comparator compares a part to a form that represents the desired dimensions. A beam of light is used to project a shadow of the object that is magnified by a lens to determine whether the part fits within the tolerance levels established.

 

436

Introduction to Measurement Methods

Six Sigma Black Belt | Measure | Measurement Systems Task: Introduction to Measurement Methods

Micrometers Micrometers, commonly referred to as "mics", are handheld measuring devices consisting of a basic C frame with the measurement occurring between a fixed anvil and a movable spindle. Micrometers are similar to calipers and have a finely threaded screw with a head that displays how much the screw has been moved in or out during use. Micrometers measure items using a combination of readings on a barrel and a thimble with accuracy to one thousandth of an inch.

  Tensile Strength Tensile strength represents the ability of a piece of metal to withstand the stress of being pulled apart. The metal part is load-tested with additional weight until the part fails. Related tests include the following: • Shear test ability measures the resistance to a sliding type of action with parallel forces. • Compression test ability measures the results of forces on the outside of the item pushing towards each other. • Fatigue test ability measures the repeated cycles of an action designed to cause eventual failure in the product or item.

 

437

Introduction to Measurement Methods

Six Sigma Black Belt | Measure | Measurement Systems Task: Introduction to Measurement Methods

Titration Titration is a measurement method that examines the endpoint of a chemical reaction and the quantity of a reactant in the titration flask. For example, a base liquid might be added to an acid until the mixture becomes neutral. From this process, the level of acid can be measured because the quantity of the base liquid that was added is known.

 

438

Measurement Systems Analysis

Six Sigma Black Belt | Measure | Measurement Systems Concept: Measurement Systems Analysis

In order to ensure a measurement method is accurate and producing quality results, a method must be defined to test the measurement process as well as ensure that the process yields data that is statistically stable. Measurement Systems Analysis (MSA) refers to the analysis of precision and accuracy measurement methods. MSA is an experimental and mathematical method of determining how much the variation within the measurement process contributes to overall process variability. Three characteristics contribute to the effectiveness of a measurement method. These three characteristics are: • Accuracy ° ° ° • •

Linearity: How does the size of the part affect the accuracy of the measurement method? Stability: How accurately does the measurement method perform over time? Accuracy: Is there a difference between the observed average values and the master value of choice?

Reproducibility Repeatability

These three characteristics follow a hierarchical pattern. Repeatability serves as the foundation that must be present in order to achieve reproducibility. Reproducibility must be present before achieving accuracy. Repeatability and reproducibility often come under the heading of precision. Precision requires that the same measurement results are achieved for the condition of interest with the selected measurement method. A measurement method must first be repeatable. A user of the method must be able to repeat the same results given multiple opportunities with the same conditions. The method must then be reproducible. Several different users must be able to use it and achieve the same measurement results. Finally, the measurement method must be accurate. The results the method produces must hold up to an external standard or a true value given the condition of interest.

439

Gauge R and R Studies

Six Sigma Black Belt | Measure | Measurement Systems Concept: Gauge R and R Studies

Assuming that a gauge is determined to be accurate (that is, the measurements generated by the gauge are the same as those of a recognized standard), the measurements produced must be repeatable and reproducible. A study must be conducted to understand how much variance (if any) observed in the process is due to variation in the measurement system. Three methods are typically used for this purpose: • The range method quantifies both repeatability and reproducibility together. • The average and range method determines the total variability and allows repeatability and reproducibility to be separated. • The analysis of variance method (ANOVA) is the most accurate of the three methods. In addition to determining repeatability and reproducibility, ANOVA also looks at the interaction between those involved in looking at the measurement method and the attributes/parts themselves.

440

Analysis of Variance Method (ANOVA)

Six Sigma Black Belt | Measure | Measurement Systems Concept: Analysis of Variance Method (ANOVA)

ANOVA demonstrates how the total variation is partitioned using a procedure similar to the following: 1. 2. 3. 4. 5. 6. 7.

Choose a small number of parts (usually ten or fewer) in a random manner. Select a characteristic to be measured. Number the parts to identify each part specifically. Select a few technicians or inspectors - usually five or fewer Require the technicians or inspectors to measure the parts using the same measuring device. Repeat step #5 to obtain two complete sets of data. Conduct an ANOVA analysis beginning with the construction of an ANOVA table.

 

441

ANOVA Table

Six Sigma Black Belt | Measure | Measurement Systems Concept: ANOVA Table

Given two parts (numbered 1 and 2) and three inspectors (labeled A, B and C), an ANOVA table is constructed.

• • • •

ColSqs = squaring the sum of the column and dividing by the column n RowSqs = squaring the sum of the row and dividing by the row n Interaction cell square = squaring the cell total and dividing by the cell n

• •

X = 24.5 N = 12

X2 = x12 + x22 + ... + xn2 = 52.25

Correction for the Mean (CM) Total SS (TSS)

(X)2 / N = (24.5)2 / 12 = 600.25/12 = 50.02

Inspector SS (ISS)

ColSqs2 - CM = 50.81 - 50.02 = 0.79

Part SS (PSS)

RowSqs2 - CM = 50.21 - 50.02 = 0.19

Interaction SS (InSS)

CellSqs2 - CM - ISS - PSS = 51.125 - 50.02 - .79 - .19 = .125 TSS - ISS - PSS - InSS = 2.23 - .79 - .19 - .125 = 1.125 # of Inspectors - 1 = 2

Error SS (ESS) Inspector Degree of Freedom (DF) Part DF Interaction DF Total DF Error DF

X2 - CM = 52.25 - 50.02 = 2.23

# of parts - 1 = 1 Inspector DF * Part DF = 2 N - 1 = 11 Total DF - Inspector DF - Part DF - Interaction DF = 11 2-1-2=6 F = Effect MS / Error MS Var Coef for Inspectors = 4; Parts = 6; Interaction = 2

MS = SS/DF Var (variance) = (Effect MS - Error MS) / Variance Coefficient SIGe = repeatability =   square root of Error MS

442

ANOVA Table

Six Sigma Black Belt | Measure | Measurement Systems Concept: ANOVA Table

Equations for ANOVA Tables   With these values, build a summary ANOVA table to examine variation: Source Inspector

SS .79

DF MS Fcal 2 .395 2.11

F(a) 3.68

Var .052

Adj Var .052

Part

.19

1

1.01

3.06

.0004

.0004

Interaction

.125 2

2.64

-.0625 0

Error

1.12 6 5

.062 0.33 5 .187   5

 

.1875

 

Total 11 DF

 

 

Totals: .2399

.19

SIGe = .4330

.1875

% 21. 68 % 0.1 7% 0.0 % 78. 16 % 10 0.0 0%

ANOVA Table a = 0.05   Based on the table, the following can be determined: • Repeatability is the error variance and contributes 78.16% of the variation. • Reproducibility is the variation among inspectors and contributes 21.68% of the variation. • The F ratio test is 2.11 for inspectors, compared to 3.68 at the 95% confidence level - a difference cannot be deduced between inspectors. • No interaction exists - each inspector measures each part the same way. • Over 99% of variation is attributable to repeatability and inspector variance. • Process variation in this example accounts for less than 1% of the variation (.17% to be exact). Given this information, the measurement methods currently in use account for almost all of the variations viewed in the process.

443

Measurement Correlation

Six Sigma Black Belt | Measure | Measurement Systems Concept: Measurement Correlation

Measurement correlation is the comparison of the measurement values between two or more measurement systems. Measurement correlation may be made against a known standard. Both may have variation, but comparing the variation of a measurement instrument to a known standard may also identify issues with the measuring device that can be corrected. Besides repeatability and reproducibility, other components whose combined effect explains measurement correlation are: • Bias • Linearity • Precision/Tolerance (P/T)

444

Bias

Six Sigma Black Belt | Measure | Measurement Systems Concept: Bias

Bias is often due to human error. Whether intentional or not, bias can cause inaccurate or misleading results. In other words, bias causes a difference between the output of the measurement method and the true value. Types of bias include: • Participants in a study tend to remember their assessments from prior trials, so you should: ° collect assessment sheets immediately after each trial. ° change the order of the inputs, transactions or questions. ° include an adequate waiting period after the initial trial to make remembering details of the trial less likely. • Participants spend extra time when they know they are being evaluated, so give specific time frames. • Another good example of bias occurs when equipment is set wrong. For example, if the bathroom scale is set 15 pounds higher, a 150 pound person using the scale will think they weigh 165 lbs. If an instrument underestimates, the bias is negative. If an instrument overestimates, the bias is positive. The equation for bias is:

Where: • n = the number of times the standard is measured • X = the ith measurement •

i

T = the value of the standard

445

Linearity

Six Sigma Black Belt | Measure | Measurement Systems Concept: Linearity

Linearity is the variation between a known standard across the low and high ends of the gauge. The purpose of measurement linearity is to determine the reliability of a measuring instrument by indicating any linearity error or change in the accuracy of the measuring instrument. Linearity is illustrated in the diagram below.

When measuring linearity, draw a line through the data points to view a slope (b). The slope is a "best fit" line that runs through the data points. Linearity is equal to the slope multiplied by the process variation Vp (tolerance or spread). Typically, the lower the absolute value of the slope, the better the linearity.

 

446

Gauge Linearity Plot

Six Sigma Black Belt | Measure | Measurement Systems Concept: Gauge Linearity Plot

The following image depicts gauge linearity.

If gauge linearity error is relatively high, causes might include the following: • The gauge is not being calibrated properly at both the lower and upper ends of its operating range. • There are errors in the minimum or maximum master. • The gauge is worn. • The internal gauge has faulty design characteristics.

447

Precision-Tolerance

Six Sigma Black Belt | Measure | Measurement Systems Concept: Precision-Tolerance

Precision/Tolerance (P/T) is the ratio between the estimated measurement error (precision) and the tolerance of the characteristic being measured, where σm is the standard deviation of the measurement system.

Where: • m = measurement The P/T ratio needs to be small to minimize the effect of measurement error. As the P/T ratio becomes larger, the measurement method loses its ability to indicate a real change in the process. In Introduction to Statistical Quality Control, author Douglas Montgomery provides more specifics, “Values of the estimated ratio [P/T] of 0.1, or less, often are taken to imply adequate gauge capacity. This is based on the generally used rule that requires a measurement device to be calibrated in units one-tenth as large as the accuracy required in the final measurement. However, we should use caution in accepting this general rule of thumb in all cases. A gauge must be sufficiently capable to measure product accurately enough and precisely enough so that the analyst can make the correct decision. This may not necessarily require that P/T be less than 0.1." Forrest Breyfogle, in Implementing Six Sigma, utilizes illustrations of processes that require less accuracy and which have P/T ratios < 0.3.

448

Precision-Total Variation

Six Sigma Black Belt | Measure | Measurement Systems Concept: Precision-Total Variation

The formula for Precision/Total Variation (P/TV) is: Where: • σm is the standard deviation of the measurement system •

σ2p is the part-to-part variation

Be sure to keep the P/TV ratio as small as possible to reduce the effect of measurement variation. As either the P/T or P/TV ratios become larger, the measurement method loses its ability to indicate a real change in the process. The bottom line is this: When the current measurement method cannot detect variations, then you must select a new measurement method with a smaller measurement variation.

449

Control Chart Method

Six Sigma Black Belt | Measure | Measurement Systems Concept: Control Chart Method

The Measurement Systems Analysis (MSA) Reference Manual (AIAG, 1998) outlines a control chart model using averages and range to study variability in measurement methods. This model requires two or three replications (r), by two or three appraisers ( k), on 10 parts (n). The range average is found using this formula: This average range value is proportionate to the standard deviation of the process. The average range provides another source of understanding the variation using a specific measurement method.

450

Metrology

Six Sigma Black Belt | Measure | Measurement Systems Concept: Metrology

Simply put, metrology is the science of measurement. Metrology encompasses certain key elements: • The establishment of measurement standards that are precise and defined. • The use of measuring equipment to assess variability. • Regular calibration of equipment.

451

Measurement Error

Six Sigma Black Belt | Measure | Measurement Systems Concept: Measurement Error

Measurement error is the degree to which the measuring instrument differs from a true value. The formula for the error of an instrument is the following: Measurement error may result from a number of factors, including: • Operator variation: This occurs when the same operator realizes variation when using the same equipment with the same standards. • Operator to operator variation: This occurs when two or more operators realize variation in results while using the same equipment with the same standards. • Equipment variation: The equipment exhibits erratic measurement results. • Process variation: This occurs when there are two or more methods for using measurement equipment and those methods yield different results.

452

Calibration Systems

Six Sigma Black Belt | Measure | Measurement Systems Concept: Calibration Systems

According to the ASQ Online Glossary, calibration is defined as "the comparison of a measurement instrument or system of unverified accuracy to a measurement instrument or system of known accuracy to detect any variation from the required performance specification." The purpose of calibration systems can be summarized as follows: • To ensure that products and services meet the tolerance range and quality specifications. A well-maintained calibration system has a positive impact on the quality of products and services offered to the customer • To ensure that measuring equipment is recalled from use when it is time to be recalibrated. Periodic recalibration of measuring and test equipment is necessary for measurement accuracy • To ensure that measuring equipment is removed from use when it is incapable of performing its function with an agreed level of accuracy There are two main objectives of a calibration system: • To reduce quality costs through the early detection of nonconforming products and processes with the use of measuring equipment of known accuracy • To provide customers (when they request it) with an indication of a supplier’s calibration capabilities According to the Quality Engineering Handbook, the aim of all calibration activities is to determine that a measuring system's accuracy objectives are met.

453

When to Calibrate

Six Sigma Black Belt | Measure | Measurement Systems Concept: When to Calibrate

Measuring equipment should be calibrated before initial use and periodically recalibrated as often as necessary to maintain prescribed accuracies. When production is continuous, a frequency (or interval) is usually established. When production is sporadic, calibration is often done on a “prior to use” basis. The recalibration interval will depend on variables such as historical information, stability, purpose, extent of use, tendency to wear or drift, how critical the measurement is, the cost of an inaccurate measurement, the environment in which it is used, etc. Determining calibration intervals is not an arbitrary process. First, the equipment is given a thorough evaluation before being put into service, and a calibration frequency is determined based on short-term results. The starting point is typically a tightened calibration schedule based on the manufacturer’s recommendation and the application. When no calibration history exists for a particular measuring device, a track record may be established before deciding on a particular frequency of calibration. Pennella offers the following steps as a suggestion. They would be most practical when applied in a laboratory setting. • Calibrate before use for one week. If no adjustments are needed, go to the next step. • Calibrate weekly for four weeks. If history is favorable, go to the next step. • Calibrate monthly for six months. If records show no out-of-tolerance conditions result, go to the next step. • Calibrate every six months for one year. If records show no out-of-tolerance conditions, calibrate the instrument once a year. • Revert to the previous step if an out-of-tolerance condition becomes evident. Calibration intervals should not be adjusted haphazardly. Whenever intervals are to be modified, statistical analysis of the historical data is recommended. Such analysis often prevents unnecessary costs while helping to ensure the effectiveness of the system.

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Six Sigma Black Belt Measure Analyzing Process Capability

Learning Objectives

Six Sigma Black Belt | Measure | Analyzing Process Capability Concept: Learning Objectives

At the end of this Measure topic, all learners will be able to: • identify, describe and apply the elements of designing and conducting process capability studies, including identifying characteristics, identifying specifications and tolerances, developing sampling plans and verifying stability and normality. • distinguish between natural process limits and specification limits and calculate process performance metrics such as percent defective. • define, select and calculate Cp and Cpk, and assess process capability. • define, select and calculate Pp, Ppk, Cpm, and assess process performance. • • • • •

understand the assumptions and conventions appropriate when only short-term data are collected and when only attributes data are available. understand the changes in relationships that occur when long-term data are used. interpret relationships between long-term and short-term capability as it relates to technology and/or control problems. understand the cause of non-normal data and determine when it is appropriate to transform. compute sigma level and understand its relationship to Ppk.

  Portions of this topic were taken from the ASQ Six Sigma Green Belt web-based Certification Preparation Course and the ASQ Foundations in Quality Learning Series: Certified Quality Engineer.

456

Process Capability Studies

Six Sigma Black Belt | Measure | Analyzing Process Capability Concept: Process Capability Studies

A process capability study attempts to quantify whether a process can consistently meet the standards set by internal or external customers. Since this study yields a prediction, and predictions should be made from relatively stable processes, a process capability study should only be used in a relatively controlled and stable process environment. Measuring capability can be challenging because it is, by definition, a point estimate. Every process has unpredictable instability, which creates an inherent risk of estimate errors. Since there is no confidence interval related for mean and standard deviation, there is no confidence interval for capability, therefore risk cannot be quantified. The user must accept the risk of variability related to instability. Recall that variation in a process may be the result of a common cause or special cause. • If the variation is due to a common cause, the output will still form a distribution that is relatively stable as the variation is constant. In this case, a process capability study may be completed (although subject to the always present risk that variations change). • If the variation is a result of a special cause, then the output is not as stable and not as predictable. In this case, a process capability study may have problems with its accuracy. Measurements 1 & 2 reflects two measurements of the same part of the process taken at different times. Because of process stability, the measurements and capabilities estimates will be similar. Measurements 3 & 4 also reflects two measurements of the same part of the process taken at different times. Because of the process instability, though, the measurements, and thus the resulting capability estimates, will be drastically different.

 

457

Two Opinions - Process Capability Studies

Six Sigma Black Belt | Measure | Analyzing Process Capability Concept: Two Opinions - Process Capability Studies

There is some controversy about the definition and use of process capability studies. Two broad opinions of probability capability studies include: • Opinion 1: Process capability describes the overall capability of the process operating at its best. This approach does not address how well the process meets customer specifications directly. The analysis is usually completed on a short-term basis with a 1.5 sigma adjustment to compensate for drifts in long-term variability. • Opinion 2: Process capability describes how well a process functions relative to customer specifications. This approach takes a longer term view of variance and short-term or long-term views are usually not considered separately. The information presented in this topic provides general information that represents common approaches to the issue of process capability studies.

458

Process Capability Study Procedure

Six Sigma Black Belt | Measure | Analyzing Process Capability Concept: Process Capability Study Procedure

Procedure 1.

2.

3. 4. 5. 6.

Select a process to study. This process should be critical to the organization and can be selected using several techniques (e.g., a Pareto analysis or a cause-and-effect diagram). Verify or define the process parameters. The process and its parameters may have been selected in the Define phase. Verify what the process entails, its boundaries, and gain agreement on the process’s definition. Many of these steps are completed when developing a process map. Conduct a measurement systems analysis to ensure that the measurement methods produce sound data. Select a process capability analysis method. Cpk, Cp, Ppk and Pp are presented and calculated later in this sub-topic. Obtain the data and conduct an analysis. Develop an estimate of the process capability. This estimate can be compared to the standards set by internal or external customers.

After completing a process capability study, address any special causes of variation that can be isolated. If able, eliminate the special causes that are not desirable. In some cases, a special cause of variation may be desirable if it produces a better product or output. In that circumstance, if possible, attempt to make the special cause a common cause to ensure the benefit is achieved equally on all output.  

459

Identifying Characteristics

Six Sigma Black Belt | Measure | Analyzing Process Capability Concept: Identifying Characteristics

Characteristics selected to be part of a process capability study should meet certain requirements: • The characteristic should be important relative to the quality of the product or process. A process may have 15 characteristics, but only one or two should be selected for inclusion in the process capability study. • The characteristics are Ys or outcomes to process steps that meet customer requirements. The Ys are changed by changing the Xs or inputs. ° The characteristic’s value should be adjustable. ° The operating parameters that influence the characteristic should be able to be determined and controlled. • Sometimes, the characteristic selected has a history of being the most difficult item to control.

460

Specification Limits

Six Sigma Black Belt | Measure | Analyzing Process Capability Concept: Specification Limits

Specification limits are set by the customer, and result from either customer requirements or industry standards. The amount of variance (process spread) the customer is willing to accept sets the specification limits. A customer wants a supplier to produce 12-inch rulers. Specifications call for an acceptable variation of +/- 0.03 inches on each side of the target (12.00 inches). The customer is saying acceptable rulers will be from 11.97 to 12.03 inches. If the process is not meeting the customer's specification limits, two choices exist to correct the situation: • Change the process's behavior. • Change the customer's specification (requires customer approval).

Examples of Specification Limits Specification limits are commonly found in: • Blueprints • Engineering drawings and specs • Industry standards • Self-imposed standards within a shop • Federally mandated standards (e.g., emissions controls)

461

Stability and Capability

Six Sigma Black Belt | Measure | Analyzing Process Capability Concept: Stability and Capability

Think of the interaction of stability and capability as a 2x2 matrix:   Capable: Yes Capable: No

Stable: Yes 1 3

Stable: No 2 4

Stability and Capability 1. 2. 3.

4.

There is nothing further needed. While the process is currently capable, stability may need to be improved to assure continued capability. Since the process is stable, but not capable, we can be reasonably sure the lack of capability is reasonably correct. The process must be improved to become capable. The lack of stability makes it difficult to estimate the level of capability with any certainty. First, we need to reduce variation and remove special causes of variation to improve stability so we will have reasonable estimates of the centering of the process. Following that, we may need to recenter the process and/or further reduce process variation.

 

462

Drift and Process Capabilities

Six Sigma Black Belt | Measure | Analyzing Process Capability Concept: Drift and Process Capabilities

Drift, movement away from the target, is a sign of a changing process. After noticing this signal of drift, identifying the cause of the drift must occur before corrective action can be taken. In the graphic, click DRIFT to demonstrate a drifting process and observe the changing values. [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

463

Process Capability Indices

Six Sigma Black Belt | Measure | Analyzing Process Capability Concept: Process Capability Indices

The goal of performance metric indices is to establish a controlled process, and then maintain that process over time. Numbered values are a shortcut method indicating the quality level of a process in parts per million (ppm). Once the status of the process is determined, the causes in variation (based on statistical significance) may be identified. Courses of action might be to: • do nothing. • change the specifications (not very often). • center the process. • reduce the variation in the Six Sigma process spread. • accept the losses (not very often).

464

Process Limits

Six Sigma Black Belt | Measure | Analyzing Process Capability Concept: Process Limits

A stable process can be monitored to determine if changes that occur are due to factors other than random variation. Such observation determines whether changes are necessary and if any corrective actions are required. Process limits are the voice of the process based on the variation of the products produced. The supplier collects data over time to determine the variation in the units against the customer's specification. These data points collected over time establish the process curve. Having a predictable process producing 100 percent conformances is the ideal state. Day-to-day control charts help identify assignable causes to any variations that occur.

 

465

Graphing Process Capability

Six Sigma Black Belt | Measure | Analyzing Process Capability Concept: Graphing Process Capability

A process capability diagram displays both the voice of the process and the voice of the customer. To draw one of these diagrams: 1. 2.

Locate the mean of the distribution (X) and draw a normal curve that reflects the upper and lower process limits (UPL, LPL) to the data. Draw the customer specifications with the upper and lower limits for those specifications as appropriate (USL, LSL). Note that a customer may only have a lower limit or just an upper limit.

Example Given: X = 12, σ = 1, Specifications 10 +/- 5 The process is off target (nominal) but within specifications.

 

466

Graphing Tips

Six Sigma Black Belt | Measure | Analyzing Process Capability Concept: Graphing Tips

Roll over Page Resources to display practice problems and to check your answers. Be sure to label your diagrams as #1 and #2.

467

Practice Activities

Six Sigma Black Belt | Measure | Analyzing Process Capability | Graphing Tips Example: Practice Activities

Materials needed: Graph paper, pencil, ruler Directions: Create a process capability diagram for each of the situations (activities) below. Be sure to include the mean (X), process results, lower process limit (LPL) = X - 3σ, upper process limit (UPL) = X + 3σ , customer target, lower specification limit (LSL) and upper specification limit (USL). To check the your answers, roll over Page Resources and click Graphing Answers.   Graphing Activity #1: X = 7, σ = 1, Specs = 10 +/-4   Graphing Activity #2: X = 10, σ = 0.5, Specs = 10 +/- 1  

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Graphing Answers

Six Sigma Black Belt | Measure | Analyzing Process Capability | Graphing Tips Example: Graphing Answers

Practice Activity #1

Practice Activity #2

Given: X = 7, σ = 1, Specifications 10 +/-4

Given: X = 10, σ = 0.5, Specific

The process is off target and not within specifications.

Process is on target and outside

     

469

Introducing Process Capability Indices

Six Sigma Black Belt | Measure | Analyzing Process Capability Task: Introducing Process Capability Indices

Process capability indices (Cp and Cpk) and process performance indices (Pp, Ppk, and Cpm) identify the current state of the process and provide statistical evidence for comparing after-adjustment results to the starting point. Although these indices have a common purpose, they differ in their approach. According to Douglas C. Montgomery in Introduction to Statistical Quality Control, an underlying assumption of the process capability ratios “is that their usual interpretation is based on a normal distribution of process output.” Click the name of the index at left to view information about it on the right.   Cp • •

• •

Cp measures the ratio between the specification tolerance (USL-LSL) and process spread. A process that is normally distributed and is exactly mid-way between the specification limits would yield a Cp of 1 if the spread is +/- 3 standard deviations. A generally accepted minimum value for Cp is 1.33 – this differs by industry, but the larger the number the better. Limitations to this index include its requirements for both an upper and lower specification and is used once the process is centered.

  Cpk • • • •

Cpk measures the absolute distance of the mean to the nearest specification limit. Generally speaking, a Cpk of at least 1 is required and over 1.33 is desired, but this differs for industries. Cpk takes into account the centering process, unlike Cp. Together with Cp, Cpk provides a common measurement for assigning an initial process capability to center on specification limits.

 

470

Introducing Process Capability Indices

Six Sigma Black Belt | Measure | Analyzing Process Capability Task: Introducing Process Capability Indices

Pp • • •

Pp measures the ratio between the specification tolerance and process spread. Pp helps to measure improvement over time (as do Cp and Cpk) Pp signals where the process is in comparison to the customer's specifications (as does Cp and Cpk)

  Ppk • • •

Ppk measures the absolute distance of the mean to the nearest specification limit. Ppk provides an initial measurement to center on specification limits. Ppk examines variation within and between subgroups.

  Cpm • • • • • •

Cpm is also referred to as the Taguchi index. This index is touted by some to be more accurate and reliable than the other indices. Cpm is based on the notion of reducing the variation from a target value (T). T represents the target – in this index, T receives more focus than the specification limits. Variation from the target T is expressed as process variability or σ2and process centering (µ - T), where μ = process average. Cpm provides a common measurement assigning an initial process capability to a process for aligning the mean of the sample to the target.

  Note: The use of these indices and equations varies by industry and author.

471

Using Cp

Six Sigma Black Belt | Measure | Analyzing Process Capability Concept: Using Cp

Use When • • •

identifying the process's current state. measuring the actual capability of a process to operate within customer defined specification limits. the data set is from a controlled, continuous process.

Information Needed • • •

Standard deviation/Sigma (estimated from control charts or other process information) USL and LSL (specifications) Normal probability distribution knowledge

 

472

Tips for Cp

Six Sigma Black Belt | Measure | Analyzing Process Capability Concept: Tips for Cp

User Tips • • • • • • •

•

Cp only tells the amount of variation that is in the process. Cp does not tell about the process's ability to align with the target (centered on the customer requirement; this is Cpk's function). Cp requires upper and lower spec limits. For Cp - Think about firing a rifle at a target and 10 rounds are together in a 2 inch circle (very little variation). Cp measures "can it fit" while Cpk measures "does it fit." If Cp = Cpk, the process is centered. Cp desired values vary by industry, but some general guidelines may include: ° The higher, the better ° If greater than 1.33, the process is generally considered capable ° If between 1.00 and 1.33, the process may be capable but controls may be necessary ° If less than 1, the process is generally considered incapable Data must be continuous and from a process that is under relative control or stable.

473

Using Cpk

Six Sigma Black Belt | Measure | Analyzing Process Capability Concept: Using Cpk

Use When • •

you have a data set from a controlled, continuous process. Cpk does tell about the process's ability to align with the target (centered on the customer requirement).

Information Needed • • • • •

Continuous data Standard deviation/Sigma (estimated from a control chart or other process information) Customer specifications (USL and LSL) Calculate the mean of the process and use this to calculate the distance from the nearest spec (DNS) Test for normality of the probability distribution

User Tips • • • • • • • •

If Cpk = Cp, the process is centered. Generally speaking, the larger the value, the better. Data must be continuous from a controlled or stable process. Calculate Sigma from data collected from control charts or other process information. Calculate DNS. Decide which spec is the process center nearest (USL or LSL). DNS = Mean - LSL or the UPS - mean. The lesser of the two values is used from the following equations.

474

Calculating Cp and Cpk

Six Sigma Black Belt | Measure | Analyzing Process Capability Concept: Calculating Cp and Cpk

To calculate Cp: •

the tolerance band (USL - LSL) is divided by the process spread.

Example X = 10, Sigma = 1, and Specifications = 10 +/- 4 Cp = (14 - 6) / 6(1) Cp = 8 / 6 Cp = 1.33

To calculate Cpk: •

subtract X value from the nearest spec limit, then divide the value by 3 sigma

Example X = 10, Sigma = 1, and Specifications = 10 +/- 4 For USL: Cpk = (14 - 10) / 3 Cpk = 4 / 3 Cpk = 1.33 For LSL: Cpk = (10 - 6) / 3 Cpk = 4 / 3 Cpk = 1.33 When Cp = Cpk, the process is centered. Using these examples as a model, calculate Cp and Cpk for each of the 2 previously-created process capability diagrams. To check your answer, roll over Page Resources and click the appropriate example.

475

Calculation Answer #1

Six Sigma Black Belt | Measure | Analyzing Process Capability | Calculating Cp and Cpk Example: Calculation Answer #1

To calculate Cp, the tolerance band (USL - LSL) is divided by the process spread. Given: X = 7, Sigma = 1, and Specifications = 10 +/- 4 Cp = (14 - 6) / (10 - 4) Cp = 8 / 6 Cp = 1.33   To calculate Cpk, subtract X value from the nearest spec limit, then divide the value by 3 sigma Given: X = 7, Sigma = 1, and Specifications = 10 +/- 4 Cpk = (7 - 6) / 3 Cpk = 1 / 3 Cpk = 0.33

476

Calculation Answer #2

Six Sigma Black Belt | Measure | Analyzing Process Capability | Calculating Cp and Cpk Example: Calculation Answer #2

To calculate Cpk, the tolerance band (USL - LSL) is divided by the process spread. Given: X = 10, Sigma = 0.5, and Specifications = 10 +/- 1 Cp = (11 - 9) / (11.5 - 8.5) Cp = 2 / 3 Cp = 0.67   To calculate Cpk, subtract X value from the nearest spec limit, then divide the value by 3 sigma Given:X = 10, Sigma = 0.5, and Specifications = 10 +/- 1 Cpk = (11 - 10) / 1.5 Cpk = 1 / 1.5 Cpk = 0.67   Note: Process variations are too great when both Cp and Cpk are less than 1.  

477

Cp Check

Six Sigma Black Belt | Measure | Analyzing Process Capability Concept: Cp Check

Arrange the 3 graphs from lowest Cp value to highest. Click and hold the graph and then drag into the appropriate answer box. [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

478

Using Pp

Six Sigma Black Belt | Measure | Analyzing Process Capability Concept: Using Pp

Use When • •

the type of data collected is continuous. the process is not in control (as shown by process control charts or other process information).

Information Needed • • • •

Continuous data Standard deviation/sigma (generated by using actual data, not estimated) Upper and lower specification limits Normal probability distribution knowledge

User Tips • • •

Pp tells the amount of variation, but not alignment to the target (that's Ppk). Estimate sigma from data collected from control charts or other process information. To be in control, a process must only have common causes for each of the data points (no data points existing beyond the UCL or LCL).

479

Sigma and Process Capability

Six Sigma Black Belt | Measure | Analyzing Process Capability Concept: Sigma and Process Capability

When means and variances wander over time, a standard deviation (symbolized by the Greek letter σ) is the most common way to describe how data in a sample varies from its mean. A Six Sigma goal is to have 99.99976% error-free work (reducing the defects to 3.4 per million). By computing sigma and relating to a process capability index such as P pk, you can determine the number of nonconformances (or failure rate) produced by the process. To compute sigma (σ), use the following equation for a population:

Where: • N = number of items in the population • X is the mean of the population data • x is each data point To use the equation: • For each value x, calculate the difference between X (the mean) and x • Calculate the squares of these differences • Find the average of the squared differences (by dividing by N) – this equals the •

variance σ2 Compute the square root of the variance to obtain sigma

480

Using Ppk

Six Sigma Black Belt | Measure | Analyzing Process Capability Concept: Using Ppk

Use When • •

the type of data collected is continuous. the process is not in control (as shown by process control charts or other process information).

Information Needed • • • • • •

Continuous data Sample size number X and R-chart information Standard deviation/Sigma (calculated by using actual data, not estimated) USL and LSL Normal probability distribution knowledge

User Tips • •

Ppk tells alignment to the USL and LSL (not the amount of variation). Calculate sigma from actual data.

481

Using Cpm

Six Sigma Black Belt | Measure | Analyzing Process Capability Concept: Using Cpm

Use When • •

the target is not the center or mean of the USL - LSL. establishing an initial process capability during the Measure phase.

Information Needed • • • • •

Value of the target Continuous data Sample size number Standard deviation (sigma) calculated with actual data, not estimated Normal probability distribution knowledge

Where: • T = target value • μ = expected value • σ = standard deviation  

User Tips • •

Cpm is computed from data when the target spec is NOT the mean of the USL-LSL data. The higher the Cpm value, the more likely the process will produce output meetings the specs and the target.

482

Calculating Cpm

Six Sigma Black Belt | Measure | Analyzing Process Capability Concept: Calculating Cpm

To calculate Cpm: •

divide Cp by the square root of the quantity1+(X-target)2divided by standard deviation squared.

Example X = 10, Sigma = 1, and Specifications = 10 +/- 4

Using this example as a model, calculate Cpm for each of the two previously created process capability diagrams. To check your answer, roll over Page Resources and click the appropriate example.

483

Calculation Answer #1

Six Sigma Black Belt | Measure | Analyzing Process Capability | Calculating Cpm Example: Calculation Answer #1

Given: X = 7, Sigma = 1, and Specifications = 10 +/- 4 Cp = (14 - 6) / (10 - 4) Cp = 8 / 6 Cp = 1.33 Cpm = Cp / square root of 1 + (X - target)2 / standard deviation2 Cpm = 1.33 / square root of 1 + (7 - 10)2 / 12 Cpm = 1.33 / square root of 1 + 9 / 1 Cpm = 1.33 / 3.1623 Cpm = 0.421

484

Calculation Answer #2

Six Sigma Black Belt | Measure | Analyzing Process Capability | Calculating Cpm Example: Calculation Answer #2

Given: X = 10, Sigma = 0.5, and Specifications = 10 +/- 1 Cp = (11 - 9) / (11.5 - 8.5) Cp = 2 / 3 Cp = 0.67 Cpm = Cp / square root of 1 + (X - target)2 / standard deviation2 Cpm = 0.67 / square root of 1 + (10 - 10)2 / 0.52 Cpm = 0.67 / square root of 1 / 1 Cpm = 0.67 / 1 Cpm = 0.67

485

Non-Normal Data Transformations

Six Sigma Black Belt | Measure | Analyzing Process Capability Concept: Non-Normal Data Transformations

In the real world, data does not always fit a normal distribution. Since the process capability indices are based on normal distributions, a method is needed to transform non-normal data. Such transformation is usually achieved with the help of logarithms. While statistical software is helpful in making this data conversion, one example of an equation used to transform non-normal data is the following Box-Cox power transformation, where values of Y are transformed to the power of λ (lambda) (i.e., Yλ ). This relationship has the following characteristics: λ = -2

Y transformed = 1/Y2

λ = -0.5

Y transformed = 1/√Y

λ=0

Y transformed = ln (Y)

λ = 0.5

Y transformed = (√Y)

λ=2

Y transformed = Y2

A logarithm is then selected to apply to the data using the following function: Where: • x(λ) = (xλ - 1) / λ where λ ≠ 0 •

x(λ) - ln(x) where λ = 0

Where the mean of the transformed data is equal to:

 

486

Short-term Capability

Six Sigma Black Belt | Measure | Analyzing Process Capability Concept: Short-term Capability

Process capability may be examined as both short-term and long-term capability. Short-term capability is measured over a very short time period since it focuses on the machine's ability based on design and quality of construction. By focusing on one machine with one operator during one shift, you will limit the influence of other outside long-term factors, including: • operator • environmental conditions such as temperature and humidity • machine wear • different material lots Thus, short-term capability can measure the machine's ability to produce parts with a specific variability based on the customer's requirements. Short-term capability uses a limited amount of data relative to a short time and the number of pieces produced to remove the effects of long-term components. If the machines are not capable of meeting the customer's requirements, changes may have a limited impact on the machine's ability to produce acceptable parts. Remember, though, that short-term capability only provides a snapshot of the situation. Since short-term data does not contain any special cause variation (such as that found in long-term data), short-term capability is typically rated higher.

487

Converting Process Capability to PPM

Six Sigma Black Belt | Measure | Analyzing Process Capability Concept: Converting Process Capability to PPM

Tables exist transposing different capability indexes into parts per million of nonconformance. For example:

 

488

Lesson Summary

Six Sigma Black Belt | Measure Summary: Lesson Summary

Measure is about measuring what is measurable - data - data to be identified, collected, described, and displayed. Different types of data (variable and attribute) undergo different analyses.  As Phillip Crosby stated, "Quality measurement is effective only when it is done in a manner that produces information that people can understand and use." A sound sampling technique assures data accuracy and integrity. Different probability distributions as normal, Poisson, binomial, and chi-square describe the data that leads the team down the hypothesis testing roadmap during Analyze. Tools such as stem-and-leaf plots, box-and-whisker plots, run charts, scatter diagrams, Pareto charts, histograms, and probability plots depict relationships between data. Repeatability and reproducibility (Gauge R&R) correlations, linearity, percent agreement, precision and tolerance are tools for measuring or assessing the capability of the people involved in the process. By discovering if the people are consistently performing up to the standards and expectations, these tools help pinpoint problem areas and training issues. Process capability studies link the voice of the customer to the voice of the process. The customer sets the target and specification limits while the provider measures the process's results and compares it to the customer's expectations. Process performance indices such as Cp, Cpk, Pp, Ppk, and Cpm, are numerical values indicating where the process lies in terms of targets, specifications, and sigma levels.

489

Lesson Bibliography

Six Sigma Black Belt | Measure Concept: Lesson Bibliography

American Society for Quality. ASQ’s Foundations in Quality Learning Series: Certified Manager of Quality/Organizational Excellence. Milwaukee, WI: ASQ, 2005. American Society for Quality. ASQ’s Foundations in Quality Learning Series: Certified Quality Engineer. Milwaukee, WI: ASQ, 2000. American Society for Quality. Six Sigma Green Belt Certification Preparation Course, Version 1 (web-based course). Milwaukee, WI, 2006. Breyfogle, Forrest W. III. Implementing Six Sigma: Smarter Solutions® Using Statistical Methods. 2nd ed. Hoboken, NJ: John Wiley and Sons, Inc., 2003. Galloway, Dianne. Mapping Work Processes. Milwaukee, WI: ASQ Quality Press, 1994. Griffith, G.K. The Quality Technician's Handbook. 3rd ed. Englewood Cliffs, NJ: Prentice Hall, 1996. Keller, Paul.Six Sigma Demystified. New York, NY: McGraw-Hill, 2005. Lowenthal, Jeffrey N. Defining and Analyzing a Business Process: A Six Sigma Pocket Guide. Milwaukee, WI: ASQ Quality Press, 2003. Montgomery, Douglas. Introduction to Statistical Quality Control. 5th ed. Hoboken, NJ: John Wiley & Sons, Inc., 2005. Pyzdek, Thomas. The Six Sigma Handbook: A Complete Guide for Green Belts, Black Belts, and Managers at All Levels, 2nded. New York: McGraw-Hill, 2003. Smith, G.M.Statistical Process Control and Quality Improvement. Upper Saddle River, NJ: Prentice-Hall, 2001.  

490

Six Sigma Black Belt Analyze

Lesson Introduction

Six Sigma Black Belt | Analyze Introduction: Lesson Introduction

Once the Measure Phase has been completed, it is now time to move into the Analyze phase and begin exploratory data analysis. The primary focus of analysis is to begin to closely examine our output (Y) to understand the variables or inputs (Xs) and their effects. The Black Belt's responsibility is to gather the Xs identified in the Measure phase and perform analysis to narrow the Xs from possible to probable. To better understand this concept, the ASQ Body of Knowledge provides the following topics: Exploratory data analysis • Use multi-vari studies to interpret the difference between positional, cyclical and temporal variation. • Design sampling plans to investigate the largest sources of variation. • Create and interpret multi-vari charts. • Calculate the regression equation. • Apply and interpret hypothesis tests for regression statistics. • Use the regression model for estimation and prediction, and analyze the uncertainty in the estimate. • Calculate and interpret the correlation coefficient and its confidence interval. • Apply and interpret a hypothesis test for the correlation coefficient. • Understand the difference between correlation and causation. • Analyze residuals of the model. Hypothesis testing • Define, compare and contrast statistical and practical significance. • Apply and interpret the significance level, power, type I and type II errors of statistical tests. • Understand how to calculate sample size for any given hypothesis test. • Define and interpret the efficiency and bias of estimators. • Compute, interpret and draw conclusions from statistics such as standard error, tolerance intervals and confidence intervals. • Understand the distinction between confidence intervals and prediction intervals. • Apply hypothesis tests for means, variances, and proportions and interpret the results. • Define, determine applicability, apply and interpret paired-comparison parametric hypothesis tests. • Define, determine applicability, apply and interpret chi-square tests. • Define, determine applicability, apply and interpret ANOVAs. • Define, determine applicability and construct a contingency table and use it to determine statistical significance • Define, determine applicability and construct various non-parametric tests including Mood's Median, Levene's test, Kruskal-Wallis and Mann-Whitney.

492

Lesson Overview

Six Sigma Black Belt | Analyze Introduction: Lesson Overview

The tools and objectives of the Analyze phase are illustrated below.

 

493

Six Sigma Black Belt Analyze Exploratory Data Analysis

Learning Objectives

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Learning Objectives

At the end of this Analyze topic, all learners will be able to: • use multi-vari studies to interpret the difference between positional, cyclical and temporal variation. • design sampling plans to investigate the largest sources of variation. • create and interpret multi-vari charts. • calculate the regression equation. • apply and interpret hypothesis tests for regression statistics. • use the regression model for estimation and prediction and analyze the uncertainty in the estimate. • calculate and interpret the correlation coefficient and its confidence interval. • apply and interpret a hypothesis test for the correlation coefficient. • understand the difference between correlation and causation.     Portions of this topic were taken from the ASQ Six Sigma Green Belt web-based Certification Preparation Course.

495

Multi-vari Studies

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Multi-vari Studies

Data can be grouped in terms of sources of variation to help define the way measurements are partitioned. These sources describe characteristics of populations, and the following are common types that describe our everyday processes: • Classifications (by category) • Geography (of a distribution center or a plant) • Geometry (chapters of a book or locations within buildings) • People (tenure, job function or education) • Time (deadlines, cycle time or delivery time) We can stratify the data to help us understand the way our processes work by categorizing the individual measurements. This helps us understand the variation of the components as it relates to the whole process. For example, errors are being tracked in a process. The variation could be within a subgroup (within a certain batch), between subgroups (from one batch to another batch) or over time (time of day, day of week, shift or even season of the year).

496

Multi-vari Charts

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Multi-vari Charts

A Multi-vari chart is a tool that graphically displays patterns of variation and the stability or consistency of a process. It is used to identify possible Xs or families of variation in the preliminary stages of data analysis. Multi-vari charts categorize data as positional (within a subgroup), cyclical (between subgroups) and temporal (over time). You can also detect differences in the inputs (Xs) by using two diagrams presented in the Measure lesson of this course: • boxplots (e.g., box-and-whisker plots) when the (Y) is continuous and the (Xs) are discrete • scatterplots (e.g., scatter diagrams) when the (Y) is continuous and the (Xs) are also continuous

497

Boxplot Question

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Question: Boxplot Question

Temporal VariationThe number of errors produced (Y) is plotted on the y axis, and the shift (X) is the category plotted on the x axis. What can you tell from this boxplot? After making your selection, click the Ready button to see if you are correct.  

A. No relationship B. Median errors are highest for the 1st shift. C. 1st shift and 3rd shift may be statistically different. D. Median errors are lowest for the 3rd shift.

498

Scatterplot Question

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Question: Scatterplot Question

Cyclical VariationThe number of errors produced (Y) is plotted on the y axis, and the years of experience of operator (X) are plotted on the x axis. Is there a relationship between the number of errors produced and years of operator experience?

A. No relationship B. Moderate linear relationship C. Strong positive linear relationship D. Strong negative linear relationship

499

Sources of Variation

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Task: Sources of Variation

Multi-vari analysis is a tool that graphically displays variation in categories. Click each category below to learn more. Positional See also: within-part variation Within a subgroup or sample set: refers to variation of a characteristic on the same product such as part thickness, data entry on a form, pages of a document, etc.

Cyclical See also: part-to-part variation Refers to variation between subgroups or from sample to sample. Some examples are call center, sales region, processing center, staff member, etc.

500

Sources of Variation

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Task: Sources of Variation

Temporal Refers to variation in change over time, either as time on a clock/calendar or duration. Some examples are season of the year, time of day, day of week, cycle time, shift, etc.

 

501

Design Types

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Task: Design Types

The two most common designs of categorical variation are nested and crossed, with nested being the most typical. Click each design type to learn more. Nested In this type of design, one source of variation is found within or nested in another such as positional, cyclical and temporal. An example of nested design variation is given below using a loan documentation package comparing all categories together: • Within subgroup or sample set (positional): gathering data about the specific fields on a page of the form • Between subgroups or from sample to sample (cyclical): tracking data entry errors produced by loan processing associates • Over time (temporal): tracking data entry errors produced by loan processing associates by peak production times of the day Crossed In this type of design, the sources of variation can be manipulated independently, placing it in distinct order to reveal patterns. This type of design helps to identify interactions between the independent variables. An example of crossed design variation using a loan documentation package is: • positional: comparing data entry fields on two different pages of the loan documentation form. • cyclical: comparing data entry errors for two different loan processing centers. • temporal: comparing data entry errors for different days of the week.

502

Variation Question

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Variation Question

Shown below are boxplots depicting positional, cyclical and temporal variations, which are helpful in the preliminary data analysis to show early relationships and to focus and prioritize time and effort. Match each variation term to its corresponding graph by dragging the term to the box underneath the correct graph. [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

503

Multi-vari Sampling

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Multi-vari Sampling

Multi-vari analysis uses sources of variation to stratify the data to begin to turn the possible Xs into the probable Xs. Multi-vari analysis helps narrow the focus and serves as a point where we begin to gather samples to determine if the probable Xs are statistically significant.  A sampling plan is critical in investigating the largest sources of variation. Sampling plans should be designed in such a way that the resulting data will contain a representative sample of the parameters of interest. Please review each step on the following page to learn more about sampling.  

504

Multi-vari Sampling Steps

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Task: Multi-vari Sampling Steps

Click each step below to learn more about multi-vari sampling. 1. Select the process and variables to analyze. Reducing the return mail volume is a project of interest for process improvement. Reducing the return mail volume by 50% will increase the through-put accuracy of items mailed with correct addresses by the end of year 2006 and bring the company into compliance with USPS discount requirements. During the period between April and June 2006, the return mail volume for the Consumer Lending Department was 12,929 items representing 31.4% of the total return mail volume for the bank. Cost of poor quality (COPQ) elements have been identified as manual handling, overtime, rework, labor, equipment utilization, and postage totaling $125,693.00. The project objective is to reduce the Consumer Lending Department return mail items by 20% by the end of year 2006. The variables to be analyzed are: Time • Day of the week: Does the day of the week make a difference? • Week of the month: Does the week of the month make a difference? Classification • Product type: Does the product type make a difference, such as a lease, auto loan, home equity loan, etc? • Geography • Physical location: Does the building location make a difference?      2. Select the sample size and duration. The sample size required to be statistically significant with alpha = 0.05 and a target power of 0.90 = 10. 3. Record observation information. Based on the sample size necessary to achieve the desired level of significance, data were tracked for one week using check sheets to be completed by mailroom staff to track the respective variable information by shift.

 

505

Multi-vari Sampling Steps

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Task: Multi-vari Sampling Steps

4. Plot the data points. Create a boxplot for interpretation (shown in next step). 5. Analyze the graph for variation. The variances of building A and B appear to be different.

  6. Conduct further analysis. Additional analysis on the buildings will be conducted to find out why the return mail volumes are different. 7. Repeat multi-vari studies. Improvements have been implemented and one month has passed.  Shown below are boxplots reflecting return mail volume for buildings A and B.  Based on these graphs, the variances of building A and B are roughly the same.

506

Multi-vari Studies Exercise

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Multi-vari Studies Exercise

[ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

507

Regression and Correlation Introduction

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Regression and Correlation Introduction

In Six Sigma projects where the input and output variables are both continuous and we want to see if there is a relationship between the two variables, we use statistical tools called regression and correlation.  

 

508

Simple Linear Regression Introduction

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Simple Linear Regression Introduction

Regression is the analysis of relationships between variables. In regression, the relationships of the variables are expressed in the form of an equation. This allows for the prediction of the dependent variable (Y) to one or more independent variables (Xs). Linear regression analysis addresses the dual tasks of finding the best-fit relationships and testing for correlations in the data that indicate a linear relationship between the variables. This analysis defines the Xs that drive the Y in the equation to be controlled : Y = f (X1, X2, ...Xn) + e Simple Regression Equation y = β0 + β1x Linear Regression Definitions The independent variable is the variable over which we have control. The dependent variable is the variable that results from the adjustment or change in the independent variable.The dependent variable is often referred to as the response. This change is usually done to improve the result. The coefficients are those expressions in the equation that define the mathematical relationship between the independent and dependent variables. For example, b0 and b1 are the coefficients in the following expression: The hat symbol (^) is used to denote estimated and predicted values. Two types of coefficients in simple linear regression are the intercept and the slope: • The intercept  is the value of y when x is zero. It is denoted as the estimate b0. •

The population parameter for the intercept is β0. The slope is the amount of increase (or decrease) in y (rise) over a specific increase in x (run). This is denoted as the estimate b1. The population parameter for the slope is β1.

Ho: b1= 0 (Coefficient not significant)

A low p-level for this test, typically (< 0.05), means there is evidence to believe that the slope of the line is not 0.

Ha: b1≠ 0 (Coefficient significant)

     

509

Simple Linear Regression Equation

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Simple Linear Regression Equation

For the purpose of this course, the regression equation will be calculated starting with the mathematical equation for a straight line: y = b0 + b1 X , where b0 is the y intercept when X = 0 and b1 is the slope of the line. We assume for any given value of X, the observed value of Y varies in a random manner and possesses a normal probability distribution. This concept is depicted in the following diagram:

510

Method of Least Squares

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Method of Least Squares

The method of least squares is a statistical procedure to find the best-fit line that minimizes the sum of squares of the deviations of the observed values of Y from those predicted. This formalizes the scatter plot or fitted line plot procedure when plotting (X) and (Y) data on a graph. After plotting the data, use a ruler to pass through the majority of the points providing what is considered the best-fit line. The data are evaluated against the line to see obvious deviations of the data from the line. Least square estimator equations    

511

Best-Fit Line Exercise

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Best-Fit Line Exercise

  [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

512

Fitted Line Plot Exercise

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Fitted Line Plot Exercise

A jewelry store wants to ascertain the relationship between the number of repairs and the amount of time required to repair an item. A plot of this relationship is shown below. Drag the "best-fit" term to the plot depicting the "best-fit" simple regression line. [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

513

Simple Linear Regression Example

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Simple Linear Regression Example

The customer change request process within the corporate account department is a project of interest for process improvement. The department manager wants to find the relationship between the number of change requests processed per month and the cost per transaction.  

        Sum Avg x, y

Change Cost per Requests (X) Transaction (Y) 1 0.35 4 0.39 5 0.40 6 0.41 16 1.55 4 0.3875

X2

Y2

(X)(Y)

1 16 25 36 78  

0.1225 0.1521 0.1600 0.1681 0.6027  

0.35 1.56 2.00 2.46 6.37  

What are the prediction equation and results?

514

Simple Linear Regression Calculation

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Simple Linear Regression Calculation

Step 1: Perform the calculations  

515

Simple Linear Regression Prediction Equation

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Simple Linear Regression Prediction Equation

Step 2: Determine the prediction equation We may now predict (y) for a given value of (x) using the equation for a straight line: Step 3: Determine results With the above equation, we can predict the cost per transaction based on the number of customer change requests. If there are two customer change requests, the cost per transaction is 0.3389 + (0.0121) (2) = 0.363 or approximately $0.36.              

516

Uncertainty in the Estimate

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Uncertainty in the Estimate

Uncertainty in the Estimate The prediction quality of the regression equation estimates the standard deviation of the error Se, given by the formula: Looking at the simple regression example of the cost per transaction based on the number of customer change requests:

Given α =.05, the Z number for 0.95 (1-α) is 1.96. Approximately 95% of the population of the data points lie within 1.96(0.00656) = 0.013 of the regression line.

517

Simple Linear Regression Hypothesis Testing

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Simple Linear Regression Hypothesis Testing

Hypothesis tests can be applied to determine whether the independent variable (x) is useful as a predictor for the dependent variable (y). The following are the steps using the cost per transaction example for hypothesis testing in simple regression: Step 1: Determine if the conditions for the application of the test are met. • There is a population regression equation Y = β0 + β1 so that for a given value of x, the prediction equation is

• • •

Given a particular value for x, the distribution of y-values is normal. The distributions of y-values have equal standard deviations. The y-values are independent.

Step 2: Establish hypotheses.  Ho: b1 = 0 (the equation is not useful as a predictor of y - cost per transaction)  Ha: b1 ≠ 0 (the equation is useful as a predictor of y - cost per transaction) Step 3: Decide on a value of alpha. Let α = 0.05.  

518

Hypothesis Testing T-Values

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Hypothesis Testing T-Values

Step 4: Find the critical t values. Use the t – table and find the critical values with +/- tα/2 with n – 2 df. Roll over Page Resources at the bottom of the screen and click T-table. Look in the t0.025 column under 2 df (4 samples – 2). The critical values are 4.303 and -4.303. Step 5: Calculate the value of the test statistic t. The confidence interval formula is used to determine the test statistic t:

 

519

Hypothesis Testing Interpreting Results

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Hypothesis Testing Interpreting Results

Step 6: Interpret the results. If the test statistic is beyond one of the critical values: • greater than tα/2 OR •

less than  -tα/2

reject the null hypothesis; otherwise, do not reject. tcalc > tcritical = 6.91 > 4.303; therefore, we reject the null hypothesis. At a significance level of 0.05, the data support the conclusion that the prediction equation is useful for predicting the cost per transaction for a given number of change requests.

520

Simple Linear Regression Question

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Simple Linear Regression Question

The following is a simple linear regression problem for you to complete.  When finished, roll over Page Resources at the bottom of the screen and click Regression Answer to see if you are correct. A manager of a retail store wants to find the relationship between the number of boxes shipped and the number of items damaged.  A random sample of six shipments is selected and the data have been recorded as follows:   Boxes Shipped (X)

Items Damaged (Y)

X2

Y2

(X)(Y)

  18

2

324

4

36

  23

1

529

1

23

  41

3

1681

9

123

  35

1

1225

1

35

  27

1

729

1

27

  39

2

1521

4

78

S 183 u

10

6009

20

322

A 30.5 v g

1.7

 

 

,

What is the prediction equation?

521

 

Regression Answer

Six Sigma Black Belt | Analyze | Exploratory Data Analysis | Simple Linear Regression Question Example: Regression Answer

We may now predict (y) for a given value of (x) using the equation for a straight line:

With the above equation, we can predict the number of items that are damaged based on the number of boxes shipped. If there are 30 boxes shipped, the number of damaged items is 0.486 + (0.0398) (30) = 1.68.    

         

522

Multi. Linear Regression Introduction

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Multi. Linear Regression Introduction

Multiple linear regression expands on the simple linear regression model to allow for more than one independent or predictor variable. The general form for the equation is: y = b0 + b1x + ... bn+ e Where: • (b0,b1,b2 …) are the coefficients and are referred to as partial regression coefficients. The equation may be interpreted as the amount of change in y for each unit increase in x (variable) when all other xs are held constant. The hypotheses for multiple regression are: • Ho: b1 = b2 = ... = bn •

Ha: b1 ≠ 0 for at least one i

 

523

Coefficient of Determination

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Coefficient of Determination

Coefficients are estimated by minimizing the sum of squares (SS) residuals. The coefficients follow a t-distribution, which allows us to use t-tests to assess their significance. The coefficient of determination, R2, or multiple regression coefficient, is the proportion of variation in Y that can be explained by the regression model and is the square of r. In multiple regression, R2adj (adjusted value) represents the percent of explained variation when the model is adjusted for the number of terms in it. Ideally, R2 should be equal to 1, indicating that all of the variation is explained by the regression model. 0 ≤ R2 ≤1 Related to the coefficient of determination is the correlation coefficient, which ranges from -1 ≤ r ≤ 1 and determines whether there is a positive or negative correlation in the regression analysis, where r is the coefficient of correlation determined by sample data and an estimate of ρ (rho), the population parameter.

524

Coefficient of Determination Equation

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Coefficient of Determination Equation

R2 Equation R2= SSregression / SStotal = (SStotal – SSerror) / SStotal = 1- [SSerror / SStotal] Where SS = the sum of squares R2adj Equation R2adj = 1- [SSerror / (n – p)] / [SStotal  / (n -1)] Where: • n = number of data points • p = number of terms in the model including the constant Unlike R2, R2adj can become smaller when added terms provide little new information and as the number of model terms gets closer to the total sample size. Ideally, R 2adj should be maximized and as close to R2 as possible.  

525

Multi. Linear Regression Example

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Multi. Linear Regression Example

Software programs are normally used to calculate the partial regression coefficients of multiple regression. For the purpose of this course, R2adj will be the focal point so that a clear understanding of this value is evident in interpreting the results.

Example The following is an example of multiple regression building upon the simple regression model as seen previously using the data captured from a computer output session window: The manager of a commercial account department wants to find the relationship between cost per transaction and a set of predictor variables believed to be related to the cost. The terms are: • Y: Cost per transaction • X1: System issues • •

X2: Change requests X3: Exception processing

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Multi. Linear Regression Example Equation

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Multi. Linear Regression Example Equation

Data from 29 runs are collected and shown in the table below: Predictor

Coefficient

t Stat

P value

389.17 2.123

Standard Error 66.09 1.214

Constant (Y) X1 system issues X2 change requests X3 exception processing

5.89 1.75

0.000 0.092

5.3185

0.9629

5.52

0.000

-24.132

1.869

-12.92

0.000

S = 8.59782   R2 = 87.4%   R2 adj = 85.9%  The regression equation is: Y = 389.17 + 2.123 X1 (system issues) + 5.3185 X2 (change requests) - 24.132 X3  exception processing Results Looking at R2adj, it would appear 85.9% of the variation in Y is explained by this regression model. However, variable X1 (system issues), is not significant because the p-value = 0.092 which is > 0.05. The following page displays the analysis of variance multiple regression data table.

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Multi. Linear Regression Example ANOVA

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Multi. Linear Regression Example ANOVA

Analysis of Variance Table Multiple Regression Source

DF (degrees of freedom) Regression 3 Residual 25 Error Total 28

SS (sum of MS (mean F statistic P value squares) square error) 12833.9 4278.0 57.87 0.000 1848.1 73.9     14681.9

 

 

 

As seen in the previous page's data table, not all terms were significant (> 0.05). Eliminate X1 (system issues) from the equation and refit the regression model using three terms: • Constant (Y) • X2 change requests •

X3 exception processing

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Multi. Regression Example Model Refit

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Multi. Regression Example Model Refit

Predictor

Coefficient

t stat

P value

483.67 4.7963

Standard Error 39.57 0.9511

Constant Y X2 change requests X3 exception processing

12.22 5.04

0.000 0.000

-24.215

1.941

-12.48

0.000

S = 8.93207   R2 = 85.9%   R2adj = 84.8% The regression equation is now: Y = 483.67 + 4.7963 X2 (change requests) – 24.215 X3 (exception processing) Analysis of Variance Source

DF (degrees SS (sum of of freedom squares) 12607.6 2074.3

MS (mean F stat square error term) 6308.8 79.01 79.8  

Regression Residual Error Total

2 26 28

0.000  

14681.9

 

 

 

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P value

Multi. Linear Regression Example Results

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Multi. Linear Regression Example Results

The value, R2adj, as seen in the data output table on the previous page adjusts the R2 coefficient by the number of terms in the regression model. In this example, it would appear that 84.8% of the variation in Y is explained by this regression model. Shown below is the calculation of the R2adj equation using the data from the data output table: R2adj = 1- [SSerror / (n – p)] / [SStotal  / (n -1)] = 1 – [2074.3 / (29-3)] / 14681.9 / (29-1)] = 0.848  

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Regression User Tips

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Task: Regression User Tips

Click each user tip below for helpful information about regression. User Tip #1 Using the regression equation to predict a value of the dependent variable outside the range of the independent variable is not recommended since you have no evidence that the same linear relationship exists outside the observed range. For example, think about the relationship between a person’s height to age. Early on, it would seem that as age increases so does height.  Using that data to predict height past the age of 16 would indicate that you would be 10 feet tall at some point! User Tip #2 Many different relationships between Xs and Y can yield similar mathematical results. Plot the data points by hand or by using a statistical software program before interpreting any regression statistics. Linear regression is only appropriate for data that can be plotted in an approximately straight line.

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Simple Linear Correlation Introduction

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Simple Linear Correlation Introduction

Correlation measures the linear association between two variables. Correlation is important because it tells us if a relationship between variables exists. As the inputs and outputs are reviewed during the process, we can determine which of the inputs (Xs) have significant impact on the output (Y). Correlation is commonly measured by the correlation coefficient r, and the formula is:

 

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Correlation Coefficient

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Correlation Coefficient

Correlation does not imply causation. Do not assume that a scatter plot pattern means the two variables are related. It is likely that there is a correlation but possibly not causation. The correlation tool does not establish causation. Relationships over a wider range of data or a different portion of the range of data may exist. For example, there is a strong association between increased income and age or seniority. Do not assume that your income will increase because you are older or because you have more experience or seniority.

The correlation coefficient ranges from -1 ≤ r ≤ 1 and determines whether there is a positive or negative correlation in the regression analysis, where r is the correlation coefficient and an estimate of ρ (rho) the population parameter. A related value is the  coefficient of determination, denoted R2, discussed in the previous sub-topic, Simple and Multiple Least-Squares Linear Regression. It is defined as the square of the correlation coefficient and will satisfy the inequality: 0 ≤ R2 ≤ 1  

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Correlation Key Points

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Correlation Key Points

The following are key points about the correlation coefficient, r: Description Correlation coefficient range Positive values Perfect positive correlation Negative values Perfect negative correlation Moderate correlation Strong correlation No linear correlation

Value -1 ≤ r ≤ 1 +r occurs when the value of one variable increases and the other variable increases r = +1 -r occurs when the value of one variable increases and the other variable decreases r = -1 Typically when values of r range from 0.3 to 0.7 Typically when values of r range from 0.7 to 1 r=0

   

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Correlation Testing Conditions

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Correlation Testing Conditions

The following are conditions for correlation testing: • There is a population regression equation y = β0 + β1x so that for a given value of x, the mean of the response variable y is β0 + β1x. • Given a particular value for x, the distribution of y-values is normal. • The distributions of y-values have equal standard deviations. • The y-values are independent.

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Correlation Example Hypotheses

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Correlation Example Hypotheses

The following lists the steps to calculate the correlation coefficient and the t-test statistic: The customer change request process within the corporate account department is a project of interest for process improvement.  From the data that have been collected, the number of change requests processed per month seems to have a relationship to an increased cost per transaction. Given α = 0.05, is there a statistical correlation? Step 1: Establish hypotheses.   Ho: ρ = 0 or No correlation   Ha: ρ ≠ 0 Correlation (two-tail test) (reject values include both tails of the frequency distribution) In addition to ρ ≠ 0, the alternative hypothesis could be either of these: • ρ < 0 for a left-tail test (reject values are in the tail of the frequency distribution less than the critical value) • ρ > 0 for a right-tail test (reject values are in the tail of the frequency distribution greater than the critical value) Step 2: Decide on a value of α.   α = 0.05 was given      

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Correlation Example Data Table

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Correlation Example Data Table

  Change Requests (X)

Cost per Transaction (Y)

X2

Y2

(X)(Y)

  1

0.35

1

0.1225

0.35

  4

0.39

16

0.1521

1.56

  5

0.40

25

0.16

2

  6

0.41

36

0.1681

2.46

S 16 u

1.55

78

0.6027

6.37

A 4 v g

0.3875

 

 

,

 

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Correlation Example Determining Results

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Correlation Example Determining Results

Step 3: Perform the calculations.

 

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Correlation Example Critical T-Values

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Correlation Example Critical T-Values

Step 4: Determine r. Since r = .99, there is a strong positive correlation between customer change requests and cost per transaction.  Step 5: Find the critical t values. Use the T - table and find the critical values: • tα/2,2 and - tα/2,2 for the two-tail test • •

- tα,2 for the left-tail test  tα,2 for the right-tail test

For this example, we will be using the two-tail test. Roll over Page Resources at the bottom of the screen and click T-table. Look in the t-table using n – 2 degrees of freedom (4 -2 = 2 df) and the t0.025 column. The critical values are 4.303 and -4.303.

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Correlation Example Calculated T-Values

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Correlation Example Calculated T-Values

Step 6: Calculate the value of the test statistic t. For a correlation coefficient, the test statistic is:

Step 7: Interpret the results. Reject the null hypothesis if the test statistic is: • Less than - tα/2,2 or greater than tα/2,2 for • •

the two-tail test Less than - tα,2 for the left-tail test Greater than tα,2 for the right-tail test

tcalc > tcritical = 9.93 > 4.303, therefore we reject the null hypothesis (Ha: ρ ≠ 0). At a significance level of 0.05, the data support the conclusion that as the number of customer change requests increases (predictor) so does the cost per transaction (response).  

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Correlation Coefficient Confidence Interval

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Correlation Coefficient Confidence Interval

According to ASQ's Glossary and Tables for Statistical Quality Control, "a confidence interval is an estimate of the interval between two statistics that contains the true value of the parameter with some probability." For a moderately large sample size (n ≥ 25), the 100 (1 – α)% confidence interval on ρ is given by:

Where: • r is the estimate of the correlation coefficient. • ln is the natural logarithm of the quantity in parentheses behind it. • tanh(x)= (ex – e-x)/(ex + e-x) (tanh stands for hyperbolic tangent function:

•

trigonometric mathematical functions related to a hyperbola rather than a circle. Hyperbolic functions include the hyperbolic sine, hyperbolic cosine, hyperbolic tangent, hyperbolic cotangent, hyperbolic secant, and hyperbolic cosecant). Zα/2 is the multiple corresponding to a confidence level of 1 – α found from the standard normal distribution.

Result If 0 is contained in the confidence interval, then we conclude that the true correlation coefficient is not significantly different from 0.  

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Correlation Confidence Interval Example

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Correlation Confidence Interval Example

A random sample of n = 30 observations is made on the time to failure of an electronic component and the temperature at which the component is used. The correlation between the time to failure and the temperature is found to be r = 0.32. We would like to construct the 95% confidence interval on the true correlation coefficient (ρ) and determine if there is a significant correlation between time to failure and temperature. The necessary values for the 95% confidence interval are: Zα/2 = Z0.025 = 1.96

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Correlation Confidence Interval Example Continued

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Correlation Confidence Interval Example Continued

Using the values found above, we can find the left and right sides of the confidence interval:

Therefore, we are 95% confident that the true correlation coefficient lies between –0.0456 and 0.6099. Since 0 is contained in the interval, we conclude that the correlation between time to failure and temperature is not significantly different from 0, that is, there is no significant linear relationship between time to failure and temperature.  

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Correlation Exercise

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Correlation Exercise

  [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

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Diagnostics

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Diagnostics

Residuals In the equations for simple (y = b0+ b1X + e) and multiple linear regression (y = b0 + b 1x + … bn + e), residuals are described as the best estimate of the error term (e) and are the difference between the predicted response variable for any given x and the actual response:

Key assumptions of residuals in regression are: • Normally distributed with a mean of zero • Constant variance • Uncorrelated  

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Residuals

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Residuals

As seen in the following graph, the line is drawn according to the method of least squares. Residuals account for the unexplained in Y after the “best-fit’ line is drawn. Looking at the Y-axis, the residuals are the vertical distance of each individual point from the line.

 

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Residual e-value

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Residual e-value

The prediction equation from the simple regression example shown previously in the Simple and Multiple Least-Squares Linear Regression sub-topic was:

where x was the number of change requests predicting Y, the cost per transaction. Change Requests

1 4 5 6

Cost per Transaction

.35 .39 .40 .41

Predicted Cost per Transaction

.351 .387 .399 .412

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-0.001 0.003 0.001 -0.002

Residual e-value Data Plot

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Residual e-value Data Plot

As you can see from the above image, the lack of data makes it impossible to reach a conclusion about the plotting of the data. Let us take a look at the multiple regression example where other Xs such as system issues and exception processing were also analyzed in addition to change requests.  

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Residual Plots

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Task: Residual Plots

Analysis of residuals is critical in determining if regression is valid. The multiple regression example shows the relationship between cost per transaction and a set of predictor variables. Click each type of residual plot below to see an example of the plot and more information. Normal probability plot

The normal probability plot of the residuals is used to help determine whether the variables display a linear pattern consistent with a normal distribution showing points approximately on a straight line. The normal distribution was discussed in the Measure lesson of this course. This normal probability plot shows an approximately linear pattern consistent with a normal distribution. The two points in the upper-right corner of the plot may be outliers (unnatural patterns). Histogram

A histogram will help indicate if any outliers exist in the data so that they can be eliminated from the data refitting the model. This histogram indicates that outliers may exist in the data, shown by the two bars on the far right side of the plot.

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Residual Plots

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Task: Residual Plots

Residuals versus the fitted values

The plot of residuals versus the fitted values (predictors) shows that the residuals get smaller (closer to the reference line or 0) as the fitted values increase, which may indicate that the residuals have a non-constant variance. Recognizable patterns reflect a consistent variance and indicate that the model may not be valid. The error may not be random if there is a series of increasing or decreasing points or a large number of positive or negative residuals. Residuals versus the order of the data

Residuals are plotted in the order that the data was collected and can be used to find non-random error, especially of time-related effects. If a trend or pattern were evident, it would indicate that there is a time order dependency in the data and that the model might not be valid.  

550

Multicollinearity Diagnostics

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Task: Multicollinearity Diagnostics

Another type of diagnostic available to analyze residuals is the multicollinearity diagnostic, which is used to test dependencies among the Xs. The validity of the regression model depends on the assumption that the Xs are not strongly related. If two or more Xs are correlated with each other that goes against the assumption and the data are considered multicollinear. Click the multicollinearity detection methods shown below to learn more. Correlation coefficient

The correlation coefficient is a common method in detecting collinearity as previously described in the Simple Linear Correlation sub-topic of this lesson. VIF (Variance Inflation Factor)

• • • •

The VIF measures the correlation between an X and other Xs in the regression. VIF measures how much the variance of an estimated regression coefficient increases if the predictors are correlated. ri 2 is close to 1 if xi has a strong relationship with other Xs. Typically, if the VIF calculation is greater than 10, the regression coefficients may not be estimated adequately.

551

Diagnostic User Tips

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Diagnostic User Tips

It is possible for many relationships between X and Y to have similar R2 or R2adj results yet have dissimilar-looking regression plots. Always plot the data before interpreting any regression statistics.

   

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Measuring and Modeling Relationships Exercise

Six Sigma Black Belt | Analyze | Exploratory Data Analysis Concept: Measuring and Modeling Relationships Exercise

For each equation listed on the right, drag the corresponding equation name to the box on the left. [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

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Six Sigma Black Belt Analyze Hypothesis Testing

Learning Objectives

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Learning Objectives

At the end of this Analyze topic, all learners will be able to: • define, compare and contrast statistical and practical significance. • apply and interpret the significance level, power, type I and type II errors of statistical tests. • understand how to calculate sample size for any given hypothesis test. • define and interpret the efficiency and bias of estimators. • compute, interpret and draw conclusions from statistics such as standard error, tolerance intervals and confidence intervals. • understand the distinction between confidence intervals and prediction intervals. • apply hypothesis tests for means, variances and proportions, and interpret the results. • define, determine applicability, apply and interpret paired-comparison parametric hypothesis tests. • define, determine applicability, apply and interpret chi-square tests. • define, determine applicability, apply and interpret ANOVAs. • define, determine applicability and construct a contingency table, and use it to determine statistical significance. • define, determine applicability and construct various non-parametric tests including Mood's Median, Levene's test, Kruskal-Wallis and Mann-Whitney.   Portions of this topic were taken from the ASQ Six Sigma Green Belt web-based Certification Preparation Course.    

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General Sequencing

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: General Sequencing

To achieve victory in a project, both practical and statistical improvements are required.

556

Statistical vs. Practical Significance

Six Sigma Black Belt | Analyze | Hypothesis Testing Task: Statistical vs. Practical Significance

It is possible to find a difference to be statistically significant but not of practical significance. Because of the limitations of cost, risk, timing, etc., you cannot implement practical solutions for all statistically significant Xs. Click on each term below to learn more. Practical Significance Practical significance is the amount of difference, change or improvement that will add practical, economic or technical value to an organization. Example - A 20% reduction in cycle time is a practical significance in a process improvement project. This project objective/benefit exceeds the cost and risk of implementation.

Statistical Significance Statistical significance is the magnitude of difference or change required to distinguish between a true difference, change or improvement and one that could have occurred by chance. The larger the sample size, the more likely the observed difference is close to the actual difference. Example - A statistical difference of 0.25% at α = 0.05 may exist between two different sites of a large global corporation that manufacture the same product. However, the cost savings accrued by eliminating the difference is not economically justifiable.

 

557

Statistical vs. Practical Significance

Six Sigma Black Belt | Analyze | Hypothesis Testing Task: Statistical vs. Practical Significance

Determining Significance Determining practical significance in a Six Sigma project is not the responsibility of the Black Belt alone. You need to collaborate with others such as the project Champion/Sponsor and finance manager to help determine the return on investment (ROI) associated with the project objective.

   

558

Hypothesis Testing Introduction

Six Sigma Black Belt | Analyze | Hypothesis Testing Task: Hypothesis Testing Introduction

Statistical significance is determined by using hypothesis testing. Click each term below to learn more. Hypothesis Testing A hypothesis is a theory about the relationships between variables. Statistical analysis is used to determine if the observed differences between two or more samples are due to random chance or to true differences in the samples. Null Hypothesis A null hypothesis assumes no difference exists between or among the parameters being tested and is often the opposite of what is hoped to be proven through the testing. The null hypothesis is typically represented by the symbol Ho. Example: Ho: μ1 = μ2         Alternate Hypothesis An alternate hypothesis assumes that at least one difference exists between or among the parameters being tested. This hypothesis is typically represented by the symbol Ha. Examples: Ha : μ 1 < μ 2 Ha : μ 1 > μ 2 Ha : μ 1 ≠ μ 2     Phrasing In hypothesis testing, the phrase “to accept” the null hypothesis is not typically used. In statistical terms, the Six Sigma Black Belt can reject the null hypothesis, thus accepting the alternate hypothesis, or fail to reject the null hypothesis. This phrasing is similar to jury's stating that the defendant is not guilty, not that the defendant is innocent.

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Hypothesis Testing Steps Introduction

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Hypothesis Testing Steps Introduction

The following list provides a typical step-by-step plan for performing hypothesis testing: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

Define the practical problem. Define the practical objective. Establish hypotheses to answer the practical objective. Select the appropriate statistical test. Define the alpha (α) risk. Define the beta (β) risk. Establish delta (δ). Determine the sample size (n). Collect the data. Conduct the statistical tests. Develop statistical conclusions. Determine the practical conclusions.

In the following pages, each step will be described, including examples and information about: • Significance level • Power • Type I and Type II errors • Sample size

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Hypothesis Testing Steps 1 and 2

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Hypothesis Testing Steps 1 and 2

Step 1: Define the practical problem. From the Define and Measure phases, we have used tools such as the cause-and-effect diagram, process mapping, matrix diagrams, FMEA and graphical data analysis to identify potential Xs. Now you need statistical testing to determine significance: • Return mail volume is too high (Y = volume, X = division, X = product type, X = ancillary endorsement). • Cost per unit is too high (Y = cost, X = system downtime, X = customer requirement changes, X = exception processing). • Error rates are too high (Y = error rate, X = shift, X = product type, X = day of week). Step 2: Define the practical objective. Define logical categorizations where differences might exist so that meaningful action can be taken. Ask questions to determine what you want to prove (i.e., what questions will the hypothesis test answer?): • Are there significant differences in return mail volume between division, product types and ancillary endorsements? • Are there significant differences among the production shifts in variance of system down time? • Do error rates vary by shift, product type and day of the week?

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Hypothesis Testing Step 3

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Hypothesis Testing Step 3

Step 3: Establish hypotheses to answer the practical objective. The following is an example of hypotheses using a test of means where the mean of each shift is equal against the alternative where they are not equal: Null Hypothesis: • Ho: μ1st shift = μ2nd shift = μ3rd shift Alternate Hypothesis: • Ha: At least one mean is different  

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Hypothesis Testing Step 4

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Hypothesis Testing Step 4

Step 4: Select the appropriate statistical test. Based on the data that has been collected and the hypothesis test established to answer the practical objective, refer to the Hypothesis Testing Road Map to select statistical tests. The roadmap is a very important tool to use with each hypothesis test. Roll over Page Resources at the bottom of the screen and click on Hypothesis Testing Road Map to print out a take-away job-aid.

   

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Hypothesis Testing Roadmap

Six Sigma Black Belt | Analyze | Hypothesis Testing | Hypothesis Testing Step 4 Example: Hypothesis Testing Roadmap

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Hypothesis Testing Steps 5 and 6

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Hypothesis Testing Steps 5 and 6

Step 5: Define the Alpha (α) Risk. The Alpha Risk (i.e., Type II Error or Producer’s Risk) is the probability of rejecting the null hypothesis when it is true (i.e., rejecting a good product when it meets the acceptable quality level). Typically, (α) = 0.05 or 5%. This means there is a 95% (1-α) probability you are failing to reject the null hypothesis when it is true (correct decision). For example, the legal alpha risk is the risk an innocent person could have been convicted of a crime. Step 6: Define the Beta (β) Risk. The Beta Risk (i.e., Type II Error or Consumer’s Risk) is the probability of failing to reject the null hypothesis when there is significant difference (i.e., a product is passed on as meeting the acceptable quality level when in fact the product is bad). Typically, (β)  = 0.10 or 10%.  This means there is a 90% (1-β) probability you are rejecting the null when it is false (correct decision). Also, the power of the sampling plan is defined as 1- β; hence the smaller the β, the larger the power. For example, the legal beta risk is the risk a guilty person could have been found not guilty and been set free.  

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Hypothesis Testing Step 7

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Hypothesis Testing Step 7

 Step 7: Establish Delta (δ). Delta (δ) is the practical significant difference detected in the hypothesis test between: • proportion and a target. ° ° •

Ha: p1 - p2 < δ or Ha: p1 - p2 > δ or Ha: p1 - p2 ≠ δ

mean and a target. ° Ho: μ - μo = δ °

•

Ha: p - po < δ or Ha: p - po > δ or Ha: p - po ≠ δ

two proportions. ° Ho: p1 - p2 = δ °

•

Ho: p - po = δ

Ha: μ - μo < δ or Ha: μ - μo > δ or Ha: μ - μo ≠ δ

two means. ° Ho: μ1 - μ2 = δ °

Ha: μ1 - μ2 < δ or Ha: μ1 - μ2 > δ or Ha: μ1 - μ2 ≠ δ

Example • •

The return mail volume reduction of 10% has been determined to be a practical significance. An error rate difference of 7% has been determined to be of practical significance.

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Hypothesis Testing Step 8

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Hypothesis Testing Step 8

Step 8: Determine the sample size (n). Sample size depends on the statistical test, type of data and alpha and beta risks . There are statistical software packages to calculate sample size. It is also possible to manually calculate sample sizes using a sample size table. Roll over Page Resources at the bottom of the screen and click Table to access a table to help you calculate sample size. Calculating sample size using δ/σ: Where delta is the difference in the actual process and the project target or objective divided by the standard deviation.

Example Historically, within the XYZ Company, the average cost of a transaction is $.40 with a standard deviation of $.25. The goal of the project is to reduce the average cost to $.30.  Assuming the alpha risk of 5% and a beta risk of 10%, how many samples would be needed? • Compute δ/σ = (.40-.30)/.25 = .4. • Look in the Two Sample Test Table for an alpha risk of 5% and a beta risk of 10%. • The sample size is 133.

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Hypothesis Testing Step 8 cont.

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Hypothesis Testing Step 8 cont.

Step 8 cont. Calculate sample size using n. Using the formula on the left, where the data is continuous and Z = 1.96 at a confidence level of 95% (α/2 = 0.025 Two Tail Test), σ2 is the standard deviation, and E is the margin of error (the range of values around the estimate that probably contains the true value). This is also known as the confidence interval.

Example Historical information suggests that within mortgage loan documentation processing, the standard deviation of the exceptions per day is 10. What is the minimum sample size required at a 95% confidence level (Z=1.96) to confirm a significant shift of the mean greater than 2 exceptions per day? Compute n to find that 97 samples are needed. Sample size can also be calculated for discrete data using the formula on the left where p is the proportion defective.

User Tips • •

Increasing the sample size can reduce both the alpha and beta risk. As the number of samples taken increases, the theoretical standard deviation of the mean estimate decreases so we can reliably detect smaller and smaller differences.

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Hypothesis Testing Steps 9 - 10

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Hypothesis Testing Steps 9 - 10

Step 9: Collect the data. • Data collection is based on the sampling plan and method. Step 10: Conduct the statistical tests. • Use the Hypothesis Test Road Map to lead you in the right direction for the type of data you have collected.

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Hypothesis Testing Step 11

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Hypothesis Testing Step 11

Step 11: Develop statistical conclusions. According to Montgomery in Introduction to Statistical Quality Control, "the p–value is the smallest level of significance that would lead to rejection of the null hypothesis (Ho)." • •

Typically, if α = 0.05 and the p-value ≤ 0.05, then reject the null hypothesis and conclude that there is a significant difference. Typically, if α = 0.05 and the p-value > 0.05, then fail to reject the null hypothesis and conclude that there is not a significant difference.

Example Ho: μ1= μ2 = μ3 Ha: At least one mean is different •

With α = 0.05 and a computed p-value of 0.00, there is a significant difference between mail endorsement classifications and return mail volume. Therefore, we reject the null hypothesis.

Ho: ρ1 = ρ2 = ρ3 Ha: At least one ρi is different •

With α = 0.05 and a computed p-value of 0.12, there is not a significant difference between shift and account processing errors. Therefore, we fail to reject the null hypothesis.

Statistical conclusions can be made by comparing the test statistic (calculated value) to a critical value in a statistical table OR by using a statistical software program to calculate the p-value: • The null hypothesis will be rejected if the absolute value of the test statistic is greater than the critical value. For example: ° Reject Ho if | tcalc | > tcritical α/2, n-2 °

•

Do not reject Ho if | tcalc | < tcritical α/2, n-2

If the test statistic (calculated value) = critical value, then it is often considered to be a judgment call.

Example Ho: µ = μ0 Ha : µ ≠ μ 0 •

Account processing is not on target since tcalc > tcritical (4.74 > 2.262) therefore, reject the null hypothesis.

Ho: µ1 = μ2 Ha : µ 1 < μ 2 •

Since tcalc -2.306, we cannot reject the null hypothesis.

 

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Hypothesis Testing Step 12

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Hypothesis Testing Step 12

Step 12: Determine the practical conclusions. Restate the practical conclusion to reflect the impact in terms of cost, return on investment, technical, etc. Remember, statistical significance does not imply practical significance.

Example • •

Statistically the first quarter has the worst error rate and an increased missed account rate of 9%. Through analysis, it has been determined that distribution center G reflects a decreased productivity rate compared to the other distribution centers. In addition to low productivity, there is an increase in employee turnover of 20% for second shift employees.

571

Concepts of Hypothesis Testing Exercise

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Concepts of Hypothesis Testing Exercise

For each of the following statements, click either the True or False box:   [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

572

Point and Interval Estimation

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Point and Interval Estimation

As discussed in the Measure lesson, a population is the entire set (totality) of units, quantity of material or observations under consideration. A population may be real and finite, real and infinite or completely hypothetical. Characteristics describing a population mean are called parameters. An example of a population is all registered voters in the United States.  µ = Population Mean (Note: the mean of a population is never actually known.) σ 2 = Population variance N = Number of values (population) A sample is a group of objects actually measured in a statistical study. It is a subset of the population of interest. Statistics based on samples are used as estimators of the equivalent population parameters.  An example of a sample is a survey of 100 voters. X = Sample Mean s2 = Sample variance n = Number of values (sample) On the following page, click Continue to see an example of how sample statistics are used to make inferences about population parameters.

573

Inferences about Population Parameters

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Inferences about Population Parameters

[ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

574

Bias

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Bias

Bias is a difference between the sample and the population, caused by the sampling method. There is uncertainty about the population anytime you sample; hence the estimator is called unbiased if the average of all possible values is equal to the parameter being estimated. For example, the following equation shows the bias that changes a population variance to a sample variance: Popul Sample ation variance varia nce

N = size of the population

n = sample size

μ = population mean

X = the sample mean

Bias (As n appro aches N, the bias appro aches zero)

 

575

Unbiased Estimator

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Unbiased Estimator

The sample mean is an unbiased estimator for the population mean as a result of the Central Limit Theorem discussed earlier in the Measure Lesson of this course. The estimator is unbiased if the expected value of the estimator equals the population parameter. For example, the mean is an unbiased estimate because E(X) = μ. When a known (finite) population is sampled many times, the calculated sample averages can be different even though the population is stable. Click each sample mean to see to an example: [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

576

Estimating Population Parameters

Six Sigma Black Belt | Analyze | Hypothesis Testing Task: Estimating Population Parameters

The differences in sample averages are a result of the nature of random sampling. Given that these differences exist, the key is to estimate the true population parameter with a known degree of certainty. Click each term below to learn more. Confidence Intervals According to ASQ's Glossary and Tables for Statistical Quality Control, "a confidence interval is the estimate of the interval between two statistics that contains the true value of the parameter with some probability. This probability is called the confidence level of the estimate. Confidence intervals for the mean are independent of the population distribution if the sample size is large. Confidence levels typically used are 90%, 95% and 99%. As n increases, the confidence intervals get tighter as the endpoints converge on the true parameter. The interval either contains the parameter or it does not." • If it does, the probability that the population parameter is in the interval is called the confidence coefficient or confidence level = 1 – alpha. For example, a 95% confidence interval would have a 5% alpha risk. • If it does not, the parameter would be considered to be rejected. The alpha risk = 1 – confidence interval and is the probability that the population parameter is not in the interval. Standard Error According to the ASQ Glossary, standard error, abbreviated Se, is the standard deviation of a sample statistic or estimator indicating the amount of error that will occur when a sample mean is used to estimate the mean of a population. When dealing with sample statistics, we either refer to standard deviation of the sample statistic or to the standard error of the mean as shown by:

 

577

Estimating Population Parameters

Six Sigma Black Belt | Analyze | Hypothesis Testing Task: Estimating Population Parameters

Prediction Interval The prediction interval is an interval based on the predicted value that is likely to contain the values of future observations. The prediction interval will be wider than the confidence interval because it contains bounds on individual observations rather than a bound on the mean of a group of observations.

Where: • xp = value of the predictor variable • • •

yp = calculated response variable using the regression equation Se and Sxx have been defined previously df = n - 2

  Tolerance Interval According to Six Sigma for the Next Millennium: A CSSBB Guidebook by Pries, a tolerance interval “is the stated coverage for a fixed proportion of the population with a declared confidence. There are both one-sided and two-sided tolerance intervals. The endpoints of a tolerance interval are generally referred to as tolerance limits." An application of tolerance intervals to manufacturing involves comparing specification limits designated by the client with tolerance limits that cover a specified proportion of the population.

 

578

Confidence Interval Conditions

Six Sigma Black Belt | Analyze | Hypothesis Testing Task: Confidence Interval Conditions

Click each condition below to see the corresponding confidence interval equation. Large sample (n ≥ 30) when σ is known Equation for the confidence interval of a mean (μ) of a population:

Large sample (n ≥ 30) when σ is unknown Equation for the confidence interval for a mean (μ) of a population when σ is unknown and replaced by s, an estimator of σ:

Small Sample (n ≤ 30) Equation for the confidence interval for a mean (μ) of a population:

Population Variance Confidence interval equation:

Population Standard Deviation Confidence interval equation:

579

Confidence Interval Large Sample

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Confidence Interval Large Sample

Calculate the confidence interval for a large sample (n ≥ 30) when σ is unknown and replaced by s, an estimator of σ.

Example Problem and given values: An estimate is needed for the average weight for a population of 1000 fastening snaps received from a supplier. Rather than measuring all 1000 fastening snaps, the shift manager decides to randomly select a sample of 50 for measurement. The average weight of the sample is determined to be 0.34 ounces with a standard deviation of 0.004. Calculate the confidence interval for the mean with α = 0.10.

The calculation is on the next page.

580

Confidence Interval Large Sample cont.

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Confidence Interval Large Sample cont.

Calculation Using the given information, the formulas for the endpoints of the confidence interval are:

Therefore, we are 90% confident that the population mean is between 0.33907 and 0.34093.

581

Confidence Interval Small Sample

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Confidence Interval Small Sample

Calculate the confidence interval for a small sample (n ≤ 30) for a mean (μ) of a population.

Example Problem and Given Values An auto parts manufacturer recently replaced a new machine that produces a part. Historically, under a normal processing environment the diameter of this part is 1.50. Now that a new machine is producing the part, the general manager wants to know if the diameter has changed. A random sample of 20 parts reflects an average diameter of 1.60 with a standard deviation of 0.009. Assume the diameters are normally distributed and calculate a 95% confidence interval.

The calculation is on the next page.

582

Confidence Interval Small Sample cont.

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Confidence Interval Small Sample cont.

Calculation Roll over Page Resources at the bottom of the screen and click T Distribution Table to determine the critical value. With df = 19, looking at t.025 the critical value is 2.093. Using the given information, the formulas for the endpoints of the confidence interval are:

The 95% confidence interval is (1.5958, 1.6042). The data indicate that we can be 95% confident that the mean of the population of diameters is between 1.5958 and 1.6042. Since 1.50 is not in the interval, we are 95% confident that the mean has changed.

583

Confidence Interval for Standard Deviation

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Confidence Interval for Standard Deviation

Confidence interval equation for a standard deviation (σ) of a population The confidence interval for the standard deviation subscribes to a χ2 distribution and is graphically shown as follows:

The graph depicts α/2 = 0.05: • 1-α/2 is the left confidence interval • α/2 is the right confidence interval

584

Confidence Interval for Standard Deviation cont.

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Confidence Interval for Standard Deviation cont.

Example A new process has been established in the manufacturing of ink for print cartridges. The manufacturer is interested in determining if the amount of variability in the brilliance of the color has changed. Historically, the standard deviation has been 2.75.  A random sample of 25 ink receptacles was collected, and the standard deviation was calculated to be 2.79. Assume the diameters are normally distributed and calculate a 90% confidence interval. What is your conclusion?   s = 2.75 n = 25

Roll over Page Resources and click Chi-square Distribution Table to determine the critical value, where: • df = 24 • χ2 and χ2 .05

.95

The calculation is on the next page.  

585

Confidence Interval for Standard Deviation cont.

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Confidence Interval for Standard Deviation cont.

Calculation • •

Degrees freedom (df) = 24 α / 2 = .05 and 1 – α / 2 = .95, (36.415) and (13.848)

Using the given information and formula, the calculated confidence intervals are: • Lower confidence limit = 2.233 • Upper confidence limit = 3.620 The 90% confidence interval is (2.233, 3.620). The data indicate that we can be 90% confident that the standard deviation of the population of ink receptacles is between 2.233 and 3.620. Since the historical standard deviation (2.75) is within the interval, we conclude with 90% confidence that the standard deviation has not changed.

586

Tolerance Intervals

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Tolerance Intervals

Example A sample of n = 20 from a stable process produced the following results:

Roll over Page Resources at the bottom of the screen and click Tolerance Interval Factors to determine the value of K.

We can estimate that the interval from 11.024 to 18.977 will contain 99% of the population with a confidence of 95%.

587

Point and Interval Estimation Distinctions

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Point and Interval Estimation Distinctions

Confidence, tolerance, and prediction intervals are all interrelated, yet each is distinct as to point and interval estimations.   [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

588

Point and Interval Estimation Exercise

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Point and Interval Estimation Exercise

Below are five statements about point and interval estimation. Drag the three correct statements on the left to the appropriate boxes on the right. Feedback will be given for incorrect answers. [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

589

Tests for Means, Variances, and Proportions

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Tests for Means, Variances, and Proportions

Hypothesis testing plays an important role in the Six Sigma methodology, as discussed previously in this course. Once you have the data collected and manipulated, you are ready to perform the tests that turn a practical problem into a statistical problem. According to Montgomery in Introduction to Statistical Quality Control, "The p–value is the smallest level of significance that would lead to rejection of the null hypothesis (Ho)." For statistical tests: • • • •

Choose appropriate α risk, generally 0.05 (95% confidence level). Verify correct sample size. Typically, if α = 0.05 and the p-value ≤ 0.05 (test value falling in the reject region), then reject the Ho (Null) hypothesis. Typically, if α = 0.05 and the p-value > 0.05 (test value not in the reject region), then fail to reject the Ho (Null) hypothesis.

The hypothesis test summary displays the test statistic, statistical tests, null and alternate hypotheses for means, variances and proportions. Roll over Page Resources and click Summary Chart to view and print for a take-away job-aid.  

590

Summary Chart

Six Sigma Black Belt | Analyze | Hypothesis Testing | Tests for Means, Variances, and Proportions Example: Summary Chart

 

591

Hypothesis Tests for Means

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Hypothesis Tests for Means

Ho : µ A = µ B  

H a : µ A≠ µ B  

Ho : µ A = Target or Historic Mean  

Ha : µ A ≠ Target or Historic Mean

Ho : µ A  = µB  =  µC

Ha : At least one µ is different

 

592

Tests for Means Introduction

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Tests for Means Introduction

The statistical tests for means that a Black Belt would commonly use are: • One-sample Z-test: for population mean • Two-sample Z-test: for population mean • One-sample T-test: single mean (one sample versus historic mean or target value) • Two-sample T-test : multiple means (sample from each of the two categories) • ANOVA (Analysis of Variance) (sample from three or more categories) An example of the One-sample Z-test for population mean, Two-sample Z-test for population mean, One-sample T-test, and the Two-sample T-test will be shown in this sub-topic. One-way ANOVA and Two-way ANOVA will be discussed later under the specific sub-topic of ANOVA.

593

One-Sample Z-Test for Population Mean Introduction

Six Sigma Black Belt | Analyze | Hypothesis Testing Task: One-Sample Z-Test for Population Mean Introduction

The One-sample Z-test for population mean is used when a large sample (n ≥ 30) is taken from a population and we want to compare the mean of the population to some claimed value. This test assumes the population standard deviation is known or can be reasonably estimated by the sample standard deviation and uses the Z distribution. Click the information below to learn more. Hypotheses Null hypothesis • Ho: μ = μ0        where μ0 is the claim value compared to the sample. Alternative hypothesis may take one of these forms: • Ha:  μ ≠ μ0      • •

Ha:  μ < μ0       Ha:  μ > μ0

Test Statistic Where: • x is the sample mean. • σ can be estimated by s for the sample. • n is the sample size. Critical Values/Reject Regions For Alternate Hypothesis

Reject Ho if:

Ha:  μ ≠ μ0  

z < -zα /2 or z > zα /2 

Ha:  μ < μ0   

  z < -zα

Ha:  μ > μ0   

  z > zα

594

One-Sample Z-Test Example Steps 1 and 2

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: One-Sample Z-Test Example Steps 1 and 2

Example A weight loss company is introducing a new marketing campaign and wishes to include in the advertisement that the average weight loss of a participant is 5 pounds per month. An associate from the marketing department randomly chooses 75 participant files and finds the sample has an average weight loss of 4.4 pounds per month. Suppose the standard deviation of the population is 0.2. Is the claim of 5 pounds lost per month valid? The marketing department wants a 95% confidence level in the claim. Step 1: Establish the hypotheses. Ho: μ = 5.0 Ha: μ < 5.0 (left-tail test) Step 2: Calculate the test statistic.  

595

One-Sample Z-Test Steps 3 and 4

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: One-Sample Z-Test Steps 3 and 4

Step 3: Determine critical value. • For a one-tail test, find the value that has an area of α to its right. The negative of this value is the critical value. The reject region is the area to the left of the negative value. Given a 95% confidence level, α = 0.05. From the hypothesis test, a one-tail test is used to find the area of α in the Z-table (0.05). Roll over Page Resources at the bottom of the screen and click  Z-Table. The value has an area of α to its right, 1.645. The negative value, -1.645, is the critical value. Step 4: Draw the statistical conclusion. The calculated value of -25.98 (to the left of -1.645) is in the reject region (zcalc < -zα), so therefore reject the null hypothesis. At a 95% confidence level, the data does not support the claim of an average weight loss of 5 pounds per participant. The marketing campaign should not include this claim in the advertisement.

596

Two-Sample Z-Test for Population Mean

Six Sigma Black Belt | Analyze | Hypothesis Testing Task: Two-Sample Z-Test for Population Mean

The Two-sample Z-test for population mean is used after taking 2 large samples (n ≥ 30) from 2 different populations in order to compare them. This test uses the Z-table and assumes knowing the population standard deviation, or estimated by using the sample standard deviation. Click the information below to learn more. Hypotheses Null hypothesis: • Ho: μ1= μ2 Alternative hypothesis may take one of these forms: • Ha : μ 1 ≠ μ 2 • •

Ha : μ 1 < μ 2 Ha : μ 1 > μ 2

    Test Statistic

Where: • x1 and x2 are the sample means. • •

s1 and s2 are the sample standard deviations. n1 and n2 are the sample sizes.

Critical Values/Reject Regions For Alternative Hypothesis

Reject Ho if:

Ha : μ 1 ≠ μ 2

z < -zα/2 or z > zα/2

Ha : μ 1 < μ 2

z < -zα

Ha: μ1> μ2

z > zα

Note: The steps in completing a Two-sample Z-test are the same as the One-sample Z-test, but with the appropriate calculation for the test statistic.

597

One-Sample T-test Introduction

Six Sigma Black Belt | Analyze | Hypothesis Testing Task: One-Sample T-test Introduction

The One-sample T-test is used when a small sample (n < 30) is taken from a population and you want to compare the mean of the population to some claimed value. This test assumes the population standard deviation is unknown and uses the t distribution. Click the information below to learn more. Hypotheses Null hypothesis • Ho: μ = μ0        Where: • μ0 is the claim value compared to the sample. Alternative hypothesis (may take one of these forms) • Ha:  μ ≠ μ0      • •

Ha:  μ < μ0       Ha:  μ > μ0   

Test Statistic

Where: • x is the sample mean. • s is the sample standard deviation. • n is the sample size. Critical Values/Reject Regions For Alternate Hypothesis

Reject Ho if:

Ha:  μ ≠ μ0  

t < -tα /2 or t > tα /2 

Ha:  μ < μ0   

  t < -tα

Ha:  μ > μ0   

  t > tα

Where: • t values have n - 1 degrees of freedom.

598

One-Sample T-test Example Steps 1 and 2

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: One-Sample T-test Example Steps 1 and 2

Example The Loan Reconciliation Department is reviewing the outstanding general ledger items process to determine if it is on target. The mean balance on an outstanding general ledger item is $5,500 (target value). A sample of 10 outstanding general ledger items was reviewed, reflecting a mean item balance of $5,506 with a standard deviation of $4. Is the process on target? The significance level α = 0.05. Step 1: Establish the hypotheses. Ho: µ = 5,500 Ha: µ ≠ 5,500 Step 2: Calculate the test statistic.

599

One-Sample T-test Steps 3 and 4

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: One-Sample T-test Steps 3 and 4

Step 3: Determine the critical values. Roll over Page Resources at the bottom of the screen and click T-test table to view the table. The sample size was 10, so df is n -1 or 9. Look at the t.025 column (α/2) and 9 df. The critical value is 2.262.

Step 4: Draw the statistical conclusion. • Reject Ho if tcalc < -tα /2 or tcalc > tα /2 otherwise, do not reject Ho. Since tcalc > tcritical reject the null hypothesis: 4.74 > 2.262 the process is not on target.

600

Two-Sample T-test Introduction

Six Sigma Black Belt | Analyze | Hypothesis Testing Task: Two-Sample T-test Introduction

The Two-sample T-test is used when two small samples (n < 30) are taken from two different populations and compared. There are two forms of this test: assumption of equal variances and assumption of unequal variances. Click the information below to learn more. Hypotheses For both assumptions of equal and unequal variances the hypotheses are: Null hypothesis • Ho: µ1 = µ2 The Alternate hypothesis may take one of the following forms: • Ha : µ 1 ≠ µ 2 • •

Ha : µ 1 < µ 2 Ha : µ 1 > µ 2

Test Statistic Assumption of equal variances

Where pooled variance is:

Assumption of unequal variances

Where: • x1 and x2 are the sample means. • •

s1 and s2 are the sample standard deviations. n1 and n2 are the sample sizes.

Critical Values/Reject Regions For Alternate Hypothesis

Reject Ho if:

Ha:  µ1 ≠ µ2   

t < -tα /2 or t > tα /2 

Ha:  µ1 < µ2   

  t < -tα

Ha:  µ1 > µ2   

  t > tα  

 

601

Two-Sample T-test Introduction

Six Sigma Black Belt | Analyze | Hypothesis Testing Task: Two-Sample T-test Introduction

Degrees of Freedom Assumption of equal variances • (n1 + n2) - 2 Assumption of unequal variances  

602

Two-Sample T-test Example

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Two-Sample T-test Example

Example Two call centers (A and B) are being tested to see if customer wait time is statistically the same. A sample of five wait times was taken from both call centers. The historic mean is 7.5 seconds. Are the call centers the same? Assume α = 0.05. Call Average Center A (sec)

Ind. Avg.

(Ind. -

10

7.2

2.8

7.84

7

7.2

-0.2

4

7.2

3

7.2

12  

 

Call Average Center B (sec)

Ind. Avg.

(Ind. -

 

9

8.2

0.8

0.64

0.04

 

11

8.2

2.8

7.84

-3.2

10.24

 

2

8.2

-6.2

38.443

-4.2

17.64

 

14

8.2

5.8

33.64

7.2

4.8

23.04

 

5

8.2

-3.2

10.24

 

Sum

58.8

 

 

 

Sum

90.8

Avg.)2

 

603

Avg.)2

Two-Sample T-test Steps 1 and 2

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Two-Sample T-test Steps 1 and 2

Step 1: Establish the hypotheses. Ho: μA = μB Ha : μ A ≠ μ B  

Step 2: Calculate the test statistic. In this example, the two populations with unknown means and unknown variances are assumed to be unequal.  

   

604

Two-Sample T-test Steps 3 and 4

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Two-Sample T-test Steps 3 and 4

Step 3: Determine the critical values. Roll over Page Resources at the bottom of the screen and click T-test table to view the table. In a two-sample t-test, degrees of freedom are calculated using the following formula:

  Note: The degrees of freedom should be rounded down to be conservative. Look at the t.025 column (α/2) and 7 d.f. and you will see the critical values are -2.365 and 2.365.

Step 4: Draw the statistical conclusion. • Reject Ho if tcalc < -tα /2 or tcalc > tα /2  otherwise, do not reject Ho. Since tcalc > -tα /2 fail to reject the null hypothesis: -0.37 > -2.365. There is not a statistical difference between Call Center A and Call Center B.

605

Hypothesis Tests for Variances

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Hypothesis Tests for Variances

Ho: σ 2After = σ2Before

Ha: σ 2After ≠ σ2Before

 

Ha: σ 2After > σ2Before

 

Ha: σ 2After < σ2Before

   

606

Tests for Variances Introduction

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Tests for Variances Introduction

An example of the F-test Statistic will be shown in this sub-topic of the course. Levene's Test Statistic will be discussed along with an example in the non-parametric tests sub-topic of this lesson. When comparing two populations' means using continuous data, you must first decide if a statistical difference exists in the variances (homogeneity of variance test). The normality of the data test is important because you need to know the type of distribution to determine the type of variance test to use.    

2 samples

Normal distribution F- test Non-normal   distribution

2 or more samples More than 2 samples   Bartlett’s Test Levene’s Test  

 

607

F-test Statistic Step 1

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: F-test Statistic Step 1

Example Two check processing centers are being evaluated to see if there is a difference in processing time. We want to know if the processing time variability is significantly different at the two centers. Sample sizes from Center 1 and Center 2 were 10 and 9 respectively and have sample variances of S12 = 6.89 and S22 = 4.96. Given α = 0.05, are the population variances different at a 95% confidence level? Step 1: Establish the hypotheses. Ho: σ21 = σ22 Ha: σ21 ≠ σ22    

608

F-test Statistic Steps 2 - 4

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: F-test Statistic Steps 2 - 4

Step 2: Calculate the test statistic.

Step 3: Determine the critical values. F distribution tables are entered using the degrees of freedom which are designated by ν1 and ν2 ("nu"), where: • •

ν1 = n1 - 1 = 10 - 1 = 9 ν2 = n2 - 1 = 9 - 1 = 8

Roll over Page Resources and click F-Distribution Table. • Look in the table and read across the table to find ν1 = 9 degrees of freedom. Read down the table to find ν2 = 8 degrees of freedom. At the interaction of the column and row, read the value 3.39, the right (upper) critical value given by:

•

Look in the table and read across the table to find ν1 = 8 degrees of freedom. Read down the table to find ν2 = 9 degrees of freedom. At the interaction of the column and row, read the value 3.23, the left (upper) critical value given by:

Step 4: Draw the statistical conclusion. If Fcalc > Fcritical, then reject the null hypothesis, because the variances are different. Since the calculated F value of 1.39 is between the critical values of 0.31 and 3.39, we fail to reject the null hypothesis and cannot conclude that the population variances of Center 1 and Center 2 are different at a 95% confidence level.

609

Hypothesis Tests for Proportions

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Hypothesis Tests for Proportions

Ho: pMonday = pTuesday = pWednesday = pThursday = pFriday

Ha: At least one is different

Ho: pa = Target

Ha: pa ≠ Target

Ho: pa = pb

Ha : p a ≠ p b

 

Ha : p a > p b

 

Ha : p a < p b

Note: During the discussion of tests for proportions, the target will also be referred to as "claim," "hypothesized p," and "historical value."  

 

610

Tests for Proportions Introduction

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Tests for Proportions Introduction

The statistical tests for proportion that a Black Belt would commonly use are: • One-proportion • Two-proportion • Chi-square Examples of the One-proportion and Two-proportion tests and the steps to calculate them will be shown in this sub-topic. The Chi-square test will be covered in the contingency tables and goodness-of-fit Test sub-topics later in the course. Situation Summarized data from two or more samples. Sample proportion versus historic proportion or target. Sample proportion before improvement actions versus sample proportion after improvement actions.

Statistical Test Used Chi - square 1-Proportion test 2-Proportion test

611

One-Proportion Test Introduction

Six Sigma Black Belt | Analyze | Hypothesis Testing Task: One-Proportion Test Introduction

The One-proportion test is used when taking a sample from a population and the number of units of interest is counted in the sample in order to compare the population’s mean to some claim. Click the information below to learn more. Use When • np and n (1-p) are > 5, where n is the sample size and p is the proportion.  This assumption is necessary for making a normal approximation to the binomial distribution where Z tables can be used. For example, use the One-proportion test to check if there is a statistical difference between: • Current fraction defective of a product to the historical fraction defective • Current percent of "yes" votes on a proposition to the percent in a prior election Hypotheses Null hypothesis Ho: p = po Where po is the claim value for comparing the sample. Alternate hypothesis may take one of these forms: Ha : p ≠ p o Ha : p < p o Ha : p > p o       Test Statistic

where p' = the proportion of units of interest in the sample. Critical Values/Reject Regions For Alternative Hypothesis

Reject Ho if:

Ha : p ≠ p o

z < -zα/2 or z > zα/2

Ha : p < p o

z < -zα/2

Ha : p > p o

z > zα/2

612

One-Proportion Test Example Step 1

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: One-Proportion Test Example Step 1

Example Product accuracy must be on target at 0.90, so use the one-proportion test to determine if the current process is on target. A sample n of 500 products was taken and 400 were accurate. Assume α = 0.05. Step 1: Establish the hypotheses. Ho: p = Target Ha: p < Target  

613

One-Proportion Test Step 2

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: One-Proportion Test Step 2

Step 2: Calculate the test statistic. Data was collected to calculate p (proportion of accuracy): • p = population proportion • n =sample size • x = number of items in the sample with the defined attribute • p' = sample proportion= x/n = 400/500 = 0.8 • p0 = the hypothesized proportion

     

614

One-Proportion Test Steps 3 and 4

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: One-Proportion Test Steps 3 and 4

Step 3: Determine the critical value. Using α = 0.05, rollover Page Resources at the bottom of the screen and click Normal Distribution Table. The test Z value is 1.645. Step 4: Draw the statistical conclusion. If Zcalc  < -Z critical, reject the null hypothesis. Otherwise, do not reject the null hypothesis. Since Zcalc 5 where n is the sample size and p is the proportion.  This assumption is necessary for making a normal approximation to the binomial distribution where Z tables can be used. For example, use the Two-proportion test to check if there is a statistical difference between: • Proportion defective before and after a process improvement • Percent accuracy of form completion between 2 different office locations Hypotheses Null hypothesis Ho: p1= p2 Where p1 and p2 are the proportions in the populations being compared. Alternative hypothesis may take one of these forms: Ha : p 1 ≠ p 2 Ha : p 1 < p 2 Ha : p 1 > p 2

616

Two-Proportion Test Introduction

Six Sigma Black Belt | Analyze | Hypothesis Testing Task: Two-Proportion Test Introduction

Test Statistic

p = pooled proportion                              

617

Two-Proportion Test Example Step 1

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Two-Proportion Test Example Step 1

Example Product accuracy must improve towards the target of 0.90. Process improvements have been implemented, and the project manager wants to determine if these improvements have increased accuracy. In the original sample (n) of 500, 400 were accurate. Another sample was taken after the improvements were implemented and 220 out of 250 were deemed accurate. Step 1: Establish the hypotheses. Ho: p1 = p2 Ha : p 1 < p 2

618

Two-Proportion Test Step 2

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Two-Proportion Test Step 2

Step 2: Calculate the test statistic. Data was collected to calculate p (proportion of accuracy): • p1 and p2 = population proportions • • • •

n1 and n2 = sample sizes x1 and x2 = number of items in the samples with the defined attribute p1 = x1/n1 = 400/500 = 0.8 (original sample) p2 = x2/n2 = 220/250 = 0.88 (2ndsample)

619

Two-Proportion Test Steps 3 and 4

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Two-Proportion Test Steps 3 and 4

Step 3: Determine the critical value. Using α = 0.05, rollover Page Resources at the bottom of the screen and click Normal Distribution Table. The test Z value is 1.645. Step 4: Draw the statistical conclusion. • If Z calc  < -Z critical, reject the null hypothesis. Otherwise, do not reject the null hypothesis. Since  -2.73 < -1.645, we reject the null hypothesis and conclude that the solutions implemented have improved the accuracy of the process.

620

Paired-Comparison Tests Introduction

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Paired-Comparison Tests Introduction

Paired-comparison t-tests are powerful ways to compare data sets by determining if the means of the paired samples are equal. Making both measurements on each unit in a sample allows testing on the paired differences. An example of a paired comparison is two different types of hardness tests conducted on the same sample. Once paired, a test of significance attempts to determine if the observed difference indicates whether the characteristics of the two groups are the same or different. A paired comparison experiment is an effective way to reduce the natural variability that exists among subjects and tests the null hypothesis that the average of the differences between a series of paired observations is zero. In this section, the paired t-test for two population means will be discussed along with an example.

621

Paired-Comparison Tests Example

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Paired-Comparison Tests Example

In this paired t-test for two population means example, each paired sample consists of a member of one population and that member’s corresponding member in the other population.

Example A candy company will be using a new chocolate recipe, and the plant manager suspects that the cycle time to produce chocolates will be impacted. She is claiming that there will be a need for an increase in staff. Cycle time for a sample size of 10 chocolates was tracked for each type of recipe on a machine that produces the chocolates made from both recipes. Does the data indicate that the new chocolate recipe increases cycle time when α = 0.05? Assume that the differences are normally distributed. Sample # Old recipe (time in secs.) New recipe (time in secs.) Difference, d

1 7 7 0

2 6 6 0

 

622

3 8 7 1

4 9 8 1

5 5 5 0

6 5 5 0

7 5 6 -1

8 8 8 0

9 9 7 2

10 7 7 0

μ 6.9 6.6 0.3

Paired-Comparison Tests Steps 1 and 2

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Paired-Comparison Tests Steps 1 and 2

Step 1: Establish the hypotheses. μD = μ 1 - μ2 = 0

The established hypothesis   test is a:   • Two-tail test when Ha

is a statement of does not equal ( ≠ ) Ha : µ D ≠ 0 • Left-tail test when Ha has the < sign • Right-tail test when Ha has the > sign Step 2: Calculate the test statistic. Ho: µD = 0

     

623

Paired-Comparison Tests Steps 3 and 4

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Paired-Comparison Tests Steps 3 and 4

Step 3: Determine the critical value. Roll over PageResources and click T-test table to find the critical value using degrees freedom of n -1. Since d.f. = 10 - 1 and α = 0.05 with a two-tailed test, the critical value is in the ninth row of the t.025 (2.262).

Step 4: Draw the statistical conclusion. • If t calc  > t critical  or tcalc  < -t critical, reject the null hypothesis. Otherwise, do not reject the null hypothesis. The calculated value of 1.152 is not in the reject region (1.152 < 2.262), so therefore we fail to reject the null hypothesis. At a 95% confidence level, the data suggests that the cycle time did not change using the new chocolate recipe, therefore refuting the claim that additional staff is needed.

624

Equation Exercise

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Equation Exercise

For each equation, definition, or hypothesis listed on the right, drag the corresponding answer to the appropriate box on the left. [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

625

Goodness-of-Fit Test

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Goodness-of-Fit Test

In the goodness-of-fit tests, one is comparing and observed (O) frequency distribution to an expected (E) frequency distribution. The relationship is statistically described by a hypothesis test: • Ho: Random variable is distributed as a specific distribution with given •

parameters. Ha: Random variable does not have the specific distribution with given parameters.

The formula for calculating the chi-square test statistic for this one-tail test is:

A random sample of size n is taken from the population. The degrees of freedom for this test is k – m – 1, where: • k = number of intervals or cells from the sample to form a frequency distribution • m = number of parameters estimated from the sample data

626

Goodness-of-Fit Test Step 1

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Goodness-of-Fit Test Step 1

The following example is taken from “Quality Engineering Statistics,” by Robert A. Dovich.

Example Management believes that the time between machine breakdowns follows the exponential distribution. We track a bank of identical machines for a number of hours between breakdowns. Test the hypothesis that the distribution is exponential using a 95% (α = 0.05) level of confidence. Step 1: Establish the hypotheses. Ho: Distribution is exponential. Ha: Distribution is not exponential.

627

Goodness-of-Fit Test Steps 2 and 3

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Goodness-of-Fit Test Steps 2 and 3

Step 2: Determine lambda (λ) from the observed frequencies. The data are grouped in intervals of 100 hours in the following table:  Time Between Breakdowns (Interval) Interval 0-100

>100-20 >200-30 >300-40 >400-50 >500-60 >600 0 0 0 0 0 180 63 53 33 18 6

Total

Number 325 678 of Breakdo wns From a sample of 678, the average time to breakdown was estimated at 156.6 hours: λ = 1/156.6 = 0.0064 Step 3: Calculate the expected values. Interval 0 - 100

Probability

>100 -200

e-0.0064(100)-e-0.0064(200) = 0.2493

169.0

>200 - 300

e-0.0064(200)-e-0.0064(300) = 0.1314

89.1

>300 - 400

e-0.0064(300)-e-0.0064(400) = 0.0693

47.0

>400 - 500

e-0.0064(400)-e-0.0064(500) = 0.0365

24.7

>500 - 600

e-0.0064(500)-e-0.0064(600) = 0.0193

13.1

>600

e-0.0064(600) = 0.0215 ∑ = 1.0000

14.6

   

e0–e-0.0064(100)

= 0.4727

Expected Value 320.5

678.0

628

Goodness-of-Fit Test Step 4

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Goodness-of-Fit Test Step 4

Step 4: Calculate the test statistic. Using the chi-square test statistic and the values from the previous data tables:

The degrees of freedom is computed as the number of intervals minus the number of parameters estimated (which is 1, as the mean was estimated from the sample), minus 1: df = 7 – 1 – 1 = 5  

629

Goodness-of-Fit Test Steps 5 and 6

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Goodness-of-Fit Test Steps 5 and 6

Step 5: Determine the critical value. Rollover Page Resources at the bottom of the screen and click Chi-square Distribution Table. Look for 5 (df) under the χ20.05 column. The critical value is 11.070. Step 6: Draw the statistical conclusion. • If χ2 > χ2 , then reject the null hypothesis. calc  

α,df

Since 18.878 > 11.070, we reject the null hypothesis at a 0.05 significance level. The time to breakdown for this equipment is not modeled by the exponential distribution (Ha: Distribution is not exponential).

630

ANOVA Introduction

Six Sigma Black Belt | Analyze | Hypothesis Testing Task: ANOVA Introduction

Analysis of variance (ANOVA) is a technique to determine if there are statistically significant differences among group means by analyzing group variances. An ANOVA is an analysis technique that evaluates the importance of several factors of a set of data by subdividing the variation into component parts. Click the information below to learn more about ANOVA. What does ANOVA test? ANOVA tests to determine if the means are different, not which of the means are different: Ho: μ1 = μ2 = μ3 Ha: At least one of the group means is different from the others. Similarities to Regression ANOVA is similar to regression in that it is used to investigate and model the relationship between a response variable and one or more independent variables. However, analysis of variance differs from regression in two ways: • The independent variables are qualitative (categorical). • No assumption is made about the nature of the relationship (i.e. the model does not include coefficients for variables). Relationship to the Two-sample t-test ANOVA extends the Two-sample t-test for testing the equality of two population means to a more general null hypothesis of comparing the equality of more than two means, versus them not all being equal.

631

ANOVA Fundamental Terminology

Six Sigma Black Belt | Analyze | Hypothesis Testing Task: ANOVA Fundamental Terminology

In the ANOVA sub-topic, One-way and Two-way ANOVA will be discussed along with a One-way ANOVA example. To learn more, click the terms below used in the data table for the calculation of ANOVA: Degrees of Freedom (df) The number of independent conclusions that can be drawn from the data. SSFactor Measures the variation of each group mean to the overall mean across all groups. SSError Measures the variation of each observation within each factor level to the mean of the level. Mean Square Error (MSE) SSError / df MSE is also the variance. F-test statistic The ratio of the variance between treatments to the variance within treatments = MS/MSE.  If F is near 1, then the treatment means are no different (p-value is large). P-value According to Montgomery in Introduction to Statistical Quality Control, "the p–value is the smallest level of significance that would lead to rejection of the null hypothesis (Ho)." • •

Typically, if α = 0.05 and the p-value ≤ 0.05, then reject the null hypothesis and conclude that there is a significant difference. Typically, if α = 0.05 and the p-value > 0.05, then fail to reject the null hypothesis and conclude that there is not a significant difference.

 

632

One-Way ANOVA Fundamentals

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: One-Way ANOVA Fundamentals

ANOVA Terms [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

633

One-Way ANOVA Equations

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: One-Way ANOVA Equations

Roll over each description of the One-way ANOVA to see the equation. [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

634

One-Way ANOVA Assumptions and Example

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: One-Way ANOVA Assumptions and Example

One-way ANOVA is used to determine whether data from three or more populations formed by treatment options from a single factor designed experiment indicate the population means are different. There are three basic underlying assumptions in using One-way ANOVA: • All samples are random samples from their respective populations and are independent. • Distributions of outputs for all treatment levels follow the normal distribution.  • Equal or homogeneity of variances.

Example Three call centers (A, B, and C) are being tested to see if customer wait time is statistically the same.  A sample of five wait times was taken from each call center. Is there a difference in any of the three call centers? Assume α = 0.05.

635

One-Way ANOVA Example Steps 1 and 2

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: One-Way ANOVA Example Steps 1 and 2

Step 1: Establish the hypotheses. Ho: μ1 = μ2 = μ3 Ha: At least one of the group means is different from the others. Step 2: Calculate the test statistic. Calculate the average of each call center (group) and the average of the samples:  

Call Center A

Call Center B

Call Center C

Time 1

17

28

16

Time 2

23

26

15

Time 3

18

24

17

Time 4

20

23

18

Time 5

19

26

21

Average

19.4

25.4

17.4

Overall Average

20.73

 

 

 

636

One-Way ANOVA Example Step 2 SS Factor

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: One-Way ANOVA Example Step 2 SS Factor

Step 2: Calculate SSFactor

The sum of squares is calculated by subtracting the average of each call center (group) from the overall average, squaring the result, and adding up the results and multiplying by the number of samples per call center (group): Group

Group Average Overall Average

Difference

Difference2

Call Center A

19.4

20.73

-1.33

1.7689

Call Center B

25.4

20.73

4.67

21.8089

Call Center C

17.4

20.73

-3.33

11.0889

 

 

 

Sum of diff. squared

34.6667

 

 

 

Samples per group

5

 

 

 

SS group

34.67 X 5 = 173.4

   

637

One-Way ANOVA Example Step 2 SS Error

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: One-Way ANOVA Example Step 2 SS Error

Step 2: Calculate SSError

The error of the sum of squares is calculated by summing the squared differences between each individual and its group mean and then adding the totals to get the sum of squares for the error term: Call Center A

Group Average

Difference

Difference2

SS (Sum of Squares)

17

19.4

-2.4

5.76

 

23

19.4

3.6

12.96

 

18

19.4

-1.4

1.96

 

20

19.4

0.6

0.36

 

19

19.4

-0.4

0.16

 

 

 

 

Total Call Center A

21.2

Call Center B

Group Average

Difference

Difference2

SS (Sum of Squares)

28

25.4

2.6

6.76

 

26

25.4

0.6

0.36

 

24

25.4

-1.4

1.96

 

23

25.4

-2.4

5.76

 

26

25.4

0.6

0.36

 

 

 

 

Total Call Center B

15.2

Call Center C

Group Average

Difference

Difference2

SS (Sum of Squares)

16

17.4

-1.4

1.96

 

15

17.4

-2.4

5.76

 

17

17.4

-0.4

0.16

 

18

17.4

0.6

0.36

 

21

17.4

3.6

12.96

 

 

 

 

Total Call Center C

21.2

 

 

 

Error Sum of Squares

57.6

 

638

One-Way ANOVA Example Step 2 SS Total

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: One-Way ANOVA Example Step 2 SS Total

Step 2: Calculate SSTotal

The total sum of squares is calculated by summing the squared difference of each individual value as compared to the overall average of the data: Call Center A

Overall Average

Difference

Difference2

SS (Sum of Squares)

17

20.73

-3.73

13.91

 

23

20.73

2.27

5.15

 

18

20.73

-2.73

7.45

 

20

20.73

-0.73

0.53

 

19

20.73

-1.73

2.99

 

 

 

 

Total Call Center A

30.03

Call Center B

Group Average

Difference

Difference2

SS (Sum of Squares)

28

20.73

7.27

52.85

 

26

20.73

5.27

27.77

 

24

20.73

3.27

10.69

 

23

20.73

2.27

5.15

 

26

20.73

5.27

27.77

 

 

 

 

Total Call Center B

124.23

Call Center C

Group Average

Difference

Difference2

SS (Sum of Squares)

16

20.73

-4.73

22.37

 

15

20.73

-5.73

32.83

 

17

20.73

-3.73

13.91

 

18

20.73

-2.73

7.45

 

21

20.73

0.27

0.07

 

 

 

 

Total Call Center C

76.63

 

 

 

Total Sum of Squares

231

639

One-Way ANOVA Example Step 2 Table

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: One-Way ANOVA Example Step 2 Table

Step 2: Calculate the ANOVA table. Degrees of freedom (df) is calculated for the group, error, and total sum of squares: • df group/factor = Number of groups (Call Centers) – 1 = 3 – 1 = 2 • df error = (Number of data points – 1) – (Number of groups – 1) = (15 – 1) – (3 – 1) = 12 • df total SS= Number of data points – 1 = 15 – 1 = 14 Complete the ANOVA table to determine the F value. The SSFactor, SSError, SSTotal, and df were all calculated previously. This information is transferred into the following table: Source Group Error Total

SS 173. 4 57.6 231

df 2

Mean Square 173.4 / 2 = 86.7

F (calc) 86.7 / 4.8 = 18.06

12 14

57.6 / 12 = 4.8  

   

The Mean Square is calculated by dividing the SS by df. F(calc) is determined by dividing the group mean square by the error mean square.

640

One-Way ANOVA Example Steps 3 and 4

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: One-Way ANOVA Example Steps 3 and 4

Step 3: Determine the critical value.  Fcritical is taken from the F distribution table. Roll over Page Resources at the bottom of the screen and click F Distribution Table to locate the critical value. For this example, when α = 0.05 with df = 2 in the numerator and df = 12 in the denominator the critical value is 3.89. Step 4: Draw the statistical conclusion. • If Fcalc < Fcritical fail to reject the null hypothesis.  •

If Fcalc  > Fcritical, reject the null hypothesis.

Since Fcalc > Fcritical, we reject the null hypothesis: 18.06 > 3.89. This indicates at a significance level of 0.05, that at least one of the call center average wait times is different. 

641

Two-Way ANOVA Introduction

Six Sigma Black Belt | Analyze | Hypothesis Testing Task: Two-Way ANOVA Introduction

Two-way ANOVA performs an analysis of variance for testing the equality of population means when classification of treatments is by two variables or factors. Click the introductory information below to learn more about two-way ANOVA. Assumptions • The populations from which the samples were obtained must be normally distributed. • The samples must be independent. • The variances of the populations must be equal. • The groups must have the same sample size. Use When • determining if two or more independent variables change the dependent variable. • determining if interactions between the factors change the dependent variable. Advantages For conducting a two-way ANOVA when it is appropriate rather than resorting to two separate one-way ANOVA’s: • Interactions can be investigated. • Resources can be used more efficiently. • Error variation is reduced by including a second factor, and estimating the interaction. Two-factor Design Used in the analysis of two-factor design yielding three pieces of information: • Main effects of independent factor A on the dependent variable. • Main effects of independent factor B on the dependent variable. • Interaction between factor A and B determines if a joint influence of the two independent variables on the dependent variable exists.

642

Two-Way ANOVA Terminology

Six Sigma Black Belt | Analyze | Hypothesis Testing Task: Two-Way ANOVA Terminology

The following are terms used in the Two-way ANOVA models taken from the ASQ Glossary and Tables for Statistical Quality Control, Fourth Edition, ASQ Statistics Division. Click each term below to learn more. Block A collection of experimental units more homogeneous than the full set of experimental units. Blocks are usually selected to allow for special causes, in addition to those introduced as factors to be studied. These special causes may be avoidable within blocks, thus providing a more homogeneous experimental subspace. Blocking The method of including blocks in an experiment in order to broaden the applicability of the conclusions or to minimize the impact of selected assignable causes. The randomization of the experiment is restricted and occurs within blocks. Factor A predictor variable that is varied with the intent of assessing its effect on a response variable. Factor Levels A potential setting, value, or assignment of a factor or the value of the predictor variable. Predictor Variable A variable that can contribute to the explanation of the outcome of an experiment. Replicate A single repetition of the experiment. Treatment The specific setting of factor levels for an experimental unit.

643

Two-Way ANOVA Models

Six Sigma Black Belt | Analyze | Hypothesis Testing Task: Two-Way ANOVA Models

Many of the key concepts for two-way ANOVA are either identical or similar to those of one-way ANOVA, but differ in the details of the ANOVA table. Calculations for the two-way ANOVA table are almost always completed using a statistical software program, but for the purpose of this course, only data tables and equations will be shown. Click the terms below to learn more about the fixed effects model, single replicate and the Fixed effects model with replication. Single Replicate Overview A single replicate at each combination of levels is reviewed, therefore: • n = 1 replicate • a = treatment levels (Each will be run the same number of times as there are blocking levels.) • b = blocking levels (Each additional treatment level runs the same number of times as there are treatment levels.) The second factor in ANOVA is generally referred to as blocks. Single Replicate Assumption Absence of any interaction between the two factors or the main factor and blocking factor. Single Replicate Equations Sum of squares of blocks

Where yi = sum of the ith row Sum of Squares Error SSE = TSS - SST - SSB Single Replicate Data Table Source Treatments Blocks Error Total

SS SST SSB SSE

df a-1 b-1 (a-1) (b-1) TSS N - 1

Mean Square SST/(a-1) SSB/(b-1) SSE/(a-1) (b-1)

F (calc) MST/MSE MSB/MSE  

 

 

644

Two-Way ANOVA Models

Six Sigma Black Belt | Analyze | Hypothesis Testing Task: Two-Way ANOVA Models

Replication Overview If an interaction exists, each treatment combination experiment must be replicated more than once to get an estimate of the interaction effect as well as the error, therefore: • a = number of levels for factor A • b = number of levels for factor B • n = number of replicates • k = the kth replicate in row a, column b • • • •

y111 = the first replicate in row 1, column 1 y112 = the second replicate in row 1, column 1 y11n = the nth replicate in row 1, column 1 yabn = the nth replicate in row a, column b

Replication Model Design Table

 

645

Two-Way ANOVA Models

Six Sigma Black Belt | Analyze | Hypothesis Testing Task: Two-Way ANOVA Models

Replication Equations Total Sum of Squares

Sum of Squares for factor A

Sum of Squares for factor B

Sum of Squares for the Interaction

Sum of Squares Error SSE - TSS - SSxB - SSA - SSB   Replication Data Table Source A Treatments B Treatments Interaction Error Total

SS SSA SSB SSA xB SSE

df a-1 b -1 (a-1) (b-1) ab (n – 1) TSS abn - 1

Mean Square SSA/(a -1) SSB/(b -1) SSAxB/(a -1) (b – 1)

F (calc) MSA/MSE MSB/MSE SSAxB/MSE

SSE/ab (n – 1)

 

 

 

646

ANOVA Exercise

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: ANOVA Exercise

Below are five statements about ANOVA. Drag the three correct statements on the left to the boxes on the right. Feedback will be given for incorrect answers. [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

647

Contingency Tables

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Contingency Tables

Contingency tables are used to analyze data via a two-way classification involving two factors with data that is usually attribute in nature such as frequency or counts. This tool is used to test whether two sources of variation are statistically independent. The test statistic used is the Chi-square statistic (χ2). When establishing hypotheses using contingency tables be sure to remember that the goal is not looking for differences, but testing dependency.

Example A manager wants to determine if the distribution of defect type varies by the non-overlapping shift (1st, 2nd, or 3rd) in which the product is produced. Is there a relationship between shift and defect type at α = 0.05?

648

Contingency Tables Steps 1 and 2

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Contingency Tables Steps 1 and 2

Step 1: Establish the hypotheses. • Ho: Shift and defect types are statistically independent. •

Ha: Shift and defect types are not statistically independent.

Step 2: Calculate the test statistic. Use the chi-square test statistic: Where: • O = the ith observed value • • • •

i

Ei = the ith expected value r = the number of rows in the contingency table c = the number of columns in the contingency table df = (r -1)(c-1)

   

649

Contingency Tables Step 2 Calculation of Observed

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Contingency Tables Step 2 Calculation of Observed

Step 2: Calculate the test statistic cont. Calculate the row and column totals, then the row probabilities. Row probabilities = the row total / sum of all rows.  

1st

2nd

3rd

Total

Label placement defect Wrapper thickness defect Pigment defect Total

13

17

9

39

Probabilit y from Total Column .264

7

20

7

34

.230

29

22

24

75

.507

49

59

40

148

1.000

650

Contingency Tables Step 2 Calculation of Expected

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Contingency Tables Step 2 Calculation of Expected

Step 2: Calculate the test statistic cont.

Expected Values The expected value is calculated by using the probability from the total column for each row in the observed frequencies table multiplied by the shift column total. For example, the 1st shift column total is 49 multiplied by .264 (probability from total column) = 12.89.  

1st

2nd

3rd

Label placement defect Wrapper thickness defect Pigment defect  

12.89

15.52

10.52

Probability from Total Column .264

11.27

13.57

9.20

.230

24.84

29.91

20.28

.507

651

Contingency Tables Step 2 Calc. Obs. and Exp. cont

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Contingency Tables Step 2 Calc. Obs. and Exp. cont

Step 2: Calculate the test statistic cont.

(Observed – Expected)2 / Expected Values Calculate (Observed – Expected)2 / Expected for each cell value. For example, the expected value for label placement defects produced by 1st shift employees is (13 – 12.89)2 / 12.89 = 0.001.   Label placement defect Wrapper thickness defect Pigment defect

1st 0.001 1.618 0.697

2nd 0.141 3.047 2.092

 

= 0.001 + 0.141 + 0.220 + 1.618 + 3.047 + 0.526 + 0.697 + 2.092 + 0.682 = 9.024 calculated value      

652

3rd 0.220 0.526 0.682

Contingency Tables Steps 3 and 4

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Contingency Tables Steps 3 and 4

Step 3: Determine the critical value. df = (rows – 1)(columns -1) = (3 – 1) (3 – 1) = 4.  Roll over Page Resources at the bottom of the screen and click Chi-square Distribution Table. Look under 4 degrees freedom in the χ20.05column (critical value = 9.488). Step 4: Draw the statistical conclusion. • If χ2 > χ2 , then reject the null hypothesis. calc  

α,4 critical

Since 9.024 < 9.488, we fail to reject the null hypothesis at α = 0.05 (Ho: Shift and defect types are statistically independent). The manager can conclude there is not a difference between shift and defect type.

653

Contingency Tables Exercise

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Contingency Tables Exercise

Below are five statements about contingency tables. Drag the three correct statements on the left to the boxes on the right. Feedback will be given for incorrect answers. [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

654

Non-parametric Tests

Six Sigma Black Belt | Analyze | Hypothesis Testing Task: Non-parametric Tests

The term parametric implies that an underlying distribution is assumed for the population, while non-parametric makes no assumptions regarding the population distribution; hence often called “distribution-free” tests. Click the information below to learn more about non-parametric tests. Advantage of parametric testing If the assumptions of parametric testing are met, the probability (power or 1 - β) of rejecting the null when it is false (correct decision) is higher than is the power of a corresponding non-parametric test with equal sample sizes. Advantage of non-parametric testing The test results are more robust against violation of the assumptions. Therefore, if assumptions are violated for a test based upon a parametric model, the conclusions based on parametric test significance levels (alpha risk) may be more misleading than conclusions based upon non-parametric test significance levels. When to use non-parametric tests According to “Nonparametric Statistics: An Introduction” by Jean D. Gibbons: " Use non-parametric tests if any of the following conditions are true: 1. 2. 3. 4. 5. 6. 7. 8.

The data are counts or frequencies of different types of outcomes. The data are measured on a nominal scale. The data are measured on an ordinal scale. The assumptions required for the validity of the corresponding parametric procedure are not met or cannot be verified. The shape of the distribution from which the sample is drawn is unknown. The sample size is small. The measurements are imprecise. There are outliers in the data making the median more representative than the mean.

And use non-parametric test when both of the following are true: 1. 2.

The data are collected and analyzed using an interval or ratio scale of measurement. All of the assumptions required for the validity of that parametric procedure can be verified.

"

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Non-parametric Statistical Tests

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Non-parametric Statistical Tests

When data are non-normal, the following statistical tests are commonly used to analyze data. Roll over the test name to learn more about each non-parametric statistical test. [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

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Non-parametric Hypothesis Testing

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Non-parametric Hypothesis Testing

Road Map The Hypothesis Testing Road Map was discussed earlier in this topic of the course and includes non-parametric tests. Remember, the roadmap is a very important tool that you will use with each hypothesis test. Roll over Page Resources at the bottom of the screen and click Hypothesis Testing Road Map to help discern which statistical tests are applicable for the data you are testing.    

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Hypothesis Testing Roadmap

Six Sigma Black Belt | Analyze | Hypothesis Testing | Non-parametric Hypothesis Testing Example: Hypothesis Testing Roadmap

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Moods Median Test Statistic

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Moods Median Test Statistic

The Mood's Median Test is used to determine whether there is sufficient evidence to conclude that samples are drawn from populations with different medians. The test statistic used is the chi-square test statistic:

A sample of a Mood's Median Test follows, along with the steps to perform it:

Example A health food company has launched a new energy shake that has been in production for 30 days. This shake is produced at three of the companies processing centers, and a sample size of at least 10 has been collected. The volume in ounces is measured for each container. Is the median volume per container the same for all three processing centers at a 95% significance level?   

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Moods Median Test Step 1

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Moods Median Test Step 1

Data Table Cente rA 16.2 16 16 16.1 15.9 15.8 16.2 16.1 16.3 15.7 16   n= 11

Cente rB 16 15.8 15.8 15.5 16.5 16.4 16.3 15.7 16.1 16.3     n= 10

Cente rC 15.8 15.9 16.5 16 16 16 16.2 16.1 15.9 16.4 16.3 16.2 n= 12

Step 1: Establish the hypotheses. Ha: At least one of the populations has a different median.

 

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Moods Median Test Step 2 Observed

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Moods Median Test Step 2 Observed

Step 2: Calculate the test statistic. 1. 2.

Calculate the overall median of all of the 33 samples. The overall median of all samples = 16. Construct an observed values table showing the number of data points above the overall median and another column showing the number below the overall median data points.  Half of the data points that are equal to the overall median should be counted in the “above” column and half in the “below” column. Note: The procedure for allocating values above and below the median may differ depending on the resource material or statistical software program utilized.

Observed Values   Center A Center B Center C

Number Above Overall Median 6.5 5.5 7.5

Number Below Overall Median 4.5 4.5 4.5

   

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Moods Median Test Step 2 Expected

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Moods Median Test Step 2 Expected

Step 2: Calculate the test statistic cont. 3. If the three sample populations have the same median, then each category should have half of the data points in the “above” column and half in the “below” column. Therefore, construct an expected values table entering half of the data points for each category in the “above” median column and half in the “below” median column.

Expected Values   Center A Center B Center C

Number Above Overall Median 5.5 5 6

   

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Number Below Overall Median 5.5 5 6

Moods Median Test Step 2 Calc. Obs. and Exp.

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Moods Median Test Step 2 Calc. Obs. and Exp.

Step 2: Calculate the test statistic cont.

where k = total number of observed (expected) cells. Column A

Column B

Column C

Column D

Column D/

Observed

Expected

O-E

(O-E)2

Column B

 

 

 

 

6.5

5.5

1

1

0.1818

5.5

5

0.5

0.25

0.0500

7.5

6

1.5

2.25

0.3750

4.5

5.5

-1

1

0.1818

4.5

5

-0.5

0.25

0.0500

4.5

6

-1.5

2.25

0.3750

 

 

 

 

1.2136

Note: When the observed or expected values in a given cell are < 5, cells are combined to assure that the minimum cell value is at least ≥ 5.

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Moods Median Test Steps 3 and 4

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Moods Median Test Steps 3 and 4

Step 3: Determine the critical value. Degrees of freedom (df) is k –1 where k is the number of processing centers (3 - 1 = 2). Roll over Page Resources at the bottom of the screen and click Chi-square Distribution Table to locate the critical value. Given degrees of freedom is k -1 = 2, and α = 0.05,χ2critical = 5.991. Step 4: Draw the statistical conclusion. • If χ2 > χ2 , then reject the null hypothesis. •

calc  

α, k-1 critical

Since 1.214 < 5.991, we fail to reject the null hypothesis. The median volume per container is the same for all three processing centers at a 0.05 significance level.  

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Levenes Test

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Levenes Test

Levene's Test Used to compare two or more variances, Levene's Test is appropriate for continuous data that may not be normally distributed, testing for homogeneity of variances across a set of k samples. The Levene's test statistic shown in various forms is: Rollover Page Resources and click Levene's Test Procedure to see a sample test, along with the steps to conduct it. Click Levene's Test Data to see the sample data.

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Kruskal-Wallis Test Statistic

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Kruskal-Wallis Test Statistic

The Kruskal-Wallis Test is used to determine whether several populations have different medians when the samples are independent and from populations with the same shape. This test is the variance version of the Mann-Whitney U Test. The significance statistic is H which is distributed as the χ2 distribution. Using the χ2 distribution table; where k = number of sample sets (χ2α,k-1) , the test statistic is: A sample Kruskal-Wallis Test follows, along with the steps to perform it:

Example A random sample of the population of customer satisfaction scores from three different bank branches was collected. With α = 0.05 and assuming the populations have the same shape, does the data support the statement that not all the medians are equal?

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Kruskal-Wallis Test Step 1

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Kruskal-Wallis Test Step 1

Data Table Branch A

Branch B

Branch C

99

97

95

92

99

94

95

99

99

98

98

99

98

98

98

97

97

97

96

99

96

Step 1: Establish the hypotheses.

Ha: At least one is different (Not all populations have the same median.

 

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Kruskal-Wallis Test Step 2 Calculation

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Kruskal-Wallis Test Step 2 Calculation

Step 2: Calculate the test statistic. 1.

Build a tally table and assign ranks to each value starting with the lowest. If a value occurs more than once, use the average of its ranks.

     

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Kruskal-Wallis Test Step 2 Calculation cont.

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Kruskal-Wallis Test Step 2 Calculation cont.

Step 2: Calculate the test statistic cont. 2. Transfer the ranks to the original data table and calculate a total for each sample. Branch A 99 92 95 98 97 96 Σ Ranks

Rank A 18.5 1 3.5 13 8.5 5.5 63

Branch B 97 99 99 98 97 99  

Rank B 8.5 18.5 18.5 13 8.5 18.5 98.5

  3. Enter calculated data back into the equation.    

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Branch C 95 94 99 98 97 96  

Rank C 3.5 2 18.5 13 8.5 5.5 69.5

Kruskal-Wallis Test Steps 3 and 4

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Kruskal-Wallis Test Steps 3 and 4

Step 3: Determine the critical value. Roll over Page Resources at the bottom of the screen and click the Chi-square Distribution Table. Given degrees freedom is k -1 = 2, and α = 0.05, χ2critical = 5.991. Step 4: Draw the statistical conclusion. • If H > χ2 , then reject the null hypothesis. calc  

α, k-1 critical

Since 2.65 < 5.991, we fail to reject the null hypothesis. The medians of the customer satisfaction scores for the three branches are equal.

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Mann-Whitney U Test Statistic

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Mann-Whitney U Test Statistic

The Mann-Whitney U Test is also known as "the Mann-Whitney-Wilcoxon Test" and "the Wilcoxon Rank Sum Test". The Mann-Whitney U Test performs a hypothesis test of equality of two population medians and calculates the corresponding point estimate and confidence interval when independent samples from two populations have the same shape. Critical values are obtained from the Mann-Whitney tables: • Ml and Mr refer to boundaries of the left and right rejection regions. •

For a left-tail test, reject if the test statistic is ≤ Ml:

•

For a right-tail test, reject if the test statistic is ≥ Mr:

•

For a two-tail test, reject if either of the observed values is less than or equal to the tabulated critical value:

M is the test statistic and is the sum of the ranks of the smaller sample. A sample Mann-Whitney U Test follows, along with the steps to conduct it.

Example A personal fitness center is running a promotion to attract new members. A daily sample of new membership enrollments is recorded for each shift and is shown in a data table. At a significance level of 0.05 and confirming the populations have the same shape, do the data support the hypothesis that morning shift associates sell more fitness memberships?  

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Mann-Whitney U Test Step 1

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Mann-Whitney U Test Step 1

Data Table Morning Staff

Evening Staff

10

13

13

5

9

4

3

3

7

12

5

11

12

9

 

4

Step 1: Establish the hypotheses.

 

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Mann-Whitney U Test Step 2 Calculation

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Mann-Whitney U Test Step 2 Calculation

Step 2: Calculate the test statistic. 1.

Build a tally table and assign ranks to each value starting with the lowest. If a value occurs more than once, use the average of its ranks.

# of Memberships 3 4 5 7 9 10 11 12

Tally II II II I II I I II

13

II

   

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Rank 1,2 (use 1.5) 3,4(use 3.5) 5,6 (use 5.5) 7 8,9 (use 8.5) 10 11 12,13 (use 12.5) 14,15 (use 14.5)

Mann-Whitney U Test Step 2 Calculation cont.

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Mann-Whitney U Test Step 2 Calculation cont.

Step 2: Calculate the test statistic cont. 2.   Transfer the ranks to the original data table and calculate a total for the smaller sample, which is needed for the test statistic M. Morning Staff Memberships 10 13 9 3 7 5 12     n1 = 7

Rank of Morning Staff Memberships 10 14.5 8.5 1.5 7 5.5 12.5   M = ∑ Rank Morning = 59.5  

Evening Staff Memberships 13 5 4 3 12 11 9 4   n2 = 8

3.    The calculated value is  M = ∑ Rank Morning = 59.5.

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Mann-Whitney U Test Steps 3 and 4

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Mann-Whitney U Test Steps 3 and 4

Step 3: Determine the critical value. Roll over Page Resources at the bottom of the screen and click Mann-Whitney Table. Find the entry with n1 = 7 and n2 = 8 with a right-tail α-value of 0.05 (Mr = 73). Step 4: Draw the statistical conclusion. For a right-tail test, reject if the test statistic is ≥ Mr:

Since the calculated value of the test statistic is 59.5, we fail to reject the null hypothesis; 59.5 < 73:

The conclusion is that the data do not support the hypothesis that the morning shift associates sell more fitness memberships.

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Non-parametric Tests Assessment Questions

Six Sigma Black Belt | Analyze | Hypothesis Testing Concept: Non-parametric Tests Assessment Questions

For each of the following statements, click the box for the corresponding non-parametric test. [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

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Lesson Summary

Six Sigma Black Belt | Analyze Summary: Lesson Summary

The primary focus of the Analyze phase of the Six Sigma methodology is to closely examine the output (Y), so that you may understand the variables or inputs (Xs) and their effects controlling Y. The Black Belt's responsibility includes gathering the Xs identified in the Measure phase and performing needed analysis to narrow the Xs from possible to probable prior to the launch of the Improve phase. The analysis is conducted through the use of tools such as: Exploratory data analysis • Graphical data analysis through multi-vari studies • Correlation and regression models Hypothesis testing • Statistical and practical significance • Significance level and power • Sample size calculation • Point and interval estimation • Tests for means, variances, and proportions • Paired-comparison tests • Goodness-of-fit tests • ANOVA • Contingency tables • Non-parametric tests The use of the activities and tools during the Analyze phase of the Six Sigma methodology discovers the root causes by identifying significant Xs impacting process performance. The Black Belt and the team are now ready to move forward in the project generating, selecting, testing and implementing solutions to address the root causes.

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Lesson Bibliography

Six Sigma Black Belt | Analyze Concept: Lesson Bibliography

Bibliography American Society for Quality. Six Sigma Green Belt Certification Preparation Course, Version 1 (web-based course). Milwaukee, WI, 2006. ASQ Statistics Division. Kittlitz, Rudy, editor. Glossary and Tables for Statistical Quality Control. 4th ed. Milwaukee, WI: ASQ Quality Press, 2005. Benbow, Donald W. and T.M. Kubiak. The Certified Six Sigma Black Belt Handbook. Milwaukee, WI: ASQ Quality Press, 2005. Breyfogle, Forrest W. III . Implementing Six Sigma: Smarter Solutions® Using Statistical Methods. 2nd ed. Hoboken, NJ: John Wiley & Sons, Inc., 2003. Dovich, Robert A. Quality Engineering Statistics. Milwaukee, WI: ASQ Quality Press, 1992. Gibbons, Jean Dickinson. Nonparametric Statistics: An Introduction. New York: Sage Publications, 1993. Montgomery, Douglas C. Introduction to Statistical Quality Control. 5th ed. Hoboken, NJ: John Wiley & Sons, Inc., 2005. Pries, Kim H.Six Sigma for the Next Millennium: A CSSBB Guidebook. Milwaukee, WI: ASQ Quality Press, 2006. Pyzdek, Thomas. The Six Sigma Handbook: A Complete Guide for Green Belts, Black Belts, and Managers at All Levels, 2nded. New York: McGraw-Hill, 2003. Six Sigma Academy. The Black Belt Memory JoggerTM: A Pocket Guide for Six Sigma Success. Salem, NH: Goal/QPC, 2002. Tague, Nancy R.The Quality Toolbox. 2nd ed. Milwaukee, WI: ASQ Quality Press, 2005. Windsor, Samuel E. Transactional Six Sigma for Green Belts. Milwaukee, WI: ASQ Quality Press, 2006.    

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Six Sigma Black Belt Improve

Lesson Introduction

Six Sigma Black Belt | Improve Introduction: Lesson Introduction

The Improve phase provides the tools and methods for determining and verifying the sources of variation (input variables - x). Well-designed experiments include those input variables (x) identified as critical to the process. In these experiments, input variables demonstrate the Y = f(x) relationship, where Y is a dependent variable that is a function of x. Using a design of experiments (DOE) approach produces very useful information on the relationships between factors so that experimenters may quickly move to improve the process. To better understand this concept, the ASQ Body of Knowledge provides the following topics: Design of experiments (DOE) • Define independent and dependent variables, factors and levels, response, treatment, error and replication. • Describe and apply the basic elements of experiment planning and organizing, including determining the experiment objective, selecting factors, responses, and measurement methods and choosing the appropriate design. • Define and apply the principles of power and sample size, balance, replication, order, efficiency, randomization and blocking, interaction and confounding. • Construct experiments such as completely randomized, randomized block and Latin square designs, and apply computational and graphical methods to analyze and evaluate the significance of results. • Construct these experiments and apply computational and graphical methods to analyze and evaluate the significance of results. • Construct these experiments (including Taguchi designs) and apply computational and graphical methods to analyze and evaluate the significance of results; understand the limitations of fractional factorials caused by confounding. • Apply Taguchi robustness concepts and techniques such as signal-to-noise ratio, controllable and noise factors, and robustness to external sources of variability. • Construct these experiments and apply computational and graphical methods to analyze and evaluate the significance of results. Response surface methodology • Construct these experiments and apply computational and graphical methods to analyze the significance of results. • Construct experiments such as central composite design (CCD), Box-Behnken, etc., and apply computational and graphical methods to analyze the significance of results. Evolutionary operations (EVOP) • Understand the application and strategy of EVOP.

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Lesson Overview

Six Sigma Black Belt | Improve Introduction: Lesson Overview

The tools and objectives of the Improve phase are illustrated below.

   

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Six Sigma Black Belt Improve Design of Experiments

Learning Objectives

Six Sigma Black Belt | Improve | Design of Experiments Concept: Learning Objectives

At the end of this Improve topic, all learners will be able to: • define independent and dependent variables, factors and levels, response, treatment, error and replication. • describe and apply the basic elements of experiment planning and organizing including determining the experiment objective, selecting factors, responses, and measurement methods and choosing the appropriate design. • define and apply the design principles of power and sample size, balance, replication, order, efficiency, randomization and blocking, interaction and confounding. • construct one-factor experiments such as completely randomized, randomized block and Latin square designs, and apply computational and graphical methods to analyze and evaluate the significance of results. • construct full-factorial experiments and apply computational and graphical methods to analyze and evaluate the significance of results. • construct two-level fractional factorial experiments (including Taguchi designs) and apply computational and graphical methods to analyze and evaluate the significance of results, and understand the limitations of fractional factorials caused by confounding. • apply Taguchi robustness concepts and techniques such as signal-to-noise ratio, controllable and noise factors and robustness to external sources of variability. • construct mixture experiments and apply computational and graphical methods to analyze and evaluate the significance of results. Portions of this topic were taken from the ASQ Six Sigma Green Belt web-based Certification Preparation Course.

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Introduction to Design of Experiments (DOE)

Six Sigma Black Belt | Improve | Design of Experiments Concept: Introduction to Design of Experiments (DOE)

Black belts use Design of Experiments (DOE) to craft well-designed efforts to identify which process changes yield the best possible results for sustained improvement. Whereas most experiments address only one factor at a time, the Design of Experiments (DOE) methodology focuses on multiple factors at one time. DOE provides the data that illustrates the significance to the output of input variables acting alone or interacting with one another. ASQ defines DOE as: "A branch of applied statistics dealing with planning, conducting, analyzing and interpreting controlled tests to evaluate the factors that control the value of a parameter or group of parameters." DOE provides these advantages over other, more traditional methods: • Evaluating multiple factors at the same time can reduce the time needed for experimentation. • Some well-designed experiments do not require the use of sophisticated statistical methods to understand the results at a basic level. However, computer software can be used to yield very precise results as needed. • The costs vary depending on the experiment, but the financial benefits realized from these experiments can be substantial. The graphic below depicts an example of a relationship between the components that DOE examines: • process input variables, normally referred to as x variables and as factors in DOE terminology. • process output variables, normally referred to as y variables and as responses in DOE terminology. • the relationship between input variables and output variables. • the interaction, or relationship, between input variables as it relates to the output variables.

 

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DOE Terminology

Six Sigma Black Belt | Improve | Design of Experiments Task: DOE Terminology

Certain terms are frequently used with DOE that need to be defined clearly. Click the name of the term on the left to reveal a definition and information about each. Independent variable See predictor variable. Dependent variable See response variable. Factor A predictor variable that is varied with the intent of assessing its effect on a response variable. Most often referred to as an "input variable." Factor Level A specific setting for a factor. In DOE, levels are frequently set as high and low for each factor. A potential setting, value or assignment of a factor of the value of the predictor variable. For example, if the factor is time, then the low level may be 50 minutes and the high level may be 70 minutes. Response variable A variable representing the outcome of an experiment.The response is often referred to as the output or dependent variable. Treatment The specific setting of factor levels for an experimental unit. For example, a level of temperature at 65° C and a level of time at 45 minutes describe a treatment as it relates to an output of yield. Experimental error An error from an experiment reveals variation in the outcome of identical tests. The variation in the response variable beyond that accounted for by the factors, blocks, or other assignable sources while conducting an experiment.

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DOE Terminology Continued

Six Sigma Black Belt | Improve | Design of Experiments Task: DOE Terminology Continued

Certain terms are frequently used with DOE that need to be defined clearly. Click the name of the term on the left to reveal a definition and information about each. Experimental run A single performance of an experiment for a specific set of treatment conditions. Experimental unit The smallest entity receiving a particular treatment, subsequently yielding a value of the response variable. Predictor Variable A variable that can contribute to the explanation of the outcome of an experiment. Also known as an independent variable. Repeated Measures The measurement of a response variable more than once under similar conditions. Repeated measures allow one to determine the inherent variability in the measurement system. Repeated measures are known as "duplication" or 'repetition." Replicate A single repetition of the experiment.  See also replication. Replication Performance of an experiment more than once for a given set of predictor variables. Each of the repetitions of the experiment is called a "replicate." Replication differs from repeated measures in that it is a repeat of the entire experiment for a given set of predictor variables, not just repeat of measurements of the same experiment. Note: Replication increases the precision of the estimates of the effects in an experiment. Replication is more effective when all elements contributing to the experimental error are included. In some cases replication may be limited to repeated measures under essentially the same conditions. In other cases, replication may be deliberately different, though similar, in order to make the results more general. Repetition When an experiment is conducted more than once, repetition describes this event when the factors are not reset. Subsequent test trials are run again but not necessarily under the same conditions.

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DOE Applications

Six Sigma Black Belt | Improve | Design of Experiments Concept: DOE Applications

Planning the experiment is probably the most important task in the Improve phase when using DOE. For planning to be done well, some experts estimate that 10-25% of your time spent should be devoted to planning and organizing the experiments. The purpose of DOE is to create an observable event from which data may be extracted and decisions made about the best methods to improve the process. DOE may be used most effectively in the following situations: • Identifying factors that produce a specific response or outcome • Selecting between alternative approaches to effect the best outcome In DOE, a full factorial design combines levels for each factor with levels for all other factors. This basic design ensures that all combinations are used, but if factors are many, this design may take too much time or be too costly to implement. In either case, a fractional factorial design is selected as the number of runs is fewer with fewer treatments. For example, a four-factor factorial experiment studies the effects on a golf score using four factors, each with two levels. The factors (and levels) could be: type of driver (regular or oversized), type of ball construction (balata-covered or three-piece), type of beverage (water or beer) and mode of travel (walking or riding). To run a full factorial design experiment, 16 runs would be required (illustrated below).

For a fractional factorial, only 8 runs would be required (see below).  Thus if time and funding only permits 8 rounds of golf, the fractional factorial design will provide good information about the main effects of the four factors as well as some information about how these factors interact. More detail on these designs and their differences may be found in later subtopics in this lesson.

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DOE Applications

Six Sigma Black Belt | Improve | Design of Experiments Concept: DOE Applications

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DOE Planning Process

Six Sigma Black Belt | Improve | Design of Experiments Task: DOE Planning Process

The project team decides the exact steps to follow in the Improve phase. Steps to include in the Improve phase may actually be identified in the Measure and Analyze phases and should be noted to expedite later planning in the Improve phase. What follows is a suggested guide for planning the experiment(s) to be conducted in the Improve phase. The suggested process may be modified depending on the exact situation. To use DOE, follow these steps: 1. Establish experiment objectives Objectives differ per project, but the designs typically fall into three categories to support different objectives: • Screening – used to identify which factors are most important. • Characterization – used to quantify the relationships and interaction between several factors. • Optimization – used to develop a more precise understanding of just one or two variables. 2. Identify factors to be considered • Label both input variables (x factors) and output variables (y responses) in the experiment. • Use information collected in prior phases to assist in the identification process. 3. Finalize an experiment design • Select a design for the experiment. • Choose a design type (full factorial, fractional factorial, or others) that meets the experiment’s objectives. • Determine how the factors are measured. • Consider the resources needed and determine whether a practice run or pilot experiment may be needed. 4. Run the experiment • Run the experiment and collect the data. Place initial data in the results column of a design array, a graphical representation of the experiment factors and results. Roll over Page Resources and click on Design Array for an example. • Minimize chance for human error by carefully planning where human error could occur and allow for the possibility in the planning process. • Randomize the runs to reduce confounding (defined later in this topic). • Document the results as needed depending on the experiment. 5. Analyze the results of the experiment • Review the results of the experiment(s). • Examine the relationships among input variables (factors) acting together and with regards to the output variable(s) (responses).

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DOE Planning Process

Six Sigma Black Belt | Improve | Design of Experiments Task: DOE Planning Process

6. Make decisions on next steps • Based on the results, determine next steps. • Are additional runs of the experiment needed? • Do the levels need to be modified prior to conducting the experiment again? • If the results point to an optimal solution, implement the factors and the levels of choice and look at the Control phase to sustain the desired improvements.

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Design Array

Six Sigma Black Belt | Improve | Design of Experiments | DOE Planning Process Concept: Design Array

Design Array

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Barriers to the Planning Process

Six Sigma Black Belt | Improve | Design of Experiments Concept: Barriers to the Planning Process

In all projects, barriers present themselves as obstacles to the project’s successful completion. The Improve phase of DMAIC is no exception. The following are examples of the types of barriers to watch for during planning for an experiment: • Objectives or purpose are unclear – the objectives are not developed and fully understood. • Factor levels are either set too low or too high – factor levels set inappropriately can adversely affect the data and understanding of the relationships between factors. • Unverified or misunderstood data from previous phases may lead to errors in planning and assumptions. • Experimentation is a cost, although DOE is more cost effective than some other options like OFAT (one-factor-at-a-time) experiments, the costs can be too expensive and need to be considered carefully. • Lack of management support – experiments require the full support of management in order to effectively use the resources required.

692

Selecting Experiment Factors

Six Sigma Black Belt | Improve | Design of Experiments Concept: Selecting Experiment Factors

Identifying process variables, both inputs/factors and outputs/responses, is an important part of the planning process. While the selection process varies based on the information gathered in the Analyze phase and the objectives of the experiment, variables should be selected that have the following basic characteristics: • Important to the process in question – Since many input and output variables may exist for a process, most experiments focus on only the most critical inputs and outputs for a process. Such emphasis makes it more likely to successfully improve the most relevant parts of a process and, on a practical level, limits the number of variables and the cost of conducting the experiment. • Identifiable relationships to the inputs and the outputs – If relationships are already evident based on prior information gathered, the design of the experiment can be more focused on those factors with the most positive impact on outputs. • Not extreme level values – The information related to the level values for the factors should not be extreme. Values that reflect a reasonable range around the actual performance of the factors usually yield the best results. There is no magic formula or equation for selecting the factors. The guidelines listed above and a review of the analysis work done in previous phases should provide a good basis for selection. Remember, the goal of Improve is to model the possible combination of factors and levels that yield valid and necessary results. We recommend the use of process experts for selecting experimental factors and levels based on prior analysis. The prior analysis should suggest what the critical factors are and where the levels should be set for a first run in the experiment.

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Other Planning Considerations

Six Sigma Black Belt | Improve | Design of Experiments Task: Other Planning Considerations

The DOE planning phase may include other considerations for the project team. Click the considerations on the left to reveal relevant information on the right. Iterative process One large experiment does not normally reveal enough information to make final decisions. Several iterations may be necessary so that the proper decisions may be made and the proper value settings verified. Measurement methods Ensure that measurement methods are checked out prior to the experiment to avoid errors or variations from the measurement method itself. Review measurement systems analysis to ensure methods have been reviewed and instruments calibrated as needed, etc. Process control and stability The results from an experiment are more accurate if the process in question is relatively stable. Inference space If the inference space is narrow, then the experiment is focused on a subset of a larger process – such as one specific machine, one operator, one shift, or one production line. With a narrowed or focused inference space, the chance for “noise” (variation in output from factors not directly related to inputs) is much reduced. If the inference is broad, the focus is on the entire process and the chances for noise impacting the results are much greater.

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Types of Experiment Designs

Six Sigma Black Belt | Improve | Design of Experiments Task: Types of Experiment Designs

Part of planning an experiment is selecting the experiment design. Click the type of design on the left to reveal a brief introduction of that design on the right. 2-level, 2 factor The simplest of design options, the 2-level, 2-factor design uses only four combinations or runs. The number in the first column represents the run number. The "+" symbol represents the high level; the "–" symbol represents the low level.

  Full Factorial

This design option includes all levels and all factors for a given process. The advantage of a full factorial design is that all factors and levels are part of the experiment, thus ensuring the most complete data. If there are 2 levels and 6 factors (26), then there are 64 possible runs for the experiment. A common description of factorial experiments is the designator Lf where f is the number of factors in the experiment and Lf, the number of levels. Fractional Factorial This design is best used when you are unsure about which factor influences the response outcome or when the number of factors is large (usually considered to be 5 or more). A fractional factorial uses a subset of the total runs. For example, if there are 2 levels and 6 factors (26), then there are 64 possible runs for the experiment. For a fractional factorial, the experiment could be reduced to 32 runs or perhaps even 16 runs. An example of this may be viewed later in this topic.

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Design Principles

Six Sigma Black Belt | Improve | Design of Experiments Task: Design Principles

Black Belts adhere to a set of design principles to assist in the proper experiment design. Click the name of the design principle on the left to reveal its description on the right. Power The equivalent to one minus the probability of a Type II error (1-β). A higher power is associated with a higher probability of finding a statistically significant difference. Lack of power usually occurs with smaller sample sizes. The Beta Risk (i.e., Type II Error or Consumer’s Risk) is the probability of failing to reject the null hypothesis when there is significant difference (i.e., a product is passed on as meeting the acceptable quality level when in fact the product is bad).  Typically, (β) = 0.10%.  This means there is a 90% (1-β) probability you are rejecting the null when it is false (correct decision).  Also, the power of the sampling plan is defined as 1-β, hence the smaller the β, the larger the power.  For example, the legal beta risk is the risk a guilty person could have been found not guilty and is set free. This was also discussed in the Analyze lesson. Sample Size The number of sampling units in a sample. Note: In a multistage sample, the sample size is the total number of sampling units at the conclusion of the final stage of sampling. Determining sample size is a critical decision in any experiment design. Generally, if the experimenter is interested in detecting small effects, more replicates are required than if the experimenter is interested in detecting large effects. Increasing the sample size decreases the margin of error and improves the precision of the estimate. There are several approaches to determining sample size including, but not limited to: Operating Characteristic Curves, Specifying a Standard Deviation Increase, and Confidence Interval Estimation Method. Balanced Design A design where all treatment combinations have the same number of observations.  If replication in a design exists, it would be balanced only if the replication was consistent across all the treatment combinations.  In other words, the number of replicates of each treatment combination is the same.

696

Design Principles

Six Sigma Black Belt | Improve | Design of Experiments Task: Design Principles

Replication Performance of an experiment more than once for a given set of predictor variables. Each of the repetitions of the experiment is call a replicate. Replication differs from repeated measures in that it is a repeat of the entire experiment for a given set of predictor variables, not just a repeat of measurements for the same experiment. Replication involves an independent repeat of each factor combination in random order. For example, suppose a metallurgical engineer is interested in studying the effect of two different hardening processes: oil quenching and saltwater quenching on an aluminum alloy. If he has five alloy specimens and treats them in each of the hardening processes, we will make ten observations. These should be done in random order to maintain the properties of replication. First, the experimenter can obtain an estimate of the experimental error which becomes a basic unit of measurement for determining whether observed differences in the data are really statistically different. Second, if the sample mean is used to estimate the true mean response for one of the factor levels in the experiment, replication permits the experimenter to obtain a more precise estimate of this parameter. Repetition When an experiment is conducted more than once, repetition describes this event when the factors are not changed or reset. Subsequent test trials are run again but not necessarily under the same conditions. Efficiency In experimental designs, efficiency refers to an experiment that is designed in such a way as to include the minimal number of runs and to minimize the amount of resources, personnel, and time utilized.

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Design Principles Continued

Six Sigma Black Belt | Improve | Design of Experiments Task: Design Principles Continued

Black Belts adhere to a set of design principles to assist in the proper experiment design. Click the name of the design principle on the left to reveal its description on the right. Randomization The process used to assign treatments to experimental units so each experimental unit has an equal chance of being assigned a particular treatment. Randomization validates the assumptions made in statistical analysis and prevents unknown biases from impacting conclusions. By randomization we mean that both the allocation of the experimental material and the order in which the individual runs or trials of the experiment are to be performed are arbitrarily determined. For example, suppose the specimens in a metallurgical hardness experiment are of slightly different thicknesses and the effectiveness of the quenching medium may be affected by the specimen thickness. If all the specimens subjected to the oil quench are thicker than those subjected to the saltwater quench, systematic bias may be introduced into the results. This bias handicaps one of the quenching media and consequently invalidates our results. Randomly assigning the specimens to the quenching media alleviates this problem. Blocking The method of including blocks in an experiment in order to broaden the applicability of the conclusions or to minimize the impact of selected assignable causes. The randomization of the experiment is restricted and occurs within blocks. Order The order of an experiment refers to the chronological sequence of steps to an experiment. The trials from an experiment should be carried out in a random run order. In experimental design, one of the underlying assumptions is that the observed responses should be independent of one another (i.e., the observations are independently distributed). By randomizing the experiment, we reduce bias that could result by running the experiment in a “logical” order. Interaction effect The interaction effect for which the apparent influence of one factor on the response variable depends upon one or more other factors. Existence of an interaction effect means that the factors cannot be changed independently of each other. (See example on separate page) Confounding Indistinguishably combining an effect with other effects or blocks. When done, higher-order effects are systematically aliased so as to allow estimation of lower-order effects. Sometimes, confounding results from poor planning or inadvertent changes to a design during the running of an experiment. Confounding can diminish or even invalidate the effectiveness of the experiment. (See example on separate page)

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Design Principles Continued

Six Sigma Black Belt | Improve | Design of Experiments Task: Design Principles Continued

Alias An alias is a confounded effect resulting from the nature of the designed experiment. The confounding may or may not be deliberate.

699

Interaction Example

Six Sigma Black Belt | Improve | Design of Experiments Concept: Interaction Example

Interaction occurs when one input factor depends on the level of another input factor as it relates to an output variable. An example of interactions, as found in Design and Analysis of Experiments by Douglas C. Montgomery, is typically graphed as in the examples below.

In the first example, no interaction exists as the lines are parallel. This indicates a lack of interaction between factors A and B. In the second example, interaction exists. Review the examples below to understand the patterns of interaction when using graphs such as these.

 

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Confounding Example

Six Sigma Black Belt | Improve | Design of Experiments Concept: Confounding Example

When the effects of two or more factors cannot be separated from each other, those factors are confounded or aliased to reduce the number of runs required in the experiment. In the example below, the factors are calculated by multiplying the two confounded factors together, for example:  XY = negative times negative = positive.

In the example above: • X, Y, and Z are factors. • "+" represents a high level. • "-" represents a low level. • X is confounded with YZ; Y with XZ; Z with XY. • In this example, the effects of X and YZ are distinguishable.  

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One-Factor Experiments

Six Sigma Black Belt | Improve | Design of Experiments Concept: One-Factor Experiments

As the name implies, one-factor experiments involve only one factor or input variable. In a one-factor experiment the project team selects a starting point, or baseline set of levels for each factor, then successively varying each factor over its range with the other factors held constant at the baseline level. After each factor has been tested, it is then easy to compare the results and conclude which factor most likely provides the optimal results. For more information, roll over Page Resources, and then click One-Factor Example. Often, one-factor experiments are used when the critical factor has been determined through prior analysis or when testing all factors is too costly or not practical. In these cases, a one-factor experiment allows the project team to focus on the one critical factor that can have the greatest impact on the response variable.

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One-Factor Example

Six Sigma Black Belt | Improve | Design of Experiments | One-Factor Experiments Example: One-Factor Example

Using our previous golf example, each factor is tested while the other factors remain the same – driver size, ball type, mode of travel and beverage.

The interpretation of the graph is straightforward; for example, because the slope of the mode of travel curve is negative, we would conclude that riding improves the score. Using these one-factor-at-a time graphs, we would select the optimal combination to be the regular-sized driver, riding, and drinking water. The type of golf ball seems unimportant.

703

Randomized Block Experiments

Six Sigma Black Belt | Improve | Design of Experiments Concept: Randomized Block Experiments

When focusing on just one factor in multiple treatments, it is important to maintain all other conditions as constant as possible. Since the number of tests to ensure constant conditions might be too large to practically implement, an experiment may be divided into blocks. These blocks represent planned groups that exhibit homogeneous characteristics. A randomized block experiment limits each group in the experiment to exactly one and only one measurement per treatment. For example, if an experiment is going to cover two shifts, then bias may emerge based on the shift during which the test was conducted. A randomized block plan might measure each item on each shift to reduce the chance for bias. A randomized block experiment would arbitrarily select the runs to be performed during each shift. For example, since the coolant temperature in the example below is probably the most difficult to adjust, but may in part reflect the impact of the change in shift, the best approach would be to randomly select runs to be performed during each shift. The random selection might put runs 1, 4, 5 and 8 in the first shift and runs 2, 3, 6 and 7 in the second shift. Another approach that may be used to nullify the impact of the shift change would be to do the first three replicates of each run during the first shift and the remaining two replicates of each run during the second shift.

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Latin Square Designs

Six Sigma Black Belt | Improve | Design of Experiments Concept: Latin Square Designs

A Latin square design involves three factors in which the combination of the levels of any one of them and the levels of the other two appear once and only once.  A Latin square design is often used to reduce the impact of two blocking factors by balancing out their contributions.  A basic assumption is that these block factors do not interact with the factor of interest or with each other.  This design is particularly useful when the assumptions are valid for minimizing the amount of experimentation. The Latin square design has two limitations: 1. 2.

The number of rows, columns, and treatments must all be the same (in other words, designs may be 3X3X3, 4X4X4, 5X5X5, etc.). Interactions between row and column factors are not measured.

An example of a Latin square design (3X3) is seen below.

Three aircraft with three different engine configurations are used to evaluate the maximum altitude when flown by three different pilots (A, B, and C). In this case, the two constant sources are the aircraft (1, 2, and 3) and the engine configuration (I, II, and III). The third variable – the pilots – is the experimental treatment and is applied to the source variables (aircraft and engine). Notice that the condition of interest is the maximum altitude each of the pilots can attain, not the interaction between aircraft or engine configuration. For example, if the data shows that pilot A attains consistently higher altitudes in each of the aircraft/engine configurations, then the skills and techniques of that pilot are the ones to be modeled. This is also an example of a fractional factorial as only nine of the 27 possible combinations are tested in the experiment.  

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Full-Factorial Example - Steps 1 and 2

Six Sigma Black Belt | Improve | Design of Experiments Concept: Full-Factorial Example - Steps 1 and 2

A full factorial experiment is one that contains all levels for all factors – no treatments are left out of the experiment. A detailed example of a full factorial follows. Suppose that temperature, time, and catalyst volume are three critical variables suspected of affecting the yield percentage for an industrial grade lubricant. The current yield percentage averages 82%. Step 1: Establish experiment objectives: The objective of the experiment is to maximize the yield percentage for the lubricant. The higher the yield percentage, the more product is created and more efficient is the use of resources. Step 2: Identify factors to be considered: The input variables (x) / factors are identified along with a high and low level for each:  

A. B. C.

Temperatur 115° C 135° C e: 50 minutes 70 minutes Time 94 gallons 102 gallons Volume of catalyst The output variable (y) / response is identified: Yield percentage of lubricant

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Full-Factorial Example - Steps 3 and 4

Six Sigma Black Belt | Improve | Design of Experiments Concept: Full-Factorial Example - Steps 3 and 4

Step 3: Finalize and test the design: The project team decides to use a full-factorial design, where all factors and levels are tested. In this situation, two levels and three factors are represented by a 23 full factorial experiment. This experiment has eight treatments (2x2x2 = 8). A design array is developed for the experiment:

A decision must be made on whether to run the experiment more than once. If prior analysis reveals a lot of variation in the process output (e.g., Cp or Cpk is less than 1.00, the generally accepted norm for a process that is not capable of meeting requirements), then repeating or replicating the experiment may provide enough data to see the dispersion in the output variable (y). For this scenario, assume that no output variable variation was detected in prior analysis work, so the decision is to not run the experiment more than once. Step 4: Run the experiment: Data are collected as the experiment runs. The results are recorded in the design array:

 

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Full-Factorial Example - Step 5

Six Sigma Black Belt | Improve | Design of Experiments Concept: Full-Factorial Example - Step 5

Step 5: Analyze the results of the experiment: Several methods may be used to examine the data. One method is to graph the results of the factor results with the output variables. The graph is called a "main effects plot." The mean is calculated for all the results for the low level and the high level of each factor. • Temperature: low level mean is 77.5% and high level mean is 88.0% • Time: low level mean is 82.0% and high level mean is 83.5% • Catalyst volume: low level mean is 82.5% and high level mean is 83.0%

Using this graphing technique, the data strongly suggests that there is a significant effect from the temperature factor and only a slight effect for the time and catalyst volume factors. The effect of temperature may also be calculated by summing the yield values when the temperature is high and by subtracting the yield values when the temperature is low and dividing the results by four. Temperature effect = (90+89+88+85) – (72+79+78+81) / 4 = 352-310/4 = 10.5 When the temperature is set at the high level, the yield gain is 10.5%. This increase is due to the temperature factor because during the four high temperature treatments, the other two factors were set at high two times and low two times. Similarly, calculate the effects for the other two factors: Time effect = (79+89+81+85) – (72+90+78+88) / 4 = 334-328 / 4 = 1.5 Catalyst volume effect = (78+88+81+85) – (72+90+79+89) / 4 = 332-330 / 4 = .5 The effects of changing the time to the higher level has a minor increase of 1.5%, while increasing the volume of the catalyst has a very small increase in yield of .5%

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Full-Factorial Example - Step 5 Cont. and Step 6

Six Sigma Black Belt | Improve | Design of Experiments Concept: Full-Factorial Example - Step 5 Cont. and Step 6

Similarly, the interaction effects of the factors may also be determined using a similar method. The design array is expanded to account for the interactions. The "+" or "-" indicator is determined by multiplication rules. For example, a "+" multiplied by a "-" equals a "-". A "-" multiplied by a "-" equals a "+".

Using the same process, calculate the effects of the interaction between variables: AxB effect = (72+89+78+85) – (90+79+88+81) / 4 = 324-338 / 4 = -3.5 BxC effect = (72+90+81+85) – (79+89+78+88) / 4 = 328-334 / 4 = -1.5 AxC effect = (72+79+88+85) – (90+89+78+81) / 4 = 324-338 / 4 = -3.5 AxBxC effect = (90+79+78+85) – (72+89+88+81) / 4 = 332-330 / 4 = .5 The study of interactions produces no information to contradict the original understanding that temperature (10.5%) by itself has the greatest impact on the yield percentage. All other factors and combination of factors produce no significant increase in the yield percentage and may, in some of the combinations, actually decrease it. These techniques can be verified using the analysis of variance (ANOVA) process previously discussed in detail in the Analyze and Measure lessons. Various statistical packages may be used to calculate the results. Generally, a p-value less than .05 on a specific factor demonstrates that factor is statistically significant. The percent of contribution to the results may also be determined using the ANOVA by examining the sum of squares (SS). Step 6: Make decisions on next steps: After the results of the experiment have been analyzed, decide what the next steps. In this example, the factor of statistical significance is temperature. The following are examples of possible next steps: • The first experiment could be repeated or replicated to verify results of the first run. Replication would be costly, but would add weight to the results of the first experiment. • A second experiment could be designed to build on the first. For example, the higher level of temperature (135°C) could be used for all treatments with variations allowed in the time or catalyst volume to produce additional information on optimum levels. • The higher level of temperature (135° C) could be established as the new level for the production process and the results could be monitored to compare with the previous average yield of 82%.

709

Yates Order

Six Sigma Black Belt | Improve | Design of Experiments Concept: Yates Order

When designing an experiment, the levels are assigned to each treatment in such a way as to ensure all possible combinations for all factors are included. For an experiment with a small number of factors, this is accomplished easily by observation. However, for larger experiments, the process of allocating the levels is more difficult. The Yates order is a means by which levels can be allocated to treatments of each factor. Let k equal the number of factors. Yates order is achieved for the kth column by entering the sign for the low level of the factor (usually represented by a "-" or "-1") in 2k-1 rows, starting at the top of the column. This is followed by entering the sign for the high level (usually denoted with a "+" or "+1") in 2k-1 rows. For example, the levels of a four-factor experiment would be allocated like the following: • k = 4 (with four columns). • Since there are two levels for each factor, there are 24 – or 16 – rows in total. •

• • •

The 1st column has the low level sign in the 21-1 rows (21-1 = 1) or first row, followed by the high level sign in the next row. This alternation continues until all rows are completed. The 2nd column has the low level sign in the 22-1 rows (22-1 = 2) or first two rows, followed by the high level sign in the next two rows. The 3rd column has the low level sign in the 23-1 rows (23-1 = 4) or first four rows, followed by the high level sign in the next four rows. The 4th column has the low level sign in the 24-1 rows (24-1 = 8) or first eight rows, followed by the high level sign in the next eight rows.

The design array using the Yates order for four factors looks like the diagram below:

 

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Yates Order

Six Sigma Black Belt | Improve | Design of Experiments Concept: Yates Order

 

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Fractional Factorial Experiments

Six Sigma Black Belt | Improve | Design of Experiments Concept: Fractional Factorial Experiments

A fractional factorial experimental design consists of a subset (fraction) of the factorial design.  Typically, the fraction is a simple proportion of the full set of possible treatment combinations.  For example, half-fractions, quarter-fractions, and so forth are common.  While fractional factorial designs require fewer runs, some degree of confounding occurs. A fractional factorial is often referred to as 2k factorials with k referring to the number of factors and 2, the number of levels. Using this nomenclature, a full factorial may be represented as 2k and the fractional factorial 2k-1 as to represent the subset of combinations. There are many possible fractional factorial designs and the number of possible fractional factorial designs can be represented by 2 k-p where p is the number of independent generators. For a fractional factorial, a subset of levels and treatments are used for the selected factors. In the example below, the full factorial is 23 and the fractional factorial is 23-1. Notice that the fractional only includes a subset of the possible combinations, but still uses balance in the combinations selected. In the graph below, the grayed rows are not used in the fractional factorial.

In the example above, the full factorial experiment uses all factors and all levels. The fractional factorial experiment uses only a subset of the levels (those not selected are grayed out). Analysis of the fractional factorial experiment is conducted in the same manner as a full factorial design. Roll over Page Resources and click on Example to receive further information regarding this topic.

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Example

Six Sigma Black Belt | Improve | Design of Experiments | Fractional Factorial Experiments Example: Example

Example An engineer is planning an experiment involving eight factors, each at two levels. She can afford no more than 35 runs. In this situation, a full factorial would require 28 = 256 runs and is thus not a possible design. She can use a fractional factorial design that will keep her total number of runs close to but less than 35. The 28-3 fractional factorial experimental design would require only 28-3 = 32 runs.

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Introduction to Taguchi Designs

Six Sigma Black Belt | Improve | Design of Experiments Concept: Introduction to Taguchi Designs

The Taguchi approach to experiments emphasizes two items: 1.      Reduce process variation which reduces the loss to society in general. 2.      Use a proper development approach to reduce process variation. • Identify a parameter that improves a characteristic of performance. • Identify a less expensive alternative design, material, or method that provides the same level of quality at a less expensive cost. To achieve these goals, Taguchi developed orthogonal arrays to facilitate the test strategy. Examples of orthogonal arrays are on the following pages.

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Orthogonal Arrays

Six Sigma Black Belt | Improve | Design of Experiments Concept: Orthogonal Arrays

Orthogonal designs or orthogonal arrays are balanced; they do not allow for interaction between separate factors composing the design. A 3 x 3 Latin square design is sometimes called a Taguchi L9 orthogonal array. The simplest orthogonal array (OA) is the L4, which stands for four trial runs. It falls within the two-level grouping of OAs. See example below.

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Introduction to Taguchi Robustness

Six Sigma Black Belt | Improve | Design of Experiments Concept: Introduction to Taguchi Robustness

Taguchi emphasizes the importance of consistency of product. Robustness refers to resistance to the effects of variation of some factors. For example, if Brand A chocolate bar is very soft at 100°F and brittle at 40°F, and Brand B maintains the same level of hardness at these temperature extremes, it could be said that Brand B is more robust to temperature changes in this range. Product characteristics can be made robust by reducing the variation of a few, key variables. Taguchi refers to these variables as "signal" or "noise factors." If these factors can be identified and variation in them can be reduced, the product can withstand variation in other input factors. Producing products that are robust to noise of various kinds is clearly desirable. Signal and noise factors will be discussed in more detail on the upcoming pages. Robust design aims to produce a reliable design by controlling parameters so random noise does not cause failure. Since DOE techniques help determine the best design concepts used for tolerance design, a robust DOE strategy helps create a design that improves the understanding of the relationship between product parameters, process parameters, and desired performance characteristics while being desensitized to adverse noise input variable levels that are inherent to the process. To achieve robustness, Taguchi suggests three design considerations: 1. 2.

3.

System design – Usually performed by engineers, system design involves the selection of parts, machines, process methods, and some product parameters. Parameter design – The selection of operating levels that contribute to an optimum output and are insensitive to environmental considerations (noise). This area is where quality professionals can add significant value. Tolerance design – Identifying process variations that are permissible when striving for consistent output and adjusting tolerances accordingly.

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Taguchi Loss Function

Six Sigma Black Belt | Improve | Design of Experiments Concept: Taguchi Loss Function

According to Taguchi: • Excessive variation is a result of poor manufacturing quality. Reacting to individual items inside and outside the specifications is counter-productive. • Quality engineering starts with an understanding of the cost of poor quality (COPQ). • COPQ is more than the number of items outside the specification multiplied by the cost of rework and scrap. • Cost to society also includes the loss to the customer through poor performance and reliability, early wear out, and difficulties when interfacing with other parts. Taguchi defined product quality as “the (minimum) loss imparted by the product to society from the time the product is shipped.” The Taguchi loss function translates any product deviation from its target parameter into a financial measure. Loss function: • maintains that poor quality causes increasing loss to all parties. • provides a financial value for customers' increasing dissatisfaction of product performance. • gives a financial value for increasing costs as product performance exceeds the desired target performance.

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Loss Function

Six Sigma Black Belt | Improve | Design of Experiments Concept: Loss Function

Taguchi bases loss function on the fact that quality is best at the target. With this in mind, loss occurs at points away from the target, even if the product is within specifications; meaning quality loss is zero if the characteristic is 100% at the target. To use loss function for determining the financial loss that will occur when the quality characteristic deviates from the target, one needs the following: • Cost of the defective product (A) • Tolerance; the amount of deviation from the target (Δ) • Target (m)  

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Loss Function Example

Six Sigma Black Belt | Improve | Design of Experiments Concept: Loss Function Example

Identical televisions are assembled in two locations, a Six Sigma facility (Location 1) and a non-Six Sigma facility (Location 2). The distribution of the television’s color density is within specification in both locations; however, their distributions greatly differ. Location 1 has 0.3% outside the limits, but location 2 has 0% outside the limits. Looking at the illustrations below, you can see the impact of the distribution on the loss function.  Sets built at location 2 will result in a loss approximately 3 times that of sets built in Location 1.

Location 1

Location 2    

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Loss Function Summary

Six Sigma Black Belt | Improve | Design of Experiments Concept: Loss Function Summary

Taguchi Loss Function The process’s results serve as the voice of the process. Variations tell how the process is performing. The target and specifications are the voice of the customer. The Taguchi Methods use the process’s results and the customer’s specifications to approximate the financial loss of both the suppliers and the customers. The greater the deviation the process results are from the target, the greater is the loss. Before a Taguchi loss function technical solution is introduced, conduct a business cost-benefit analysis for either reducing process variation or centering the process on the target. Remember, listening to the voice of the customer is essential for capturing requirements, feedback, and applying the knowledge to the process. Applying VOC and Taguchi loss function are ways to control costs and achieve quality. [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

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Taguchi Robustness Concepts

Six Sigma Black Belt | Improve | Design of Experiments Concept: Taguchi Robustness Concepts

As mentioned previously, robustness means resistance to the effect of variation of some factor. A product process is controlled by 3 primary factors: noise, signal, and control. These are explained below. Cont rol Fact ors

In robust parameter design, a control factor is a predictor variable that is controlled as part of the standard experimental conditions. In general, noise factors are allowed to vary with the hope that the output will vary minimally over a wide range for each control factor. Example: Items in a process that are controllable, but produce a response when triggered by a signal – design of parts within a furnace. Sign Strongly affect the mean response of the process, but are controllable and have al little affect on variation in the output response. Example: Thermostat on a Fact furnace or air conditioner. ors Nois In robust parameter design, a noise factor is a predictor variable that is hard to e control or is not desired to control as part of the standard experimental Fact conditions. In general, noise factors are allowed to vary with the hope that the ors output will vary minimally yet, they are included in an experiment to broaden the conclusions regarding control factors. Examples: Outside temperature, variations in line voltage. S/N Quantifies the effect of variation in controllable factors on the variation in the Rati process output. (This ratio has been criticized in some of the quality literature o for its importance and accuracy.)   Signal-to-noise ratios are defined so that a maximum value of the ratio minimizes variability transmitted from the noise variables. Then an analysis is performed to determine which settings of the controllable factors result in (1) the mean as close as possible to the desired target and (2) a maximum value of the signal-to-noise ratio. S/N ratio calculations are derived from the quality loss function. The objective is to maximize the performance measure that will minimize the expected loss. To meet the objective, designers select combinations of design variables that maximize the S/N ratio because the higher the ratio, the better. There are 3 cases of S/N ratios to consider: smaller is better, larger is better and nominal is best. More information will be given on the next two pages regarding formulas and examples.

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Signal-to-Noise Ratio

Six Sigma Black Belt | Improve | Design of Experiments Concept: Signal-to-Noise Ratio

S/N ratio measures the amount of unwanted noise relative to a signal's strength. Commonly used in the electronics field, airlines require passengers to shut down all electronic devices before takeoff and landing in order to reduce the background noise that could disrupt the any of the airplane’s electronic systems. Think about how this electronic example relates to conditions in the workplace for both equipment and people. As the magnitude of the process mean compared to its variation, the signal-to-noise (S/N) ratio is an excellent statistical performance metric for determining the best values/levels of the control factors. Taguchi developed the S/N ratio as a mathematical equation indicating the experimental effect’s influence above the effect of experimental error due to chance. Simply stated, S/N ratio is the estimated effect of all the noise factors on the product’s performance characteristics. Designers use S/N ratio calculations, derived from the quality loss function, to maximize the performance measure that will minimize the expected loss. To meet the objective, designers select combinations of design variables that maximize the S/N ratio because the higher the ratio the better. There are three cases of S/N ratios to consider: smaller is better, larger is better, and nominal is best. Smaller-is-Better

 

Larger-is-Better

   Nominal-is-Best  

 

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Robustness Example

Six Sigma Black Belt | Improve | Design of Experiments Task: Robustness Example

The Taguchi robustness concepts, in their simplest terms, involve the selection of process or operating conditions where uncontrolled external variability does not affect the product or process. The buttons below present a case where you must design a product so an unwanted variable does not affect the output of the process. Click each to learn more. Amp 1

The classic example is that of an amplifier, which takes a signal and increases it. The graph shows the plot of the output signal (dependent variable) as it changes with the input voltage (independent variable). Amp 2

Line voltage does vary and on occasion, it can be as low as 105 volts or even less, and it can surge to 125 volts or higher. Adding the mean and the range of variability to the graph shows the effect varying line voltage has on the output. In essence, both the signal and variability have amplified.

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Robustness Example

Six Sigma Black Belt | Improve | Design of Experiments Task: Robustness Example

Amp 3

Designing the amplifier to operate normally on 140 volts instead of 120 would be on a different portion of the response curve of the amplifier. This amplifier is now robust to the fluctuations of the input voltage because the variation of line voltages minimizes output.

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Design Process

Six Sigma Black Belt | Improve | Design of Experiments Task: Design Process

Taguchi’s approach to design emphasizes continuous improvement and includes three different aspects of design process: system design, parameter design, and tolerance design. Click on each to learn more. System Design • Also called "concept design" • Establishes basic engineering and design concepts; the overall architecture • Produces a prototype model to define initial product or product-design characteristic settings Parameter Design • Also known as "DOE" • Identifies settings that minimize variation • Finds the combination of control factor settings allowing the system to achieve its ideal function • Is insensitive to uncontrollable variables Tolerance Design • Sets tolerances to minimize the cumulative product manufacturing and lifetime costs; online quality control. • Focuses resources to reduce and control variation in a few critical dimensions (as per the Pareto principle). • Identifies tolerances that when tightened, produce substantial performance improvements. • Determines economic design of safety factors. • Studies the trade-off between extra cost for tighter tolerance and improved quality; also finds the most economical tolerances. Conclusion By identifying controllable parameters, the designer can develop a series of experiments to determine the factor with the greatest positive influence on the output of the desired product. Selecting a design or process that is insensitive to uncontrolled sources of variation improves quality.  

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Mixture Experiments

Six Sigma Black Belt | Improve | Design of Experiments Concept: Mixture Experiments

Mixture experiments are used when the levels of factors which are the components or ingredients of a mixture are not independent. A mixture experiment occurs when the factors selected are proportions of the group of components being blended. Since these proportions must sum to 100%, some standard mixture designs exist to facilitate this approach. The response or outcome in a mixture experiment is assumed to depend on the proportion of components in the mixture and not on the relative amounts in the mixture. Mixture design accounts for the dependence of response on proportionality of ingredients. The purpose of a mixture experiment is to model the blended components so that predictions of the response for any combination of the components can be made and so a measure of the influence of each component on the response can be made. A common example of a mixture experiment is the simplex-lattice design. This design is the approach used in the example on the following pages.

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Simplex-Lattice Example

Six Sigma Black Belt | Improve | Design of Experiments Concept: Simplex-Lattice Example

The simplex-lattice is an example of a boundary point design. This design approach places all of the design points on the external boundaries of the design. In an example, consider three chemicals being mixed together to obtain a new product yield. The example’s parameters include the following: • Three chemicals denoted as A, B, and C • Four equally spaced levels (or proportions) for each chemical: ° ° ° ° • • •

0 or 0% 0.333 or 33.3% 0.667 or 66.7% 1.0 or 100%

q = the number of factors = 3 1/m = the size of the proportion; in this example, levels are set at 1/3 For a {3,3} lattice (where q =3, and m=3), 10 design runs are determined with all possible proportion combinations.

Using the information above, a design array is determined similar to factorial designs:

The combinations displayed in the design array may be graphed in unique ways that make the mixture designs stand out against other experiment designs. The graph below is determined by the intersection of the level indicators on the outer edge of the graph.

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Simplex-Lattice Example

Six Sigma Black Belt | Improve | Design of Experiments Concept: Simplex-Lattice Example

The design of the experiment follows the unique limitation that all proportions must equal 1. The design points in each simplex lattice may be determined by the equation: (q+m-1)! / (M!(q-1)!) The analysis of the data follows the same pattern as other experiment designs, using ANOVA and other methods previously presented in this and other lessons.  

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Six Sigma Black Belt Improve Response Surface Methodology

Learning Objectives

Six Sigma Black Belt | Improve | Response Surface Methodology Concept: Learning Objectives

At the end of this Improve topic, all learners will be able to: • construct steepest ascent/descent experiments and apply computational and graphical methods to analyze the significance of results. • construct higher-order experiments such as central composite design (CCD) and Box-Behnken and apply computational and graphical methods to analyze the significance of results.

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Introduction to Response Surface Methodology

Six Sigma Black Belt | Improve | Response Surface Methodology Concept: Introduction to Response Surface Methodology

Response surface methodology (RSM) is a collection of mathematical and statistical techniques useful for the modeling and analysis of problems in which a response of interest is influenced by several variables and the objective is to optimize this response.  RSM is a sequential procedure that couples the concepts of experimental design and optimization theory.  The purpose of this methodology is to determine the optimum operating conditions for a given set of process variables.  Optimum operating conditions are arrived at by modeling the functional relationship between a set of independent variables and the response variable, using experimental design techniques. For some variables, RSM requires more trials than using the two-level fractional factorials that have been discussed in this lesson. For such cases, the number of variables may need to be reduced through prior analysis in previous phases, technical considerations, or fractional factorial experiments. Two-level fractional factorials assume that the response is linear between the levels considered for the factors involved in the experiment. This two-level approach is adequate for solving many problems and for facilitating useful designs. When a design needs to accommodate a situation where the response needs to be treated as a function of the levels of only a few input variables/factors, RSM adequately serves that role.

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Steepest Ascent or Descent

Six Sigma Black Belt | Improve | Response Surface Methodology Concept: Steepest Ascent or Descent

If two factors (X1, X2) are placed on an x-axis and y-axis, their effect on the response variable may sometimes be viewed in a contour plot. Contour plots show lines of constant response and are used to help the experimenter understand the response surface for the purpose of more rapidly converging on the optimum point.  When the response surface is a plane, the contour plot will contain parallel straight lines.  When the response surface is “twisted” indicating significant interaction, the contour lines will be curved.  Thus, interaction is a form of curvature in the underlying response surface model for the experiment. The method of steepest ascent (where "ascent" means improvement in the measurement of interest) is a well-known optimization technique that can be used to systematically climb a response surface in specific step sizes to seek out an optimum point. The goal of a steepest ascent approach to design is to move from an initial point in the two-factor space (X1, X2) in the direction of steepest ascent to achieve the greatest rate of increase in the response variable per distance traveled or maximum point. In general, the path of steepest ascent is perpendicular to the lines on the contour. By contrast, the method of steepest descent applies when searching for the minimum point. An example of contour may be viewed below. The nature of the contour curves in the vicinity of (+,+) suggests a path of steepest ascent: • in the "northeast" direction. • about 30o above the horizontal.

   

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Simplex Approaches to Steepest Ascent

Six Sigma Black Belt | Improve | Response Surface Methodology Concept: Simplex Approaches to Steepest Ascent

A simplex approach to steepest ascent requires the following: • One more point than the number of independent variables. • Move away from the lowest response point through the center of the other two points to an equal distance on the other side. • Repeat this process dropping the lowest point each time. An example of this approach may be seen below:

In this example, three points are used initially (all points labeled “A”) since there are two factors (see the rules listed above). Move from the lowest point (A70%) through the center of the line between A80% and A83% to a point equal distance away from the line between those two points. This produces the point labeled B90% as point A70% is dropped. Next, repeat the process taking the lowest point A80% and moving through the center point between A83% and B90% to a point equal distance on the other side, which is C92%.

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Central Composite Design

Six Sigma Black Belt | Improve | Response Surface Methodology Concept: Central Composite Design

A central composite design (CCD) uses an embedded factorial or fractional factorial that has a group of “star points” on the external part of the diagram. This combination provides an opportunity to estimate curvature. A CCD contains twice the number of star points as there are factors in the experiment. For a CCD, if the distance from the center to any factorial point is +/- 1 unit, then the distance from the center point to one of the star points is +/- a where a>1. The value of a depends on the number of factors involved and the design properties. The equation for a = [number of factorial runs]1/4. Examples of the three basic types of CCD designs are graphed and explained below:

CCC – Circumscribed • Original form of CCD • Star points establish new end points for factor levels • Requires 5 levels for each factor • Symmetry is spherical, circular, or hyperspherical CCF – Face Centered • Star points are center of each face • a= +/- 1 • Requires 3 levels for each factor CCI – Inscribed • Used when factor settings are truly the limits • Star points equal the factor settings for levels • A scaled down CCC design • Requires 5 levels for each factor  

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Box-Behnken Design

Six Sigma Black Belt | Improve | Response Surface Methodology Concept: Box-Behnken Design

The Box-Behnken design is unique in that it does not contain an embedded factorial or fractional factorial matrix. The treatment combinations are found at the mid-points of edges of the process spaces in the design. The Box-Behnken requires three levels for each factor. The primary limitation of this design is that blocking techniques are far fewer when compared to other central composite designs. The graph below depicts a Box-Behnken design for three factors (13 runs are illustrated):

The qualities found in the Box-Behnken design compared to other CCDs are: • Requires fewer treatment combinations than a CCD for cases of three or four factors. • Requires three levels for each factor rather than the five needed in most CCD designs. • Its “missing corners” are helpful when extreme values from the combination of factors are not needed or should be minimized.

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Box Behnken Runs

Six Sigma Black Belt | Improve | Response Surface Methodology Concept: Box Behnken Runs

The chart below illustrates the number of runs for Box-Behnken designs compared to central composite designs:    

     

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Six Sigma Black Belt Improve Evolutionary Operations

Learning Objectives

Six Sigma Black Belt | Improve | Evolutionary Operations Concept: Learning Objectives

At the end of this Improve topic, all learners will be able to understand the application and strategy of evolutionary operations (EVOP).

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Introduction to EVOP

Six Sigma Black Belt | Improve | Evolutionary Operations Concept: Introduction to EVOP

Introduction The purpose of the evolutionary operations methodology(EVOP) is to improve a process through systematic changes in the operating conditions of a given set of factors. An experimental design is established and conducted through a series of phases and cycles. The effects are tested for statistical significance against experimental error when such error can be calculated. When a factor is found to be significant, the operating conditions for that factor are reset and the experiment conducted again.  This process continues until no further gain is achieved. Hence, the concept of an evolution is established.

EVOP Analysis Steps 1. 2. 3. 4.

5.

Determine the process factors, operating conditions (i.e., high, low level), and response variables. Establish the experimental design to be conducted. Conduct two cycles before computing experimental error. Compare the effects of the factors to the experimental error. If the effects fall within the range of the experimental error, conclude that they are not significant and conduct another cycle. If one or more effects fall outside the range of experimental error, reset the operating conditions and begin another phase. Conclude the EVOP when no further gain is evident.

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Advantages of EVOP

Six Sigma Black Belt | Improve | Evolutionary Operations Concept: Advantages of EVOP

For finding an optimal solution, EVOP has several advantages: • Process does not need to be shut down as is the case with a designed experiment – the process still makes usable product. • Can run conditions that are within the normal operating parameters of the process. • Data are collected at predetermined conditions in the process. • The operating region slowly and methodically moves in the direction of improvement in results. • Conservative approach that may find more favor in some organizations that resist rapid change. • Fosters an environment of continuous improvement because the method is a simple mechanism and can be a part of normal day-to-day operations thus allowing adjustments and monitoring as part of daily work. EVOP also has a few disadvantages: • Since the factor level changes are relatively small, repeat runs are often needed for each phase. • The experiments are generally longer in duration than traditional designed experiments because only a few factors are changed in a given phase or cycle.

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EVOP Process

Six Sigma Black Belt | Improve | Evolutionary Operations Concept: EVOP Process

Definitions that should be considered prior to understanding the process steps: • Cycle represents one iteration of data collection at each point in the design. • Phase refers to a new iteration of cycles aimed at a previously defined condition. The phase is completed when the conditions are changed in response to improved results.

Example Process: 1.

2.

3. 4.

To run a two-factor or three-factor experiment (EVOP’s are not limited to two or three-factor experiments): Repeat the experiment and, after the second cycle, begin to measure the error and significance of results. (ANOVA tables are often used for this purpose as well as statistical software.) Continue the experiment for a third cycle and, if a factor is demonstrated to be significant, begin a second phase with a new set of conditions based on the significant results. • If factors are not statistically significant, consider increasing the range of the levels for these factors, or • Consider replacing these factors with different factors. If no factor is significant after eight cycles, change the factor levels or select new factors. When no further gain is evident, run new experiments to verify it with new factors or factor levels; then conclude the EVOP.

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Example of EVOP

Six Sigma Black Belt | Improve | Evolutionary Operations Concept: Example of EVOP

A plant has a chemical process that produces a commercial solvent when several chemicals are mixed together. An EVOP is structured with two factors: temperature and reaction time. The current process setting for temperature is 175o C. Levels are selected at 165o C and 185o C. The current process setting for reaction time is 50 minutes. Levels are selected at 46 minutes and 54 minutes. The result of the first cycle might look like the diagram below:

Interpreting the graph: • The first data point obtained (175o C and 50 min) produces a yield of 86% • • •

•

(Shown as 1:86% - cycle:result). The second data point obtained (185o C and 54 minutes) produces a yield of 83% (Shown as 2:83% - cycle:result). The chart above represents just one cycle of data obtained. A second cycle would be conducted. This cycle consisted of 5 runs. The data produced is then placed in an ANOVA table using statistical software to analyze results and determine if there is a statistical significance in the results. Roll over Page Resources to view the ANOVA table associated with this example. If the data analyzed suggests that temperature is statistically significant and produces a higher yield, then a second phase is begun with the factor of temperature centered on the higher temperature and the same time factor. ° For example, a new phase might begin with a temperature centered on 185o C (175° 185°, and 195° C) and maintain the time centered on 50 minutes.

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ANOVA Table

Six Sigma Black Belt | Improve | Evolutionary Operations | Example of EVOP Example: ANOVA Table

 

 

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Lesson Summary

Six Sigma Black Belt | Improve Summary: Lesson Summary

The Improve phase is about addressing root causes with solutions. Solutions must be developed, tried, and implemented with the support of data. To accomplish this, solutions should be developed using a planned, systematic approach aimed at eliminating or reducing the impact of the identified root cause. • The purpose of DOE is to provide the most efficient and economical method of reaching valid and relevant conclusions from the experiment. • Planning the experiment is probably the most important DOE task. SSBBs must adhere to a set of design principles to assist in the proper experiment design. • One-factor experiments involve only 1 factor or input variable, multi-factor experiments are designed to evaluated multiple factors set at multiple levels, and full-factorial experiments use an experiment to test each possible combination of the factors. • Taguchi Methods are a variation of full-factorial DOE design using a limited number of experimental runs. Taguchi’s robust design aims to produce a reliable design by controlling parameters so random noise does not cause failure. • SSBBs use mixture experiments when the levels of factors that are the components or ingredients of a mixture are not independent; thus blended into a group of components. This experiment models the blended components in order to predict a response for any combination. • Response surface methodology determines how a set of quantitative factors over a specified region affects response in order to set optimal levels for the variables.

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Lesson Bibliography

Six Sigma Black Belt | Improve Concept: Lesson Bibliography

Bibliography American Society for Quality. ASQ’s Foundations in Quality Learning Series: Certified Manager of Quality/Organizational Excellence. Milwaukee, WI: ASQ, 2005. American Society for Quality. ASQ’s Foundations in Quality Learning Series: Certified Quality Auditor. Milwaukee, WI: ASQ, 2004. American Society for Quality. ASQ’s Foundations in Quality Learning Series: Certified Quality Engineer. Milwaukee, WI: ASQ, 2000. American Society for Quality. "Glossary and Index." ASQ's Certified Quality Engineer Self-Directed Lean Program. Milwaukee, WI: ASQ, 2000 American Society for Quality. Six Sigma Green Belt Certification Preparation Course, Version 1 (web-based course). Milwaukee, WI, 2006. ASQ Statistics Division. Kittlitz, Rudy, editor. Glossary and Tables for Statistical Quality Control. 4th ed. Milwaukee, WI: ASQ Quality Press, 2005. Beezer, Rob. "Graeco-Latin Squares." Rob Beezer. 09 Jan 1995. University of Puget Sound. 18 Jul 2006. Benbow, Donald W. and T.M. Kubiak. The Certified Six Sigma Black Belt Handbook. Milwaukee, WI: ASQ Quality Press, 2005. Benbow, Donald, Roger Berger, Ahmad Elshennawy, H. Fred Walker, editors.The Certified Quality Engineer Handbook. Milwaukee, WI: ASQ Quality Press, 2002. Bossert, James, editor. The Supplier Management Handbook, 6thEdition. Milwaukee, WI: ASQ Quality Press, 2004. Keiningham, Timothy and Terry Vavra. The Customer Delight Principle. New York, NY: McGraw-Hill, 2001. Montgomery, Douglas C. Design and Analysis of Experiments, 6th ed. Hoboken, NJ: John Wiley & Sons, Inc., 2005. Oakes, Duke and Russell Westcott, editors. The Certified Quality Manager Handbook. 2nd ed. Milwaukee, WI: ASQ Quality Press, 2001. Westcott, Russell, editor. The Certified Manager of Quality/Organizational Excellence Handbook. 3rd ed. Milwaukee, WI: ASQ Quality Press, 2006.

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Six Sigma Black Belt Control

Lesson Introduction

Six Sigma Black Belt | Control Introduction: Lesson Introduction

The Control lessonprovides an overview of how to select, construct, interpret and apply critical aspects of statistical process control. To better understand this concept, the ASQ Body of Knowledge provides the following topics: Statistical process control • Understand objectives and benefits of SPC. • Select critical characteristics for monitoring by control chart. • Define and apply the principle of rational subgrouping. • Identify, select, construct and apply the following types of control charts: ° ° ° ° ° ° ° ° • •

X and R X and s ImR / X-MR X~ and R p np c u

Interpret control charts and distinguish between common and special causes using rules for determining statistical control. Define and explain PRE-control and perform PRE-control calculations and analysis.

Advanced statistical process control • Understand appropriate uses of short-run SPC, exponentially weighted moving average (EWMA), CUSUM charts and MAMR. Lean tools for control • Apply appropriate lean tools as they relate to the Control Phase of DMAIC: ° ° ° ° ° ° °

5S Visual factory Kaizen Kanban Poka-yoke Total productive maintenance (TPM) Standard work

Measurement system re-analysis • Understand the need to improve measurement system capability as process capability improves. • Evaluate the use of control measurement systems and ensure that measurement capability is sufficient for its intended use.    

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Lesson Overview

Six Sigma Black Belt | Control Introduction: Lesson Overview

The tools and objectives of the Control phase are illustrated below.

 

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Six Sigma Black Belt Control Statistical Process Control

Learning Objectives

Six Sigma Black Belt | Control | Statistical Process Control Concept: Learning Objectives

At the end of this Control topic, all learners will be able to: • understand objectives and benefits of SPC (e.g., controlling process performance, distinguishing special from common causes). • select critical characteristics for monitoring by control chart. • define and apply the principle of rational subgrouping. • identify, select, construct and apply control charts such as: ° X and R. ° X and s. ° ImR / X-MR. ° X~ and R. ° p. ° np. ° c. ° u. • •

interpret control charts and distinguish between common and special causes using rules for determining statistical control. define and explain PRE-control and perform PRE-control calculations and analysis.

  Portions of this topic were taken from the ASQ Quality Process Analyst web-based Certification Preparation Course and the ASQ Foundations in Quality Learning Series: Certified Quality Engineer.

750

SPC Introduction

Six Sigma Black Belt | Control | Statistical Process Control Concept: SPC Introduction

"A phenomenon will be said to be controlled, when through the use of past experience, we can predict, at least within limits, how the phenomenon may be expected to behave in the future." Walter A. Shewhart Pioneered by Walter Shewhart in the 1920s and later enhanced by W. Edwards Deming, statistical process control (SPC) is a statistical method for measuring, monitoring, controlling, and improving a process. The basic rule of SPC is to leave the variations from common causes to chance, but to identify and eliminate special causes. Since all processes are subject to variation, SPC relies on the statistical evidence instead of on intuition. SPC focuses on optimizing continuous improvement by using statistical tools for analyzing data, making inferences about process behavior, and then making appropriate decisions. Variation is defined as "a change in the process data; a characteristic or a function that results from some cause." Statistical process control begins with the recognition that all processes contain variation. No matter how consistent the production appears to be, measurement of the process data will indicate a level of dispersion or variability in the data. The management and improvement of variation are at the very heart of the strategy of statistical process control.

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SPC Objectives and Benefits

Six Sigma Black Belt | Control | Statistical Process Control Task: SPC Objectives and Benefits

When Shewhart developed his theory of statistical control, the approach was new and innovative. Today, SPC is considered by most to be a foundational tool in any quality management process. Click below to learn more. Objectives • To use the data generated by the process, called the “voice of the process,” to inform the Six Sigma Black Belt and team members when intervention is or is not required. • To reduce variation, increase knowledge about a process and steer the process in the desired way. • To detect quickly the occurrence of special causes of process shifts so that investigation of the process and corrective action may be undertaken before many nonconforming (defective) units are manufactured.   Benefits SPC will maximize profits and improve customer service by providing the tools to: • Monitor processes for maintaining control • Detect special causes • Serve as decision-making aids • Reduce the need for inspection • Increase product consistency • Improve product quality • Decrease scrap and rework • Increase production output • Streamline processes

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SPC Objectives and Benefits

Six Sigma Black Belt | Control | Statistical Process Control Task: SPC Objectives and Benefits

Tools Quality management processes may vary in the SPC tools utilized. Typical tools of SPC include: • Control charts • Pre-control charts • Flow charts • Run charts • Pareto charts and analysis • Fishbone diagrams • Histograms • Process capability analysis • Scatter diagrams • Sampling plans • Regression and correlation • Hypothesis testing • Design of experiments • Analysis of variance

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Common and Special Causes

Six Sigma Black Belt | Control | Statistical Process Control Task: Common and Special Causes

The basic rule of SPC is that variation from common causes (controlled) should be left to chance, but special causes (uncontrolled) should be identified and eliminated. Shewhart called the causes “common” and “assignable” respectively; however, the terms common and special are more frequently used today. Click below to learn more. Common causes Common causes are sources of process variation that are inherent in a process over time. A process that has only common causes operating is said to be in statistical control. A common cause is sometimes referred to as a "chance cause" or "random cause".

Examples of common causes • variation in raw material • variation in ambient temperature and humidity • variation in electrical or pneumatic sources • variation within equipment (worn bearings) • variation in the input data Special causes Special causes or assignable causes are sources of process variation (other than inherent process variation) periodically disrupting the process. A process that has special causes operating is said to lack statistical control. Examples of special causes • tool wear • large changes in raw materials • broken equipment Type I SPC Error Occurs when we treat a behavior as a special cause when no change has occurred in the process. Also referred to as "over control".

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Common and Special Causes

Six Sigma Black Belt | Control | Statistical Process Control Task: Common and Special Causes

Type II SPC Error Occurs when we do not treat a behavior as a special cause when in fact it is a special cause. Also referred to as "under control".

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Selection of Variable

Six Sigma Black Belt | Control | Statistical Process Control Concept: Selection of Variable

According to the Glossary and Tables for Statistical Quality Control, Fourth Edition, ASQ Statistics Division, a control chart plots a statistical measure of a series of samples in a particular order to steer the process regarding that measure and to control and reduce variation. Two key notes to consider are: 1. 2.

The order is usually time or sample number ordered-based. The control chart operates most effectively when the measure is a process characteristic correlated with an ultimate product or service characteristic.

Because of the Improve Phase of the DMAIC process, the Black Belt and team have implemented improvements to the variables or inputs (Xs) in the process causing variation in the output (Y). Once these improvements are in place, it is important to monitor the process. Select statistically and practically significant variables for monitoring that are critical to quality (CTQ) when establishing control charts. It is possible to monitor multiple variables using separate control charts.    

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Rational Subgrouping

Six Sigma Black Belt | Control | Statistical Process Control Task: Rational Subgrouping

Rational subgrouping is a subset defined by a specific factor. As a sample with variations caused by conditions producing random effects, the rational subgroup identifies and separates variations by special causes. Rational subgroups are our attempt to be sure that we are asking the right questions about the data. Selecting the appropriate control chart to use depends on the subgroups. Click below to learn more about rational subgrouping. Select the Measurement • Identify the best data to track. • Focus on the vital few, not the trivial many. • Select the best data for a few charts. • Produce elements of the subgroup in closely similar identical ways. Number of Subgroups • Establishing rational subgroups is important for dividing observations. • Compute statistics for each subgroup separately before plotting on the control chart. • Desire a minimal chance for variations within each subgroup: ° For example, 5 subgroups of 5 typically provide more useful information than 1 subgroup of 25 because the elapsed time between samples is minimized, providing more opportunities to detect process shift. The common cause variation can be measured with little or no influence from the special cause variation. Defect or Defective • Defect - An undesirable result on a product; also known as "a nonconformity". • Defective - An entire unit failing to meet specifications; also known as "a nonconformance". Note: A unit may have multiple defects. Sample Size Generally, 2 to 10 items produced under essentially the same conditions.  

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Rational Subgrouping Example

Six Sigma Black Belt | Control | Statistical Process Control Task: Rational Subgrouping Example

Rational subgroups are subgroups of data collected under relatively homogeneous conditions and is structured in a way that allows for the monitoring of the sources of variation that interest us. Rational subgroups are our attempt to be sure that we are asking the right questions about the data. Click below to see an example of rational subgrouping. Example A SSBB desires to monitor a process that manufactures PET (plastic) bottles for the beverage industry. The bottles are injection-molded on a multicavity carousel. The particular carousel contains 4 cavities and the SSBB initially decides to take 3 bottles from each cavity each hour and measure a critical characteristic. The data might look like the table below (where M1, M2, and M3 are the 3 measures). Option 1 Every hour, take 3 samples (subgroups) of 4 bottles (n = 4) at random. Plot the process (on one chart). Positives • Each hour has 3 averages and 3 ranges to plot. • The range indicates overall process variation. • Chart provides overall assessment of the quality during the time period. • Option provides data for overall assessment of process capability. • This is the easiest method of sampling. Negatives • Data is sampled without regard as to which cavity. • Sampling does not provide cavity-specific data to assist in finding causes of variation. Option 2 Every hour, take 3 samples (subgroups) of 4 bottles (n = 4) or one bottle from each cavity. Plot chart for process on 1 chart. Positives • Data records the cavity the bottle is from. • Each hour has 3 averages and 3 ranges to plot. • Chart shows overall quality during the time period. • Chart provides data for overall assessment of process capability. • Range reflects the difference between the cavities. Negatives • Chart requires more time collecting and recording data. • Data displays assessment by cavity, but requires additional analysis, not immediate feedback.

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Rational Subgrouping Example

Six Sigma Black Belt | Control | Statistical Process Control Task: Rational Subgrouping Example

Option 3 Every hour, take 4 samples (subgroups) and 3 bottles (n = 3) with each sample from a different cavity. Plot each cavity on separate charts. Positives • Maintaining 4 separate charts (one per cavity). • Each chart with one mean and one range to plot each hour. • Easy identification of where (which cavity) changes in the process occur. • Areas in need of improvement readily targeted. • Specific cavity capability data provided. • Most information relative to the process provided. Negatives • Requires more time for data collection and plotting • Requires collecting more data to establish the control limits Key Questions Each option is appropriate depending on the circumstances. Key questions to consider are: • How capable is the process? • Is monitoring overall quality more important than detecting the shifts? • How easy is it to identify a special cause when it occurs? • How much does it cost to collect the data and perform the tests?

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Rational Subgrouping Exercise

Six Sigma Black Belt | Control | Statistical Process Control Concept: Rational Subgrouping Exercise

The following example is taken from The Certified Six Sigma Black Belt Handbook by Donald W. Benbow and T.M. Kubiak. " Suppose a candy-making process uses 40 pistons to deposit 40 chocolate pieces on a moving sheet of wax paper in a 5 X 8 array on a conveyor belt. Below are 2 options illustrating how a rational subgrouping of 5 are selected: • Option 1: The first 5 chocolates in each row formed by 5 different pistons. • Option 2: The upper left-hand chocolate formed in 5 consecutive arrays by the same piston. " [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

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Control Charts

Six Sigma Black Belt | Control | Statistical Process Control Concept: Control Charts

Description Originated by Walter Shewhart, control charts are a type of graph for studying how a process changes over time. By comparing data points to a central line average, with an upper control limit (UCL) and lower control limit (LCL), users can note variation, track common causes, and seek special causes. Alternative names are "statistical process control charts" and "Shewhart charts". Run charts display data measures over time without the central line average and the limits.

Control Chart Benefits • • •

The addition of calculated control limits facilitates the ability to detect special or assignable causes of variation. The current process is displayed and compared to the improved process by identifying shifts in either average or variation. Since every process varies within predictable limits, identifying assignable causes and addressing them will save money.

 

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Basic Control Charts

Six Sigma Black Belt | Control | Statistical Process Control Concept: Basic Control Charts

Procedure 1.

Choose the appropriate control chart for your data (Information about specific types to come). 2. Determine the appropriate time period for collecting and plotting data. 3. Collect data and construct the chart with trial control limits using rational subgrouping. 4. Analyze the chart to determine process stability, looking for out-of-control signals. 5. Resolve any control issues, looking for assignable causes. 6. Recalculate the limits as necessary. 7. Prepare charts and instructions for production use. 8. Take samples and record data on the control chart. 9. Look for out-of-control conditions. 10. When out-of-control conditions occur, take appropriate action. Otherwise, leave the process alone.

Use When • • • • • •

Controlling ongoing processes by finding and correcting problems as they occur. Predicting the expected range of outcomes from a process. Determining if a process is in statistical control. Differentiating variation from non-routine events or common causes. Determining whether the quality improvement should aim to prevent specific problems or make fundamental process changes. The process is in control.

User Tips • •

Time is always the horizontal (X) axis. Control charts must have: ° Centerline (average) ° An upper control limit (UCL) and lower control limit (LCL) ° Data points ° Title ° Legend ° Labeled axes

• • •

When starting a new control chart, the process must be in control. The control limits calculated from the first 20 points are conditional limits. Recalculate the control limits after collecting at least 25-30 ordered points from a period when the process is operating in control. Developing a control chart with fewer than 25-30 points may not be statistically valid. If encountering an outlier when developing the control chart, investigate to see if there is an assignable cause; if so, eliminate the point from the analysis.

• •

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Types of Control Charts

Six Sigma Black Belt | Control | Statistical Process Control Concept: Types of Control Charts

Different types of control charts exist depending on the measurement used. This topic reviews two basic categories of control: variable charts and attribute charts. Variable charts • Constructed from variable data (data that consists of measurements like weight, length, etc.) • Variable data contains more information than data that simply qualifies or counts something. • Consequently, variable charts are some of the most powerful tools in quality improvement. • Types: Average and range (X and R), median and range (X~ and R), average and standard deviation (X and s), and individual and moving range (X-MR, I-MR, or I-mR). • Samples are taken in 2-10 subgroups at predetermined intervals with the statistic (mean, range, or standard deviation) calculated and recorded on the chart. Attribute charts • Use attribute data (data that counts items, such as the number of rejects or the number of errors). • Control charts based on attribute data are generally less powerful. • Sometimes more difficult to interpret than variable charts. • Types: p-charts, np-charts, c-charts, u-charts. • Samples are taken from lots of material where the number of defective units in the sample are counted (for p and np-charts) or the number of individual defects are counted for a defined unit (c and u-charts). The structure of both types of control charts is similar, but the statistical construction of the control limits is quite different due to the differences in the distributions in each.

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Control Charts Roadmap

Six Sigma Black Belt | Control | Statistical Process Control Concept: Control Charts Roadmap

The roadmap below leads users to the appropriate control chart. To introduce a control chart type in upcoming sections, this map will reappear highlighting the path (characteristics) of the particular control chart. Study each to learn the characteristics of each control chart.

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Introducing Variable Control Charts

Six Sigma Black Belt | Control | Statistical Process Control Concept: Introducing Variable Control Charts

Variable control charts monitor key measurable product characteristics or process variables. The formulas assume the normal distribution and limits are established based on plus or minus 3 standard deviations; thus, the chance of a part falling outside of the upper or lower control limit is 0.37%. For easier calculation of the limits, there is a table of control chart factors. Examples of factors are the A2 for the X chart and X~, as well as D3 and D4 for the R chart. Selection of the factor to use depends on the formula and the subgroup size (n). The subgroup is the sample of size n taken. For each subgroup, the SSBB will calculate the statistic of interest (X, X~, R, or s), and then plot it on the control charts. • Subgroups for X and R-charts and X~ and R-charts are generally 2 to 10 units. • Typically, an odd number of readings in each sample, 3 being the most common, is used with X~ and R-charts. The median of the sample is plotted rather than the average. • Subgroups for X and s-charts are usually greater than 10. In the formulas, the variable k is the number of subgroups taken. When k appears in formulas, take an average for all the subgroups (X, R, or s). Keep in mind when using the formulas for the R and s-charts, the control limits cannot go below zero. The lower control limit will be zero if the formula for the lower control limits gives a negative number. The X-MR charts have some additional considerations when using the term subgroup and with the formulas. The lesson will cover these at a later time.

765

Variable Equations

Six Sigma Black Belt | Control | Statistical Process Control Concept: Variable Equations

When working with control charts, one must calculate upper and lower control limits. Print this page as a reference for upcoming calculations.

766

X-bar and R

Six Sigma Black Belt | Control | Statistical Process Control Concept: X-bar and R

The average and range chart or X and R chart is the first type of variable control chart we will explore.

767

Calculating X-bar and R

Six Sigma Black Belt | Control | Statistical Process Control Task: Calculating X-bar and R

 

Collect data by subgroup

768

Calculating X-bar and R

Six Sigma Black Belt | Control | Statistical Process Control Task: Calculating X-bar and R

Calculate the mean for each subgroup

Calculate the range within each subgroup

769

Calculating X-bar and R

Six Sigma Black Belt | Control | Statistical Process Control Task: Calculating X-bar and R

Calculate the grand mean

Calculate the mean of the ranges

770

Calculating X-bar and R

Six Sigma Black Belt | Control | Statistical Process Control Task: Calculating X-bar and R

Find the appropriate A2 value from ref table

Calculate the UCL and LCL for the mean

771

Calculating X-bar and R

Six Sigma Black Belt | Control | Statistical Process Control Task: Calculating X-bar and R

From ref table, find the D4 and D3 values

Calculate the UCL and LCL for the ranges

772

Calculating X-bar and R

Six Sigma Black Belt | Control | Statistical Process Control Task: Calculating X-bar and R

Finished

773

Graphing X-bar and R

Six Sigma Black Belt | Control | Statistical Process Control Task: Graphing X-bar and R

 

For mean, draw the range, spacing, and labels

Use the grand mean to draw the centerline

774

Graphing X-bar and R

Six Sigma Black Belt | Control | Statistical Process Control Task: Graphing X-bar and R

Draw a line to display the UCL and LCL

Plot the subgroup means

Connect each point to form a line graph

775

Graphing X-bar and R

Six Sigma Black Belt | Control | Statistical Process Control Task: Graphing X-bar and R

Draw the y-axis and show the range of values

Use the range mean to draw the centerline

Draw a line to display the UCL and LCL

Plot the subgroup means

776

Graphing X-bar and R

Six Sigma Black Belt | Control | Statistical Process Control Task: Graphing X-bar and R

Connect each point to form a line graph

777

Completed X-bar and R Graph

Six Sigma Black Belt | Control | Statistical Process Control Concept: Completed X-bar and R Graph

The image on the right is an example of a completed X and R graph.

 

778

Activity: X-bar and R

Six Sigma Black Belt | Control | Statistical Process Control Concept: Activity: X-bar and R

With the data below, create an X and R control chart. When finished, roll over Page Resources, and then click the appropriate X and R Answer tab to check your work.

779

X-bar and R Answer Math

Six Sigma Black Belt | Control | Statistical Process Control | Activity: X-bar and R Example: X-bar and R Answer Math

780

X-bar and R Answer Table

Six Sigma Black Belt | Control | Statistical Process Control | Activity: X-bar and R Example: X-bar and R Answer Table

 

781

X-bar and R Answer Graph

Six Sigma Black Belt | Control | Statistical Process Control | Activity: X-bar and R Example: X-bar and R Answer Graph

 

782

Summary: X-bar and R

Six Sigma Black Belt | Control | Statistical Process Control Concept: Summary: X-bar and R

The X and R (average and range chart) has become the “workhorse” for many companies as they implement statistical process control. These charts are very useful because they are sensitive enough to detect early signals of process drift or target shift. Advantages • Easy to construct. • Easy to interpret. • Information from data is needed to perform process capability studies. • When a process can be sufficiently monitored by collecting variable data in small subgroups. • Can be sensitive to process changes and provide early warning; providing opportunity to act before situation worsens. Disadvantage • Can only be used when data is available to collect in subgroups.

783

Median (X-tilde and R)

Six Sigma Black Belt | Control | Statistical Process Control Concept: Median (X-tilde and R)

The median control chart or X~ and R chart is calculated using the same formulas as the X and R chart. The median control chart is different from the average and range chart in that it is easier to use and requires fewer calculations because the median is plotted rather than the average of the sample. Typically, the ease of using arithmetic is the advantage of using a median chart.

784

Calculating X-tilde and R

Six Sigma Black Belt | Control | Statistical Process Control Task: Calculating X-tilde and R

 

Collect data by subgroup

785

Calculating X-tilde and R

Six Sigma Black Belt | Control | Statistical Process Control Task: Calculating X-tilde and R

Determine the median for each subgroup

Calculate the range within each subgroup

786

Calculating X-tilde and R

Six Sigma Black Belt | Control | Statistical Process Control Task: Calculating X-tilde and R

Calculate the average of the subgroup medians

Calculate the mean of the ranges

787

Calculating X-tilde and R

Six Sigma Black Belt | Control | Statistical Process Control Task: Calculating X-tilde and R

Find the appropriate A2 value from ref table

Calculate the UCL and LCL for the median

788

Calculating X-tilde and R

Six Sigma Black Belt | Control | Statistical Process Control Task: Calculating X-tilde and R

From ref table, find the D3 and D4 values

Calculate the UCL and LCL for the ranges

789

Calculating X-tilde and R

Six Sigma Black Belt | Control | Statistical Process Control Task: Calculating X-tilde and R

Finished

790

Graphing X-tilde and R

Six Sigma Black Belt | Control | Statistical Process Control Task: Graphing X-tilde and R

 

For median, draw the range, spacing and labels

Determine the centerline of the subgroup medians

791

Graphing X-tilde and R

Six Sigma Black Belt | Control | Statistical Process Control Task: Graphing X-tilde and R

Draw a line to display the UCL and LCL

Plot all data points from the samples

Connect the middle point in successive samples

792

Graphing X-tilde and R

Six Sigma Black Belt | Control | Statistical Process Control Task: Graphing X-tilde and R

Draw the y-axis and show the range of values

Use the range mean to draw the centerline

Draw a line to display the UCL and LCL

Plot the subgroup means

793

Graphing X-tilde and R

Six Sigma Black Belt | Control | Statistical Process Control Task: Graphing X-tilde and R

Connect each point to form a line graph

794

Completed X-tilde and R Graph

Six Sigma Black Belt | Control | Statistical Process Control Concept: Completed X-tilde and R Graph

The image on the right is an example of a completed X~ and R (median) graph.

 

795

Activity: X-tilde and R

Six Sigma Black Belt | Control | Statistical Process Control Concept: Activity: X-tilde and R

With the data below, create an X~ and R control chart. When you are finished, roll over Page Resources and click the appropriate X~ and R Answer tab to check your work.

796

X-tilde and R Answer Math

Six Sigma Black Belt | Control | Statistical Process Control | Activity: X-tilde and R Example: X-tilde and R Answer Math

797

X-tilde and R Answer Table

Six Sigma Black Belt | Control | Statistical Process Control | Activity: X-tilde and R Example: X-tilde and R Answer Table

 

798

X-tilde and R Answer Graph

Six Sigma Black Belt | Control | Statistical Process Control | Activity: X-tilde and R Example: X-tilde and R Answer Graph

 

799

Summary: X-tilde and R

Six Sigma Black Belt | Control | Statistical Process Control Concept: Summary: X-tilde and R

The X~ and R (median) chart is an alternative to the X and R chart and is easier to use because it requires fewer calculations. The median chart is often used when outliers are expected. Advantages • Easy to use • Shows the process variation • Shows both the median and the spread Disadvantages • Less efficient, exhibiting more variation than the X and R chart • Difficult to detect trends and other anomalies in the range

800

X-bar and s

Six Sigma Black Belt | Control | Statistical Process Control Concept: X-bar and s

The average and standard deviation chart (X and s) is the next type of variable chart to explore. This chart is quite similar to the average and range chart except that the statistic used to measure subgroup dispersion is the subgroup standard deviation instead of the subgroup range.

801

Calculating X-bar and s

Six Sigma Black Belt | Control | Statistical Process Control Task: Calculating X-bar and s

 

Collect data by subgroup

802

Calculating X-bar and s

Six Sigma Black Belt | Control | Statistical Process Control Task: Calculating X-bar and s

Calculate the mean for each subgroup

Calculate the std dev within each subgroup

803

Calculating X-bar and s

Six Sigma Black Belt | Control | Statistical Process Control Task: Calculating X-bar and s

Calculate the grand mean

Calculate the mean of the std dev values

804

Calculating X-bar and s

Six Sigma Black Belt | Control | Statistical Process Control Task: Calculating X-bar and s

Find the appropriate A3 value from ref table

Calculate the UCL and LCL for the mean

805

Calculating X-bar and s

Six Sigma Black Belt | Control | Statistical Process Control Task: Calculating X-bar and s

Find the B3 and B4 values from ref table

Calculate the UCL and LCL for std dev

806

Calculating X-bar and s

Six Sigma Black Belt | Control | Statistical Process Control Task: Calculating X-bar and s

Finished

807

Graphing X-bar and s

Six Sigma Black Belt | Control | Statistical Process Control Task: Graphing X-bar and s

 

For mean, draw the range, spacing and labels

Use the grand mean to draw the centerline

808

Graphing X-bar and s

Six Sigma Black Belt | Control | Statistical Process Control Task: Graphing X-bar and s

Draw a line to display the UCL and LCL

Plot the subgroup means

Connect each point to form a line graph

809

Graphing X-bar and s

Six Sigma Black Belt | Control | Statistical Process Control Task: Graphing X-bar and s

Draw the y-axis and show the range of values

Use the std dev mean to draw the centerline

Draw a line to display the UCL and LCL

Plot the subgroup means

810

Graphing X-bar and s

Six Sigma Black Belt | Control | Statistical Process Control Task: Graphing X-bar and s

Connect each point to form a line graph

811

Completed X-bar and s Graph

Six Sigma Black Belt | Control | Statistical Process Control Concept: Completed X-bar and s Graph

The image on the right is an example of a completed X and s graph.

 

812

Activity: X-bar and s

Six Sigma Black Belt | Control | Statistical Process Control Concept: Activity: X-bar and s

With the sample data below, create an X and s control chart. When you are finished, roll over Page Resources and click the appropriate X and s Answer to check your work.

813

X-bar and s Answer Math

Six Sigma Black Belt | Control | Statistical Process Control | Activity: X-bar and s Example: X-bar and s Answer Math

814

X-bar and s Answer Table

Six Sigma Black Belt | Control | Statistical Process Control | Activity: X-bar and s Example: X-bar and s Answer Table

 

815

X-bar and s Answer Graph

Six Sigma Black Belt | Control | Statistical Process Control | Activity: X-bar and s Example: X-bar and s Answer Graph

816

Summary: X-bar and s

Six Sigma Black Belt | Control | Statistical Process Control Concept: Summary: X-bar and s

The X and s (average and standard deviation) chart is not used nearly as much as the X and R chart. One reason for the limited use of the X and s chart is simply that it is more complex to construct and use. Advantages • When the subgroup sizes are fairly large (greater than 10), it is often beneficial to consider the average and standard deviation chart, since using the range as the measure of dispersion may not yield a good estimate of process variability. • It may also be used when more sensitivity in detecting a process shift is desired, as in the case where the product being manufactured is quite expensive and any change in the process could either cause quality problems or add unnecessary costs. Disadvantages • May issue false signals at a much higher rate than other types of control charts. • Is complex to construct and use.

817

Introducing Moving Range

Six Sigma Black Belt | Control | Statistical Process Control Concept: Introducing Moving Range

Because of the type of data available and the situation, various control charts may be applicable. Given the unknowns of future projects and situations, the Six Sigma Black Belt may prefer to use the individual and moving range (X-MR, I-MR) control chart. Black Belt's often use this chart with limited data, such as when production rates are slow, testing costs are very high, or there is a high level of uncertainty relative to future projects. It has also found use where data are plentiful, such as in the case of automatic testing of every unit where no basis exists for establishing subgroups. On a typical moving range chart, calculate the range between two successive units (n = 2), but more successive units may be included in the range calculation. The factors for calculating upper and lower control limits on the MR-chart are the same as used in the R-chart. On the X-chart, plot every observation and calculate the upper and lower limits using the factor E2.

818

X-MR

Six Sigma Black Belt | Control | Statistical Process Control Concept: X-MR

The individual and moving range chart (X-MR, I-MR) is applicable when the sample size used for process monitoring is n = 1. Roll over Page Resources, and then click Using X-MR to see a list of applicable uses of X-MR control charts.

819

Using X-MR

Six Sigma Black Belt | Control | Statistical Process Control | X-MR Example: Using X-MR

Examples Using X-MR Charts X-MR charts are applicable to situations when the sample size is n = 1. Examples include: • The early stages of a process when one is not quite sure of the structure of the process data. • Monthly data. • When analyzing every unit (thus no basis for rational subgrouping). • Slow production rates with long intervals between observations. • When differences in measurements are too small to create an objective difference. • When measurements differ only because of laboratory or analysis error. • Taking multiple measurements on the same unit (as thickness measurements on different places of a sheet of aluminum).  

820

Calculating X-MR

Six Sigma Black Belt | Control | Statistical Process Control Task: Calculating X-MR

 

Collect data

Calculate the range between consecutive data

Calculate the mean for the data

821

Calculating X-MR

Six Sigma Black Belt | Control | Statistical Process Control Task: Calculating X-MR

Find E2 constant in ref table

Calculate the mean for the MR

Calculate the UCL and LCL for the mean

822

Calculating X-MR

Six Sigma Black Belt | Control | Statistical Process Control Task: Calculating X-MR

Find D3 and D4 constant in ref table

Calculate the UCL and LCL for MR

Finished

 

823

Graphing X-MR

Six Sigma Black Belt | Control | Statistical Process Control Task: Graphing X-MR

 

For mean, draw the range, spacing and labels

Use the mean to draw the centerline

824

Graphing X-MR

Six Sigma Black Belt | Control | Statistical Process Control Task: Graphing X-MR

Draw a line to display the UCL and LCL

Plot the individual measurements

Connect each point to form a line graph

825

Graphing X-MR

Six Sigma Black Belt | Control | Statistical Process Control Task: Graphing X-MR

Draw the y-axis and show the range of values

Use the MR mean to draw the centerline

Draw a line to display the UCL and LCL

826

Graphing X-MR

Six Sigma Black Belt | Control | Statistical Process Control Task: Graphing X-MR

Plot the moving range

Connect each point to form a line graph

827

Completed X-MR Graph

Six Sigma Black Belt | Control | Statistical Process Control Concept: Completed X-MR Graph

The image on the right is an example of a completed X-MR graph.

 

828

Activity: X-MR

Six Sigma Black Belt | Control | Statistical Process Control Concept: Activity: X-MR

With the data below, create an X-MR control chart. When you are finished, roll over Page Resources and click the appropriate X-MR Answer to check your work.  

829

X-MR Answer Math

Six Sigma Black Belt | Control | Statistical Process Control | Activity: X-MR Example: X-MR Answer Math

830

X-MR Answer Table

Six Sigma Black Belt | Control | Statistical Process Control | Activity: X-MR Example: X-MR Answer Table

 

831

X-MR Answer Graph

Six Sigma Black Belt | Control | Statistical Process Control | Activity: X-MR Example: X-MR Answer Graph

832

Summary: X-MR

Six Sigma Black Belt | Control | Statistical Process Control Concept: Summary: X-MR

An X-MR (individuals and moving range) chart is quite useful, since it is constructed with individual measures (that is, the subgroup size is one). The X-MR chart is applicable to many different situations, since there are many scenarios when the most obvious subgroup size is one (monthly data, etc.). A SSBB can use the individuals and moving range chart early in the production of a new product or the implementation of a new process. Then later, after more process knowledge is gained, it would be better to switch to a more sensitive chart. Advantages • Useful even in a situation with small amounts of data. • Easy to construct and apply. • Useful in the early stages of a new process when not much is known about the structure of the data. Disadvantage • Cannot discern between common cause and special cause variation.

833

Summary: Variable Charts

Six Sigma Black Belt | Control | Statistical Process Control Task: Summary: Variable Charts

Variable control charts have many advantages, especially the sensitivity they exhibit when designed appropriately. To learn more about some guidelines regarding the choice of variable charts, click each chart type below. X and R Average and range (X and R) charts are some of the most often used charts in SPC. The subgroup size for these charts is less than 10 and usually between 3 and 5. When designed effectively, these charts can be very sensitive and provide for excellent process monitoring. Since the average range of the subgroup drives the width of the control limits for the average chart, the subgroup size and selection process are crucial for these charts. X~ and R The median control chart or X~ and R chart is similar to the X and R chart and is calculated using the same formulas. The subgroup size for these charts is less than 10. The median control chart is different from the average and range chart in that it is easier to use and requires fewer calculations, as the median is plotted rather than the average of the sample. Typically, the ease of using arithmetic is the main advantage in using a median chart,which may also be used when anticipating outliers. X and s Average and standard deviation (X and s) charts are like the average and range charts in many ways, but the subgroup size is greater than 10. The large subgroup size means that X and s charts can be very sensitive to changes in the process. Thus, they are often used when you desire greater sensitivity and are willing to increase the cost of sampling. X-MR Six Sigma Black Belts often use individual and moving ranges (X-MR) charts at the beginning of a process launch when data is in short supply and each item processed is important. Since the subgroup size is one for this chart, it is widely applicable, especially in situations where small amounts of data are available.

834

Attribute Equations

Six Sigma Black Belt | Control | Statistical Process Control Concept: Attribute Equations

When working with attribute data charts, it is important to differentiate these related terms. • Defect - An undesirable result on a product; also known as a nonconformity. • Defective - An entire unit failing to meet specifications; also known as a nonconformance. Note: A unit may have multiple defects. On a form, an incorrectly completed block is a defect, thus one form may have multiple defects. However, any form with at least one defect would be defective. In monitoring form accuracy, one might count the number of defective forms or the total number of individual defects in a given number of forms. Of the attribute control charts, p and np-charts monitor percent defective (also known as fraction defective and fraction nonconforming) while c and u-charts are counts of defects. In the respective formulas, the variable k is the number of subgroups taken. When k appears in formulas, take an average for all the subgroups. Print this page as a reference for upcoming calculations with attribute charts.

835

Attribute Equations

Six Sigma Black Belt | Control | Statistical Process Control Concept: Attribute Equations

836

p-Charts

Six Sigma Black Belt | Control | Statistical Process Control Concept: p-Charts

The p-chart is one of the most-used types of attribute charts. It shows the proportion of defective items in successive samples of equal or varying size. Consider the proportion as the number of defectives divided by the number in the sample. To develop the control limits for a p-chart, consider the case where we are inspecting a variable sample size and recording the number of nonconforming items in each sample.

837

Introducing the p-Chart

Six Sigma Black Belt | Control | Statistical Process Control Task: Introducing the p-Chart

The p-chart monitors the proportion defective in successive samples of equal or varying size. Click each item below to learn more. Identify p • Take a sample of size n from a large lot and then count the total number of defective units. • For each sample, calculate a value of p as the number defective divided by the sample size, and then plot this proportion value on the chart. Centerline To calculate the centerline of the p-chart, • p, the summation of np, is the same as saying the sum of the total number of defective units.

•

The summation of n is just the total number of items in all the samples.

Variable Sample Sizes • Sample size n does not affect the centerline on a p-chart, however, the calculation of the upper and lower control limits is dependent on the sample size. • Where a sample size is variable, a common technique is to calculate the upper and lower control limits using the average sample size. • When using a chart with control limits, evaluate any points occurring near the upper or lower control limits to determine if, when the actual limits for the sample size are used, an out-of-control condition exists. Alternative Methods Once establishing the process average p, alternative methods are available to handle variable sample sizes. • If using a computer to monitor the process, it is common to calculate the limits based on every sample size. Some refer to this process as having moving limits. OR • •

Put two sets of limits on the chart, calculated using the maximum and minimum anticipated sample sizes. Then evaluate the points falling in between these two limits to determine if, when actual limits for the sample size are used, they signal out-of-control conditions.

838

Calculating p-Charts

Six Sigma Black Belt | Control | Statistical Process Control Task: Calculating p-Charts

 

Collect data by sample

839

Calculating p-Charts

Six Sigma Black Belt | Control | Statistical Process Control Task: Calculating p-Charts

Calculate the totals

Calculate the p value for each shipment (defectives per lot)

840

Calculating p-Charts

Six Sigma Black Belt | Control | Statistical Process Control Task: Calculating p-Charts

Calculate p-bar for data set (centerline)

If no moving limits, calc avg sample size

841

Calculating p-Charts

Six Sigma Black Belt | Control | Statistical Process Control Task: Calculating p-Charts

Calculate the UCL and LCL

Finished

842

Graphing p-Charts

Six Sigma Black Belt | Control | Statistical Process Control Task: Graphing p-Charts

 

Draw the range, spacing and labels

843

Graphing p-Charts

Six Sigma Black Belt | Control | Statistical Process Control Task: Graphing p-Charts

Use p-bar to draw the centerline

Draw a line to display the UCL and LCL

844

Graphing p-Charts

Six Sigma Black Belt | Control | Statistical Process Control Task: Graphing p-Charts

Plot the sample p values

Connect each point to form a line graph

845

Activity: p-Charts

Six Sigma Black Belt | Control | Statistical Process Control Concept: Activity: p-Charts

With the data below, create a p-Chart. When finished, roll over Page Resources and click the appropriate p-Chart Answer to check your work.

846

p-Chart Answer Math

Six Sigma Black Belt | Control | Statistical Process Control | Activity: p-Charts Example: p-Chart Answer Math

847

p-Chart Answer Table

Six Sigma Black Belt | Control | Statistical Process Control | Activity: p-Charts Example: p-Chart Answer Table

 

848

p-Chart Answer Graph

Six Sigma Black Belt | Control | Statistical Process Control | Activity: p-Charts Example: p-Chart Answer Graph

849

np-Charts

Six Sigma Black Belt | Control | Statistical Process Control Concept: np-Charts

The np-chart, number of defective units, is related to the p-chart. The np-chart is a control chart of the counts of nonconforming items (defectives) in successive samples of constant size. The np-chart can be used in place of the p-chart to plot the counts of nonconforming items (defectives) when there is a constant sample size. In effect, using np-charts involves converting from proportions to a plot of the actual counts.

850

Calculating np-Charts

Six Sigma Black Belt | Control | Statistical Process Control Task: Calculating np-Charts

  Collect data by sample

Calculate the total defective items

851

Calculating np-Charts

Six Sigma Black Belt | Control | Statistical Process Control Task: Calculating np-Charts

Calculate np-bar (centerline) for data

Calculate p-bar (needed to calculate UCL and LCL)

Calculate the UCL and LCL

852

Calculating np-Charts

Six Sigma Black Belt | Control | Statistical Process Control Task: Calculating np-Charts

Finished

853

Graphing np-Charts

Six Sigma Black Belt | Control | Statistical Process Control Task: Graphing np-Charts

 

Draw the range, spacing and labels

Use np-bar to draw the centerline

854

Graphing np-Charts

Six Sigma Black Belt | Control | Statistical Process Control Task: Graphing np-Charts

Draw a line to display the UCL and LCL

Plot the number of defectives by sample

Connect each point to form a line graph

855

Activity: np-Charts

Six Sigma Black Belt | Control | Statistical Process Control Concept: Activity: np-Charts

With the data below, create an np-Chart. When finished, roll over Page Resources and click the appropriate np-Chart Answer to check your work.

856

np-Chart Answer Math

Six Sigma Black Belt | Control | Statistical Process Control | Activity: np-Charts Example: np-Chart Answer Math

857

np-Chart Answer Table

Six Sigma Black Belt | Control | Statistical Process Control | Activity: np-Charts Example: np-Chart Answer Table

 

858

np-Chart Answer Graph

Six Sigma Black Belt | Control | Statistical Process Control | Activity: np-Charts Example: np-Chart Answer Graph

859

Summary: p and np Charts

Six Sigma Black Belt | Control | Statistical Process Control Concept: Summary: p and np Charts

• •

•

The centerlines in p and np-charts may not be midway between the control limits because sometimes the lower control limit is zero. Binomial distribution serves as the statistical model for both p and np-charts, thus, Six Sigma Black Belts often misuse p and np-charts because they fail to realize that the data does not meet the conditions of a binomial model. As Donald J. Wheeler writes in Advanced Topics in Statistical Process Control, "there are several conditions to meet before the binomial model is applicable and p and np-charts are appropriate: ° Each item must either possess or not possess the characteristic in question to the quality standard (items judged as acceptable or not acceptable, good or bad, etc.). ° The probability that a given item possesses the characteristic of interest is independent of whether there are or not preceding items." Six Sigma Black Belts often use X-MR charts instead of p and np-charts, especially when there is doubt about meeting the binomial model conditions.

860

Introducing c and u

Six Sigma Black Belt | Control | Statistical Process Control Task: Introducing c and u

C-charts and u-charts are based on Poisson distribution and work with the count of individual defects rather than numbers of defective units (used in the p and np-charts). Six Sigma Black Belts use c and u-charts where there are opportunities for many defects per defined inspection unit. For additional overview information on c and u-charts, click each item below. Defects and Units With c and u-charts, it is very important to define the defects and the unit. The unit is the area of opportunity to count the defects. Inspection Unit 50 miles of pipeline 10 yards of cloth 50 circuit boards 100 forms

Type of Defects Counted Weld defects Blemishes, snags Solder joint defects, damaged components Incorrect data entry, missing data

  C-Chart Formula The c-chart formulas assume counting the number of defects in the same area of opportunity. The c in the formulas is the number of defects found in the defined inspection unit, and that is plotted on the chart. For example, if the inspection unit is 100 forms, count the defects on a sample of 100 forms and plot that number on the c-chart.

  U-Chart Formula With a u-chart, the number of inspection units may vary. The u-chart requires an additional calculation with each sample to determine the average number of defects per inspection unit. The n in the formulas is the number of inspection units in the sample.

• • • •

A firm generates 250 forms in a given day and inspection found 27 errors. Since a sample contains 100 forms, 2.5 inspected units were examined (250 forms/ 100 forms/sample). To calculate u (defects per unit), divide the number of errors by the inspection unit (27 errors / 2.5 inspection units). Plot the u = 10.8 defects per unit on the control chart.

861

Introducing c and u

Six Sigma Black Belt | Control | Statistical Process Control Task: Introducing c and u

U and Variable Sample Size Because the u-chart equations for the upper and lower control limits are dependent on the number of inspection units (n), use the same alternatives relative to handling the variable sample size as with the p-charts: • Use the average sample size to develop the limits and evaluate points close to the limits. • Calculate the limits for each sample based on n.

862

c-Charts

Six Sigma Black Belt | Control | Statistical Process Control Concept: c-Charts

Use the c-chart, c standing for counts, when you are interested in the number of defects per inspection unit. The formulas for the control limits for the c chart (and the u chart, which is discussed later) are based upon the Poisson model.

863

Calculating c-Charts

Six Sigma Black Belt | Control | Statistical Process Control Task: Calculating c-Charts

 

Collect data by sample

Calculate the total defects

864

Calculating c-Charts

Six Sigma Black Belt | Control | Statistical Process Control Task: Calculating c-Charts

Calculate c-bar (centerline) for the entire data set

Calculate the UCL and LCL

Finished

865

Graphing c-Charts

Six Sigma Black Belt | Control | Statistical Process Control Task: Graphing c-Charts

 

Draw the range, spacing and labels

Use c-bar to draw the centerline

866

Graphing c-Charts

Six Sigma Black Belt | Control | Statistical Process Control Task: Graphing c-Charts

Draw a line to display the UCL and LCL

Plot the number of defects

867

Graphing c-Charts

Six Sigma Black Belt | Control | Statistical Process Control Task: Graphing c-Charts

Connect each point to form a line graph

868

Activity: c-Charts

Six Sigma Black Belt | Control | Statistical Process Control Concept: Activity: c-Charts

With the data below, create a c-Chart. When finished, roll over Page Resources and click the appropriate c-Chart Answer to check your work.

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c-Chart Answer Math

Six Sigma Black Belt | Control | Statistical Process Control | Activity: c-Charts Example: c-Chart Answer Math

870

c-Chart Answer Table

Six Sigma Black Belt | Control | Statistical Process Control | Activity: c-Charts Example: c-Chart Answer Table

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c-Chart Answer Graph

Six Sigma Black Belt | Control | Statistical Process Control | Activity: c-Charts Example: c-Chart Answer Graph

 

872

u-Charts

Six Sigma Black Belt | Control | Statistical Process Control Concept: u-Charts

The u-chart monitors the defects (nonconformities) per unit when the number of inspection units is allowed to vary.

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Calculating u-Charts

Six Sigma Black Belt | Control | Statistical Process Control Task: Calculating u-Charts

 

Collect data by sample

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Calculating u-Charts

Six Sigma Black Belt | Control | Statistical Process Control Task: Calculating u-Charts

Calculate the total rolls shipped

Calculate the total defects

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Calculating u-Charts

Six Sigma Black Belt | Control | Statistical Process Control Task: Calculating u-Charts

Calculate u-bar (centerline) for all the data

Calculate the UCL and LCL for n = 1

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Calculating u-Charts

Six Sigma Black Belt | Control | Statistical Process Control Task: Calculating u-Charts

Calculate the UCL and LCL for n = 2

Finished

877

Graphing u-Charts

Six Sigma Black Belt | Control | Statistical Process Control Task: Graphing u-Charts

 

Draw the range, spacing and labels

Use u-bar to draw the centerline

878

Graphing u-Charts

Six Sigma Black Belt | Control | Statistical Process Control Task: Graphing u-Charts

Draw a line to display the UCL and LCL

Plot the total number of defects per unit

Connect each point to form a line graph

879

Activity: u-Charts

Six Sigma Black Belt | Control | Statistical Process Control Concept: Activity: u-Charts

With the data below, create a u-Chart. When finished, roll over Page Resources and click the appropriate u-Chart Answer to check your work.

880

u-Chart Answer Math

Six Sigma Black Belt | Control | Statistical Process Control | Activity: u-Charts Example: u-Chart Answer Math

881

u-Chart Answer Table

Six Sigma Black Belt | Control | Statistical Process Control | Activity: u-Charts Example: u-Chart Answer Table

 

882

u-Chart Answer Graph

Six Sigma Black Belt | Control | Statistical Process Control | Activity: u-Charts Example: u-Chart Answer Graph

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Summary: C and U-Charts

Six Sigma Black Belt | Control | Statistical Process Control Concept: Summary: C and U-Charts

Use the c-chart to monitor the number of defects (nonconformities). The application of the c-chart requires the inspection unit to be defined clearly and the areas of opportunity to be consistent. The u-chart monitors the defects (nonconformities) per unit. It essentially changes the counts into rates in cases where the area of opportunity varies from sample to sample. The Poisson model is the statistical model that is the foundation of c and u-charts. Like the binomial model for p and np-charts, the Poisson model has several conditions that must be met: • The counts must be discrete events. • The counts must be clearly defined with an unambiguous area of opportunity described. • The events must be independent. • The defects (nonconformities) must be few compared to the areas of opportunity. Advantage • Can be used where the nonconformities from many potential sources may be found in a single inspection. Disadvantage • Requires a constant sample size.

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Summary: Attribute Charts

Six Sigma Black Belt | Control | Statistical Process Control Task: Summary: Attribute Charts

Six Sigma Black Belts often use attribute charts to monitor the quality of a complex unit when the data are easy to obtain. Many companies are including attribute gauging in their measurement systems. Attribute charts are some of the first charts a SSBB may attempt to use. The SSBB will likely discover that a critical process characteristic needs to be monitored with a variable chart. Click each type of attribute chart below to learn more about them and about how to select the appropriate chart. p-Chart The most often used, the p-chart, uses fraction nonconforming data. It provides an estimate of the ongoing quality level, and it is easy to use. A customer might request using a p-chart to ensure a certain quality level is being obtained. Remember that p-charts have the advantage of being applicable when the subgroup size varies. np-Chart The np-chart, a cousin of the p-chart, records the number of defective units (nonconformances) and is more difficult to use when the subgroup size varies. c-Chart The c-chart monitors the number of nonconformities (defects) and requires the inspection unit to be defined clearly and the area of opportunity to be consistent. u-Chart The u-chart monitors the nonconformities (defects) per unit. It essentially changes the counts into rates in cases where the area of opportunity varies from sample to sample.

885

Causes for Variations

Six Sigma Black Belt | Control | Statistical Process Control Concept: Causes for Variations

"Variation there will always be, between people, in output, in service, in product. What is the variation trying to tell us?" W. Edwards Deming Variations in output are due to one of the two types of causes: common and special (assignable). It is estimated that 85% of all process problems are due to common causes. Study the chart below to compare common and special causes.

886

Interpreting Control Charts

Six Sigma Black Belt | Control | Statistical Process Control Concept: Interpreting Control Charts

Interpreting control charts is a learned behavior based upon increased process knowledge. No shortcuts exist to becoming competent at the skill of interpreting control charts and it is most certainly not a skill learned without practice. The distinction between common and special causes is critical in statistical process control. For Shewhart and Deming, this distinction is the distinction between a process surrounded by "noise" and one sending a "signal." Improving the process is the central goal of using control charts. Control charts provide a "voice of the process" that enables a Black Belt to identify special causes of variation and remove them, thus allowing for a stable and more consistent process. A control chart becomes a useful tool after initial development. After establishing and basing the control limits on a stable, in-control process, charts put in the work area allow operational personnel to monitor the process by collecting data and plotting points on a regular basis. Personnel can act upon the signals from the chart when conditions indicate the process is moving or has gone out of control.

887

Process Stability

Six Sigma Black Belt | Control | Statistical Process Control Concept: Process Stability

Before taking appropriate action, a SSBB must identify the state the process. In Advanced Topics in Statistical Process Control, Donald Wheeler argues that a process can occupy one of 4 states: • Ideal state: A predictable process fully meeting the requirements. • Threshold state: A predictable process that is not always meeting the requirements. • Brink of chaos: An unpredictable process currently meeting the requirements. • State of chaos: An unpredictable process that is currently not meeting the requirements. Scroll this page to the bottom, then click each of the labels to learn more about process states. [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

888

Common Signs

Six Sigma Black Belt | Control | Statistical Process Control Concept: Common Signs

To see some of the common signs of an out-of-control condition on a control chart, roll over each term below to see a chart example. When finished, roll over Page Resources and then click Rules for a set of written guidelines to follow when interpreting control charts. [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

889

Rules

Six Sigma Black Belt | Control | Statistical Process Control | Common Signs Example: Rules

Standard Out of Control Conditions The following conditions are based on Western Electric Rules. The lists of conditions may vary depending on the resource used. 1. 2. 3. 4. 5. 6. 7. 8.

1 point more than 3σ from the center line (either side) 9 points in a row on the same side of the center line 6 points in a row, all increasing or decreasing 14 points in a row, alternating up and down 2 out of 3 points more than 2σ from the center line (same side) 4 out of 5 points more than 1σ from the center line (same side) 15 points in a row within 1σ from the center line (either side) 8 points in a row more than 1σ from the center line (either side)

890

Pre-control Introduction

Six Sigma Black Belt | Control | Statistical Process Control Task: Pre-control Introduction

According to originator Dorian Shainin, pre-control is a simple algorithm based on tolerances which is used for controlling a process. Pre-control is a method of detecting and preventing failures and assumes the process is producing a measurable product, with varying characteristics according to some distribution. Click below to learn more about using pre-control charts. Pre-control zones Pre-control zones include halfway between the target and each specification limit. Each zone between the lines has colors resembling a traffic signal with green (acceptable), yellow (alert), and red (unacceptable).

  Traditional pre-control charts Specification limits were originally used with the first pre-control charts to establish regions/zones, which have been deemed somewhat controversial. •

•

•

 

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If the process stayed within 1/2 of the specification or tolerance width, then it was allowed to run. If two consecutive samples were in either yellow range, then the process was adjusted or fixed. Any sample in the red zone was cause for stopping and repairing the process.

Pre-control Introduction

Six Sigma Black Belt | Control | Statistical Process Control Task: Pre-control Introduction

Six Sigma Method of Pre-control The Six Sigma Method of Pre-control utilizes process capability limits instead of specification limits to set the green, yellow, and red zones and is therefore considered more robust than the traditional use of pre-control charts.

• •

The limits of each zone are calculated based on the distribution of the characteristic measured, not on the tolerances. Units that fall in the yellow or red zones trigger an alarm before defects are produced.

  Pre-control rules Rule 1: • If two parts are in the green zone, take no action – continue to run. Rule 2: • If the first part is in the green or yellow zones, then check the second part. • If second part is in the green zone, then continue to run. • If first part is in the yellow zone and the second part is also in the yellow zone on the same side, adjust the process. • If first part is in the yellow zone and the second part is also in the yellow zone on the opposite side, stop and investigate the process. Rule 3: • If any part is in the red zone, then stop. • Investigate, adjust, or reset the process. • Re-qualify the process and begin again with Rule 1.

892

Foundation of Pre-control

Six Sigma Black Belt | Control | Statistical Process Control Concept: Foundation of Pre-control

Two samples are taken at specified intervals that depend upon the individual process being controlled.  • If the first sample “A” is in the green zone, then the second sample can occur within any region except red. The process is allowed to continue with no adjustment. • If, however, “A” occurs in either yellow zone, then if the “B” sample also occurs in either yellow zone, the process is stopped and fixed or adjusted before more parts are made. • If the process is stopped, 5 consecutive “parts” must be made in the green zone before the process is allowed to continue. Roll over Page Resources at the bottom of the screen and click Pre-control Probability Table to see the probabilities: • The sum of the probabilities of the 3 zones (red, yellow, and green) must equal 1. • Therefore, the probability that a unit falls in either of the red zones is 0.0013.  

893

Pre-control Steps

Six Sigma Black Belt | Control | Statistical Process Control Task: Pre-control Steps

Six Sigma Method of Pre-control Preliminary Activities The following are the steps in setting up the Six Sigma Method of pre-control for a process. Click below to learn more. 1. Calculate σst Determine the short-term sigma, which estimates the inherent machine capability. σst + σlt = σtotal Where: • σlt is the long-term sigma which includes factors other than the internal properties of the machine such as: ° Environment ° People ° Tool wear •

σtotal is the total sigma estimating the variability in the final product.

  2. Process Improvement (DOE) Improve the process to the extent practical by conducting a Design of Experiment (DOE). 3. Calculate Pre-control limits Recalculate short-term sigma (σst should be > 4 before using pre-control) then calculate the pre-control limits: • The green zone is ±1.5σ. • The yellow zone is -3σ and -1.5σ and 1.5σ and 3σ. • The red zone is beyond ±3.0σ.

894

Pre-control Steps

Six Sigma Black Belt | Control | Statistical Process Control Task: Pre-control Steps

4. Qualify the process To qualify the process, five consecutive samples must be in the green zone:

  5. Operate the process and sample Once the process is qualified, continue to operate the process taking 2 samples at appropriate intervals.

 

895

Pre-control Advantages and Disadvantages

Six Sigma Black Belt | Control | Statistical Process Control Concept: Pre-control Advantages and Disadvantages

In response to the debate about the use of pre-control charts, here are some of their advantages and disadvantages listed below. Advantages • Easy to implement and interpret. • Use in initial setup operations to determine if the product is centered between the tolerances. • Easy to detect shifts in process centering or increases in process spread. • Serves as a set up plan for short production runs. Disadvantages • Lacks information about how to reduce variability or how to return the process into control. • Too limited to use for process with a capability ratio greater than 1.0. • Small sample size limits the ability of the chart to detect moderate to large shifts.

896

SPC Exercise

Six Sigma Black Belt | Control | Statistical Process Control Concept: SPC Exercise

[ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

897

Six Sigma Black Belt Control Advanced Statistical Process Control

Learning Objectives

Six Sigma Black Belt | Control | Advanced Statistical Process Control Concept: Learning Objectives

At the end of this Control topic, all learners will be able to understand appropriate uses of short-run SPC, exponentially weighted moving average (EWMA), CUSUM charts and MAMR.       Portions of this topic were taken from the ASQ Foundations in Quality Learning Series: Certified Quality Engineer.

899

Short-Run SPC Introduction

Six Sigma Black Belt | Control | Advanced Statistical Process Control Concept: Short-Run SPC Introduction

Short-run or low-volume production is common in manufacturing systems and includes manufacturing processes that produce built-to-order products or quick turnaround production. The short-run control chart can also be used in other industries such as general services and healthcare when data are collected infrequently. These processes often are so short that not enough data can be collected to construct standard control charts. Statistical process control techniques have been developed to accommodate short-run production for both variables data and attributes data. Examples of control charts for both situations are presented. If possible, collect approximately 20 samples before you construct the control charts for short production runs are constructed. In the examples presented in this subtopic, ten samples will be used for illustration purposes. Roll over Page Resources at the bottom of the screen and click Short-run SPC Decision Flowchart to use as a job-aid in determining what type of chart is appropriate for your process.

900

Short-Run SPC Decision Flowchart

Six Sigma Black Belt | Control | Advanced Statistical Process Control | Short-Run SPC Introduction Example: Short-Run SPC Decision Flowchart

 

901

Var. Data Short-Run SPC Step 1 Measurements

Six Sigma Black Belt | Control | Advanced Statistical Process Control Concept: Var. Data Short-Run SPC Step 1 Measurements

For short production runs with variables data, the most commonly used control charting procedures are the X and R charts (also referred to as "nominal X and R charts"). The following are the steps for setting up the nominal X and R charts for short production runs:

Step 1: Measurements For a given process, say there are k samples measured, each with n observations, denoted by xij, as shown in the table below: Samples 1 2

Measurem ents x11, x12, x13 , ..., x1n x21, x22, x …, x2n

23,

: k

: xk1, xk2, xk3 , , xkn

   

902

Var. Data SPC Step 1 Nominal Defined

Six Sigma Black Belt | Control | Advanced Statistical Process Control Concept: Var. Data SPC Step 1 Nominal Defined

Step 1: Measurements/Deviations from Nominal Let Ti represent the nominal value for the ith sample, that is, there are k nominal values (not necessarily distinct), T1, T2, …, Tk. The data that will be plotted on a control chart are the deviations from the nominal, not the actual measured variables, and are denoted by dij, as shown in the table below, where dij = xij – Ti: Sample Number

Measurement Nominal, Ti s

Deviations from Nominal, dij

1

x11, x12, x13, …, x1n

d11 = x11 – T1

T1

d12 = x12 – T1, … d1n = x1n – T1

2

x21, x22, x23, …, x2n

  d21 = x21 – T2

T2

d22 = x22 – T2, … d2n = x2n – T2

: k

    dk1 = xk1 – Tk

: : xk1, xk2, xk3, , Tk xkn

dk2 = xk2 – Tk, … dkn = xkn – Tk  

 

903

Var. Data SPC Step 2 Deviations Defined

Six Sigma Black Belt | Control | Advanced Statistical Process Control Concept: Var. Data SPC Step 2 Deviations Defined

Step 2: Measurements/Deviations from Nominal/ di and Ri. The deviations, dij, are the new set of data that will be used to find the center line and control limits. Once the deviations from the nominal are found, the summary statistics, di and Ri, are calculated for all k samples, as shown in the table below:

    :::              

904

Var. Data Short-Run SPC Steps 3 - 5

Six Sigma Black Belt | Control | Advanced Statistical Process Control Task: Var. Data Short-Run SPC Steps 3 - 5

Variables Data Steps Continued Click the steps below to learn more. Step 3: Calculate the control limits for the average deviations Control limits for the average deviations can now be calculated using the same formula as given for control limits for the average but now with d-double overbar in place of X. The control limits for the average deviation from the nominal are:

where A2 is the control chart factor as shown before with subgroup size of n. Step 4: Calculate the control limits for the range Control limits for the range can now be calculated using the ranges from the deviations from the nominal. The control limits for the range are:

where D4 and D3 are the control chart factors for a subgroup of size n. Step 5: Create the control charts Control charts for both measures can now be created. The control charts will include: • upper and lower control limits • center line • statistics for each sample number Assumption necessary to apply this formula for the control limits: • The process standard deviation is approximately the same for all parts. Assumptions There are two basic assumptions that should be considered in order to apply the nominal X and R charts: • The process standard deviation is approximately the same for all parts. If this is not a valid assumption, an alternative control charting procedure should be used. • The procedure works best when the sample sizes are the same for each part number.

905

Var. Data Short-Run SPC Example Intro

Six Sigma Black Belt | Control | Advanced Statistical Process Control Concept: Var. Data Short-Run SPC Example Intro

Example The following data was collected over a two-day period on three parts. A total of ten subgroups were measured. This process represents a short production run because it will be running for only a five-day period. The three parts are given by A, B, and C, each with the following nominal values: • T A = 200 • •

T B = 70 T C = 35

The data found over a two-day period is shown the table on the right.   In this problem, k = 10 (number of samples) and n = 3 (number of measurements in each sample).

Sample Number

Part Type

Measureme nts xi1, xi2, xi3

1

A

2

A

3

A

4 5 6 7 8 9 10

B B B B C C C

 

906

202, 205, 201 199, 201, 203 198, 204, 207 73, 77, 75 78, 77, 74 72, 71, 76 68, 66, 71 37, 35, 35 32, 35, 34 31, 33, 38

Var. Data Short-Run SPC Example Step 1

Six Sigma Black Belt | Control | Advanced Statistical Process Control Concept: Var. Data Short-Run SPC Example Step 1

Step 1: Add the nominal values for each part to the table along with the deviations from the nominal. Sample Number

Part Type

Measurements Nominal Value, Deviations from Nominal, xi1, xi2, xi3 Ti dij = xij – Ti

1 2 3 4 5 6 7 8 9 10

A A A B B B B C C C

202, 205, 201 199, 201, 203 198, 204, 207 73, 77, 75 78, 77, 74 72, 71, 76 68, 66, 71 37, 35, 35 32, 35, 34 31, 33, 38

907

200 200 200 70 70 70 70 35 35 35

2, 5, 1 –1, 1, 3 –2, 4, 7 3, 7, 5 8, 7, 4 2, 1, 6 –2, –4, 1 2, 0, 0 –3, 0, –1 –4, –2, 3

Var. Data Short-Run SPC Example Step 2

Six Sigma Black Belt | Control | Advanced Statistical Process Control Concept: Var. Data Short-Run SPC Example Step 2

Step 2: Using the deviations as the new data set, the average deviation and range of the deviation can be found: Sample Number

Part Type Measurem Nominal ents Value, xi1, xi2, xi3 Ti

1

A

2

A

3

A

4 5 6 7 8 9 10  

B B B B C C C  

202, 205, 201 199, 201, 203 198, 204, 207 73, 77, 75 78, 77, 74 72, 71, 76 68, 66, 71 37, 35, 35 32, 35, 34 31, 33, 38  

Deviations Average Range, from deviations, Ri Nominal, di dij = xij – Ti

200

2, 5, 1

2.67

4

200

–1, 1, 3

1

4

200

–2, 4, 7

3

9

70 70 70 70 35 35 35  

3, 7, 5 8, 7, 4 2, 1, 6 –2, –4, 1 2, 0, 0 –3, 0, –1 –4, –2, 3  

5 6.33 3 -1.67 0.67 -1.33 -1

4 4 5 5 2 3 7

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Var. Data Short-Run SPC Example Step 3

Six Sigma Black Belt | Control | Advanced Statistical Process Control Concept: Var. Data Short-Run SPC Example Step 3

Step 3: Calculate the control limits for the average deviation, d-double overbar: Roll over Page Resources at the bottom of the screen and click Factors for Control Charts to find A2 for n = 3.

   

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Var. Data Short-Run SPC Example Step 4

Six Sigma Black Belt | Control | Advanced Statistical Process Control Concept: Var. Data Short-Run SPC Example Step 4

Step 4: Calculate the control limits for the range: Roll over Page Resources at the bottom of the screen and click Factors for Control Charts to find D3 and D4 with n = 3.

 

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Var. Data Short-Run SPC Example Step 5

Six Sigma Black Belt | Control | Advanced Statistical Process Control Concept: Var. Data Short-Run SPC Example Step 5

Step 5: Establish the control charts for the deviations:

   

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Attribute Data Short-Run SPC Introduction

Six Sigma Black Belt | Control | Advanced Statistical Process Control Concept: Attribute Data Short-Run SPC Introduction

The attribute control charts for long, continuous production runs are the: • p-chart • np-chart • c-chart • u-chart The properties behind these charts will be used to set up short-run control charts for attribute data. The short-run control charts for attribute data are actually standardized control charts. The attribute for the control chart of interest is standardized, and this standardized value is plotted on a control chart. To illustrate, consider the standardized value using the process nonconforming (i.e., p-chart):

The standardized attribute is found by subtracting the mean value and then dividing this difference by the attribute’s standard deviation. The new value is denoted by Zi.

912

Attribute Data Short-Run SPC Properties

Six Sigma Black Belt | Control | Advanced Statistical Process Control Task: Attribute Data Short-Run SPC Properties

Click below to learn about the properties of standardized control charts: 1. Each data point is standardized. • pi becomes a Zi • • •

npi becomes a Zi ci becomes a Zi ui becomes a Zi

For example, the standardized value using the p-chart is:

    2. The standardized random variable Zi is normally distributed.

    3. The center line for the standardized charts is 0.

 

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Attribute Data Short-Run SPC Properties

Six Sigma Black Belt | Control | Advanced Statistical Process Control Task: Attribute Data Short-Run SPC Properties

4. The control limits for the standardized charts are –3 and 3.

 

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Attribute Data Short-Run SPC Control Charts

Six Sigma Black Belt | Control | Advanced Statistical Process Control Concept: Attribute Data Short-Run SPC Control Charts

The standardized attribute control charts for short production runs are summarized in the following table: Attribute Control Chart

At tri bu te

Sta nda rd Dev iati on

Statistic Plotted on the Control Chart

of Attr ibut e p-chart

np-chart

c-chart

ci

u-chart

ui

 

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Attribute Data Short-Run SPC Example Intro

Six Sigma Black Belt | Control | Advanced Statistical Process Control Concept: Attribute Data Short-Run SPC Example Intro

Example Surface defects are counted on ten metal plates, all of the same surface size. The process the data comes from is considered a short production run. The surface defects on the ten metal plates are shown in the following table: Plate Number 1 2 3 4 5 6 7 8 9 10 Total

Number of Surface Defects 3 2 0 1 4 7 2 0 1 3 23

   

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Attribute Data Short-Run SPC Example Step 1

Six Sigma Black Belt | Control | Advanced Statistical Process Control Concept: Attribute Data Short-Run SPC Example Step 1

Step 1: Calculate the average number of nonconformities, c: It is important to determine whether the process is in control in terms of the surface defects (number of nonconformities).

where there are a total of 23 surface defects and 10 samples.

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Attribute Data Short-Run SPC Example Step 2

Six Sigma Black Belt | Control | Advanced Statistical Process Control Concept: Attribute Data Short-Run SPC Example Step 2

Step 2: Calculate the standardized values using:

The standardized values are given in the table below. Plate Number 1

Number of Surface Defects 3

 

Plate Number

2

2

 

7

2

3

0

 

8

0

4

1

9

1

5

4

 

   

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Number of Surface Defects 6 7

10

3

Attribute Data Short-Run SPC Example Step 3

Six Sigma Black Belt | Control | Advanced Statistical Process Control Concept: Attribute Data Short-Run SPC Example Step 3

Step 3: Plot the standardized values on a control chart with limits of -3 and 3 and a center line of 0:

Note: There appears to be one observation beyond the upper control limit, and the process appears to be out of control.

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EWMA Introduction

Six Sigma Black Belt | Control | Advanced Statistical Process Control Task: EWMA Introduction

According to the Glossary and Tables for Statistical Quality Control, the exponentially weighted moving average (EWMA) chart is a variable control chart where each new result is averaged with the previous average value using an experimentally determined weighting factor, λ (lambda). Click on the information below to learn more about EWMA charts. Equation Begins with a group of successive averages (or individual values if the subgroup size is 1). Each future value is a weighted average of the values that precede it. The recursive formula is given below:

where λ is the weighting constant (usually between 0.2 and 0.4).   Key Points • Usually only averages plotted and range omitted. • The action signal, a single point out of limits. • Also known as the Geometric Moving Average (GMA) chart. • Used extensively in time-series modeling and in forecasting. • Allows the user to detect smaller shifts in the process than with traditional control charts. • Ideal to use with individual observations.

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EWMA Example

Six Sigma Black Belt | Control | Advanced Statistical Process Control Concept: EWMA Example

Example A manufacturer of small electric motors has just finished a pilot run of eight motors. One of the critical dimensions is the diameter of the shaft on the journal end. With this limited production run, the company would like to know how consistently they are producing the diameters. The data is given below (in millimeters). Data Table 12 14 15 16 11 14 15 13 The data represents diameters for the first through the eighth motors, so the time sequence of manufacture is preserved.

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EWMA Example Steps 1 and 2

Six Sigma Black Belt | Control | Advanced Statistical Process Control Concept: EWMA Example Steps 1 and 2

Step 1: Choose a starting value and establish λ. Our initial value is the average of the first three points (12, 14, 15), with λ = 0.20: xi-1 = 13.67 (shown in the table below step 2) xi = 12

Step 2: Calculate the moving range and apply the recursive formula for the moving average. Moving range is the absolute difference between consecutive points. Note that the range is always positive. The first moving range is 2 (the absolute difference between 12 and 14), and the second moving range is 1 (the absolute difference between 14 and 15). Thus, the moving ranges for the entire set of data shown in the MR column below. Applying the recursive formula yields the following:

Order

xi

(x) EWMA

MR

1 2 3 4 5 6 7 8   ∑x x

12 14 15 16 11 14 15 13   110 13. 67

13.67 13.74 13.99 14.39 13.71 13.77 14.02 13.82      

  2 1 1 5 3 1 2      

   

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EWMA Example Step 3

Six Sigma Black Belt | Control | Advanced Statistical Process Control Concept: EWMA Example Step 3

Step 3: Calculate the control limits The upper and lower control limits for the EWMA chart are fairly complex to calculate, and software is usually used. However, if it is necessary to calculate the limits by hand, the following equation is used:

where d2 is a control chart constant found by rolling over Page Resources at the bottom of the screen and clicking Factors for Control Charts for n = 2. Now the control limits can be calculated as follows:

 

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Factors for Control Charts

Six Sigma Black Belt | Control | Advanced Statistical Process Control | EWMA Example Step 3 Example: Factors for Control Charts

 

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EWMA Example Step 4

Six Sigma Black Belt | Control | Advanced Statistical Process Control Concept: EWMA Example Step 4

Step 4: Establish the control chart This example uses individual values, but the EWMA chart can be used with any collection of subgroup data.

   

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CUSUM Charts Introduction

Six Sigma Black Belt | Control | Advanced Statistical Process Control Task: CUSUM Charts Introduction

According to the Glossary and Tables for Statistical Quality Control, the cumulative sum control chart (CUSUM) is used with variable data and calculates the cumulative sum of the deviations from target to detect shifts in the level of the measurement. Click the information below to learn more about CUSUM control charts. Key points • May be suitable when necessary to detect small process shifts faster than with a comparable Shewhart control chart. • The chart is effective with samples of size n = 1 where rational subgroups are frequently of size one. Examples of utilization are in the chemical and process industries and in discrete parts manufacturing. • The CUSUM chart can be graphical (V-mask) or tabular (algorithmic). • Unlike standard charts, all previous measurements for CUSUM charts are included in the calculation for the latest plot. • Establishing and maintaining the CUSUM chart are complicated. Definitions and formulas The formulas and examples provided for CUSUM charts are taken from The Certified Six Sigma Black Belt Handbook by Donald W. Benbow and T.M. Kubiak. Roll over Page Resources at the bottom of the screen and click CUSUM Definitions and Formulas and CUSUM Formulas for Individuals and Subgroup Averages to view and print a listing of definitions and formulas for individuals and subgroup averages.

926

CUSUM Charts Introduction

Six Sigma Black Belt | Control | Advanced Statistical Process Control Task: CUSUM Charts Introduction

V-mask A V-mask resembles a sideways V. The chart is used to determine whether each plotted point falls within the boundaries of the V-mark. According to The Certified Six Sigma Black Belt Handbook by Donald W. Benbow and T.M. Kubiak, "Points falling outside are considered to signal a shift in the process mean. Each time a point is plotted, the V-mask is shifted to the right. The geometry associated with the construction of the V-mask is based on a combination of specified and computed values." The graph below shows how the formulas relate.

 

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CUSUM Example

Six Sigma Black Belt | Control | Advanced Statistical Process Control Task: CUSUM Example

CUSUM charts are fairly complex to calculate, and software is usually used. The following steps demonstrate the construction of the CUSUM chart. Roll over Page Resources at the bottom of the screen and click CUSUM Chart Example Data Table to view and/ or print while going through the steps. Click each step below to learn about the construction of the CUSUM chart. 1. Collect a set of data. The data are given in Column B of the CUSUM chart example data table. 2. Specify a target value, u0. Select u0 = 50. 3. Compute deviations from target and range. Compute Columns D and E from the CUSUM chart example data table. 4. Compute Sigma (X). Compute the average of Column E from the CUSUM chart example data table: R = 2.08 d2 is a control chart constant found by rolling over Page Resources at the bottom of the screen and clicking Factors for Control Charts for n = 2.

2.08/1.128 = 1.85 5. Determine a value for K. For convenience, set K (the slope of the V-mask) = Sigma (X) = 1.85. 6. Compute values for k, d, H, and h. Although they are computed as single values, they are shown in the CUSUM Chart Example Data Table as columnar data for the reader's convenience and to facilitate the ease of calculating subsequent columns. Using the formulas previously stated: • k = 1.00 • d = 2.50 • H = 4.63 • h = 2.50

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CUSUM Example

Six Sigma Black Belt | Control | Advanced Statistical Process Control Task: CUSUM Example

7. Compute values for Zi, Si, and Ti. Using the CUSUM Chart Example Data Table, compute the values for: • Normalized deviation from the target value (Column L)

•

Equivalent to the upper boundary of the V-mask (Column M)

•

Equivalent to the lower boundary of the V-mask (Column N)

•

Enter the respective data in Columns O and P for each data point.

  8. Interpret results and take action accordingly. Determine Column Q from the CUSUM chart example data table and take action accordingly: • If Si > h or Ti > -h, a shift in the process mean is considered to have occurred. Note: The example shows the steps in constructing an individual average. Please refer to Advanced Topics in Statistical Process Control by D.J. Wheeler for the subgroup average approach.

929

MAMR Introduction

Six Sigma Black Belt | Control | Advanced Statistical Process Control Task: MAMR Introduction

The Moving Average and Moving Range (MAMR) charts provide a graph of the moving average of a process characteristic and the moving range. This type of chart is used with variables data. Click the information below to more about the MAMR chart. Key points • May be suitable when necessary to detect smaller process shifts than with a comparable Shewhart control chart. • Appropriate to use when data are collected periodically or it may take considerable time to produce a single item. • Relevant when it may be desirable to dampen the effects of over control. Selection of a moving average length • The overall sensitivity of the chart to detect process shifts is affected by the selection of the moving average length. Generally, the longer the length, the less sensitive the chart is to detecting shifts. • Specific selection of the length should be made with consideration to the out-of-control detection rules being used. When the moving average length becomes a practical consideration, you should consult a more rigorous source on this topic, such as Advanced Topics in Statistical Process Control, by D.J. Wheeler, or a statistical software program. Selection of a method for estimating sigma Method 1 • Average moving range Method 2 • Median moving range: when using this method for a, the following formulas apply: Moving average chart: Median moving range: Constant found by rolling over Page Resources at the bottom of the screen and clicking Factors for Control Charts.

A4

Moving range chart Constants found by rolling over Page Resources at the bottom of the screen and clicking Factors for Control Charts.

D5 and D6

Although the use of the average moving range is more popular, variability present in the data may suggest the use of the dispersion statistics. However, according to Wheeler in Advanced Topics in Statistical Process Control, control limits are computed by using a variety of dispersion statistics (e.g., range, median moving range, standard deviation) and Wheeler concludes "there is no practical difference between any of the sets of limits."  

930

MAMR Introduction

Six Sigma Black Belt | Control | Advanced Statistical Process Control Task: MAMR Introduction

Rational subgrouping As with any control chart, consideration to rational subgrouping remains vital. The upcoming example assumes a rational subgroup of 1 with a moving average length of 3. If statistical and technical considerations were appropriate for a rational subgroup of 5, the average of each subgroup would constitute a point in the moving average of length 3. Note: Statistical software packages allow the user to set the subgroup size. Interpretation of the charts By nature of their construction, points on moving average charts and moving ranges charts do not represent independent subgroups. Therefore, these points are correlated. While single points exceeding the control limits may still be used as out-of-control, other tests such as zone run tests may lead to false conclusions. Some software packages recognize this and limit the out-of-control tests on the moving range charts to the following: • One point more than three sigma from the centerline. • Nine points in a row on the same side of the centerline. • Six points in a row, all increasing or all decreasing. • Fourteen points in a row, alternating up and down. Roll over Page Resources and click Out-of-Control Tests Moving Range Chart to see the corresponding graphs for the above mentioned rules.   The information and example provided for MAMR charts are taken from The Certified Six Sigma Black Belt Handbook by Donald W. Benbow and T.M. Kubiak.

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Out-of-Control Tests Moving Range Chart

Six Sigma Black Belt | Control | Advanced Statistical Process Control | MAMR Introduction Tip: Out-of-Control Tests Moving Range Chart

 

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MAMR Example

Six Sigma Black Belt | Control | Advanced Statistical Process Control Task: MAMR Example

The following steps depict the construction of the MAMR chart. Roll over Page Resources at the bottom of the screen and click MAMR Chart Example Data Table to view and/or print while going through the steps. Click each step below to learn about the construction of the MAMR chart. 1. Collect a set of data. The data are given in Column B of the MAMR Chart Example Data Table. 2. Specify the length of the moving average. For this example, the moving average length will be set at 3. 3. Calculate the moving averages. The moving averages are given in Column C of the MAMR Chart Example Data Table. 4. Calculate the moving ranges. The moving ranges are given in Column D of the MAMR Chart Example Data Table. 5. Calculate the centerline of the moving average chart. The centerline of the moving average chart is:

    6. Calculate the centerline of the moving range chart. The centerline of the moving range chart is:

  7. Compute the moving range chart LCL and UCL. MR LCL and UCL

           

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MAMR Example

Six Sigma Black Belt | Control | Advanced Statistical Process Control Task: MAMR Example

8. Compute the moving average chart LCL and UCL. MA LCL and UCL

              9. Plot the chart and interpret the results.

 

934

Six Sigma Black Belt Control Lean Tools for Control

Learning Objectives

Six Sigma Black Belt | Control | Lean Tools for Control Concept: Learning Objectives

At the end of this Control topic, all learners will be able to apply appropriate lean tools as they relate to the Control phase of DMAIC such as: • 5S. • visual factory. • kaizen. • kanban. • poka-yoke. • total productive maintenance (TPM). • standard work.

936

Use of Lean Tools in the Control Phase

Six Sigma Black Belt | Control | Lean Tools for Control Task: Use of Lean Tools in the Control Phase

In the Control Phase of the DMAIC process, lean tools are used to monitor the improvements implemented. Click on each lean term below to learn how the tool is utilized in this phase. Note: The use of lean tools in other areas of DMAIC is covered in the next lesson of this course, Lean Enterprises. 5S Japanese originally, 5S stands for five "s" words. The 5S method assists in the organization of the work place the and standardization of work procedures. • Sorting (Seiri) - Keep only what is necessary in the work area. Example: A commercial cleaning company implemented a mobile cleaning station containing products and equipment used daily, while other products and equipment were stored in a supply closet at each customer location. • Storage/Set in Order (Seiton) - Organize the way necessary items are kept, making it easier to find and utilize. Example: A fast-food restaurant's walk-in refrigeration unit contains labeled shelves and bins storing food by packaging size and frequency of use. • Shining (Seiso) - Cleanliness of the work environment and the equipment to facilitate a quality process and product. Example: A spa cleans and sanitizes all equipment and tools after each customer to avoid the spread of bacteria. • Standardizing (Seiketsu) - Tasks, procedures, schedules and the persons responsible for helping keep the workplace in a clean and organized manner are parts of the control plan for the business unit or department. Example: Formalized process and procedures are incorporated into the training material and new hire training class. • Sustaining (Shitsuke) - Indoctrinate the practice of 5S into your organization's culture until it becomes part of your standard operating procedures. Example: New hire orientation provides each associate an employee handbook containing principles and philosophies embracing the practice of 5S.

937

Use of Lean Tools in the Control Phase

Six Sigma Black Belt | Control | Lean Tools for Control Task: Use of Lean Tools in the Control Phase

Visual Factory Setting up the workplace with signs, labels, color-coded markings, etc. to increase the awareness of personnel working in different work areas and multiple shifts to ensure consistency in a process. Visual aids help reduce variation in the process which can ultimately lead to defects. Example: The branch network and mail operations of a bank implemented a color-coded payment system where each type of payment would be assigned a colored bag to ensure proper processing.

  Kaizen Kaizen is a Japanese term that is translated to mean continuous improvement focusing on low-cost, gradual improvement. The term is commonly used when referring to a small incremental change. To truly sustain Kaizen for the long term, 5S and standardized work must be in place in an organization, and the attitudes of employees from top management down to the associate level will have to change in order for Kaizen to be implemented successfully. Example: A "job-swap" program is implemented in an organization where associates "swap" positions for a half-day to learn about the up-stream or down-stream tasks in a shared process. A debriefing session is held monthly for the participants to discuss their experiences and to solicit ideas for improvement in the process.

 

938

Use of Lean Tools in the Control Phase

Six Sigma Black Belt | Control | Lean Tools for Control Task: Use of Lean Tools in the Control Phase

Kanban Kanban is a system of continuous supply of components, supplies, and information so that workers have what they need, where they need it, when they need it. Kanban is a Japanese term, kan meaning "card," ban meaning "signal." The kanban system works by signaling the need to replenish stock or materials or to produce more of an item (also called "pull" approach). Example: A supermarket's checkout scanners are Kanban signals sending electronic messages to the warehouse to restock low inventory items.

  Poka-yoke Poka-yoke is a Japanese term that means "to avoid inadvertent errors." Poka-yoke is often referred to as 'mistake-proofing'. A poka-yoke device is one that prevents incorrect parts from being made or assembled, or easily identifies a flaw or error and helps to eliminate variations in process. Example: A financial institution's loan booking system requires all data entry fields on a screen to be populated before allowing the associate to move to the next screen, preventing an incomplete account set-up.

 

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Use of Lean Tools in the Control Phase

Six Sigma Black Belt | Control | Lean Tools for Control Task: Use of Lean Tools in the Control Phase

Total Productive Maintenance TPM is a systematic approach for continuous improvement of maintenance activities having an impact on the control of a process. This strategy's main goal is to maximize equipment usefulness across its lifespan. TPM increases the Overall Equipment Effectiveness (O.E.E.), a combination of the uptime, cycle time efficiency, and quality output of the equipment: Uptime% x Speed% x Quality% = O.E.E. % Example: On a scheduled basis, a financial institution's statement processing machine is taken out of service for cleaning, adjustment, and replacement of worn parts, belts, inks, etc. The operator performs a daily checklist of maintenance duties. Monthly, a representative from the vendor assists in phases of the process. Standard Work Identification and agreement on the optimal way to perform each task/step in a process becomes the standard operating procedure or standard work procedure. Standard work contributes to process control by minimizing the variation in the product flowing through the process. There are three basic elements involved: • Takt time – matches the time to deliver a service, produce a part or finished product to the pace of sales and is the basis for allocating work among workers. • Standard in-process inventory – the minimum number of items or parts, including units in machines, required to keep a cell or process moving. • Sequence – the order in which associates perform tasks at various processes. Example: Workstations for associates in a call center were standardized with forms and files allowing employees to use any available area.

940

Six Sigma Black Belt Control Measurement System Re-analysis

Learning Objectives

Six Sigma Black Belt | Control | Measurement System Re-analysis Concept: Learning Objectives

At the end of this Control topic, all learners will be able to: • understand the need to improve measurement system capability as process capability improves. • evaluate the use of control measurement systems and ensure that measurement capability is sufficient for its intended use.         Portions of this topic were taken from the ASQ Six Sigma Green Belt web-based Certification Preparation Course and the ASQ Foundations in Quality Learning Series: Certified Quality Engineer.

942

Measuring System Improvement

Six Sigma Black Belt | Control | Measurement System Re-analysis Task: Measuring System Improvement

After implementing solutions, we must re-assess the process and determine if the process has been statistically improved. Various tools such as measurement system capability re-analysis, post improvement capability analysis, graphical data analysis and statistical testing are used to answer the question, "Did the improvements have a significant impact?" Statistically validated outcomes will help demonstrate our process improvements. Click each term below to learn more. Measurement system capability re-analysis The measurement system capability analysis (Gauge R & R) used during the Measure phase can be used to see if there is an improvement with repeatability, reproducibility, and accuracy. Conduct a Gauge R & R study and compare the results from the study administered during the Measure phase. Guidance for Acceptable ranges of Gauge R & R % of Measurement Error to Total Tolerance

Acceptability

Total measurement error of less than 10% of total tolerance

Acceptable measuring equipment.

Total measurement Possibly acceptable based on the importance of the application, error of 10% to 30% of cost of the measuring equipment, cost of repairs, etc. total tolerance Total measurement Generally unacceptable; every effort should be made to error of more than 30% identify and correct the problem. Customers should be of total tolerance involved in determining how the problem will be resolved.

943

Measuring System Improvement

Six Sigma Black Belt | Control | Measurement System Re-analysis Task: Measuring System Improvement

Post improvement capability analysis Estimating process improvements necessitates a comparison between the past process performance with the improved process performance. A process capability study should be completed during the Measure Phase to see how “capable” the process is performing. Then latera post improvement capability analysis should be conducted to see how “capable” the improved process is performing. The image below shows the change in distribution type of a cycle time reduction project starting as a normal distribution and changing to a Weibull distribution after improvements were implemented. The Weibull distribution suggests the process is approaching entitlement or inherent capability.

 

944

Measuring System Improvement

Six Sigma Black Belt | Control | Measurement System Re-analysis Task: Measuring System Improvement

Graphical data analysis The impact of implemented solutions can be observed using primary metric charts, control charts, histograms, Pareto charts, etc. The continual tracking of metrics should be part of the implementation plan and may also be a source of potential new projects. Below is an example of a primary metric tracking errors per shift. The implemented improvements have reduced errors.

  Statistical testing Improvement validation using statistical testing comparing the “before” process to the improved process is necessary to see if a statistically significant gain has been realized from implementing the proposed solutions. The two-proportion test example in the Analyze lesson of this course provides an example.   Continuous improvement efforts As an organization evolves in embracing the Six Sigma methodology, process capability evaluation becomes part of the ongoing continuous improvement. Measurement capabilities may need to be improved to achieve the desired level of control.

 

945

Measuring System Improvement

Six Sigma Black Belt | Control | Measurement System Re-analysis Task: Measuring System Improvement

 

946

Control Measurement Systems

Six Sigma Black Belt | Control | Measurement System Re-analysis Task: Control Measurement Systems

The assurance of highest quality requires accurate equipment to measure and test the quality of products or services. Measurement systems (sometimes referred to as "measurement capability systems") test the quality of products and services. During the Control Phase, "sustaining the gain" is a goal, and the measurement system helps achieve this goal. Listed below are terms and types of measurement systems used in the Control Phase of DMAIC. Click below to learn more. Measurement accuracy A true value is established and the distribution of measurement deviations from the known value is tracked. A measurement system is deemed "inaccurate" when the value is consistently incorrect or over- or under-estimated.

Gauge Repeatability Gauge repeatability (a.k.a., "equipment variation") is the variation in measurements obtained when one operator uses the same gauge for measuring the identical characteristics of the same parts. Can the same operator get the same measurement using the same gauge on the same part in two or more trials?

Gauge Reproducibility Gauge reproducibility (a.k.a., "appraiser variation") is the variation in the average of the measurements made by different operators using the same gage while measuring the identical characteristic on the same parts. Can two different people get the same measurement using the same gauge?

947

Control Measurement Systems

Six Sigma Black Belt | Control | Measurement System Re-analysis Task: Control Measurement Systems

Gauge R & R with variables Variable Gauge R & R studies provide a quantitative value for the part characteristic being tested, determining the accuracy of the measurement system and the calibration process. For example, a variable gauge study will provide a measurement (known or true value) to compare measured pieces or parts showing how close the test value is to the known value. The test value is compared to the specification limits to discern qualitative decision-making about part or piece characteristics. Examples of variable gauges include: • Micrometers • Line rulers • Vernier calipers • Bench fixture gages Gauge R & R with attributes An Attribute Gauge R & R is used when looking at measurements or counts such as: • Pass or fail • Accept or reject This tool is utilized to detect variation in inspection methods between operators/associates who are the most intimate with the process or product. Attribute Gauge R & R Steps 1. 2. 3. 4.

5.

Collect a group of 30-40 inputs/transactions to be evaluated. Having 30+ as a sample size is ideal to produce reliable results. Determine the known or true value. A rule of thumb is to have at least two experts review each input/transaction and come to agreement. Identify the participants in the study. The individuals chosen should be the people making the decisions on a regular basis. Administer the assessment to the participants. The structure of the study requires that each participant evaluate the particular input/transaction twice. For example: • During Trial 1, Operator 1 evaluates all the samples then Operator 2 will evaluate the samples. • The administrator will then collect the samples, record Trial 1, and change the order of the samples to avoid bias. • Trial 2 will be administered to Operator 1 then Operator 2. • The administrator will collect the samples and record Trial 2. Analyze the recorded data. Spreadsheets or statistical software worksheets can be used to enter and analyze the results. Enter the assessment results into separate columns labeled for the: • Known • O1T1 (Operator 1, Trial 1) • O1T2 (Operator 1, Trial 2) • O2T1 (Operator 2, Trial 1) • O2T2 (Operator 2, Trial 2)

948

Control Measurement Systems

Six Sigma Black Belt | Control | Measurement System Re-analysis Task: Control Measurement Systems

Destructive Testing Destructive testing uses techniques such as tensile testing (determining the strength of a material by subjecting a test specimen to an increasing pull until rupture occurs) which can inflict damage or impair the usefulness of the product tested. Examples of destructive testing include: • testing a flashbulb • testing a bullet • cross-sectioning a weld An obvious shortcoming of destructive testing is if all units are tested (damaged), there will be no product left. Destructive testing, therefore, relies on acceptance sampling, the process of • Taking a sample out of a group or lot of items. • Evaluating the items taken. • Making a decision to accept or reject the lot based on pre-determined criteria.   Note: Measurement Systems are described in the Measure lesson of this course.

949

Control Exercise

Six Sigma Black Belt | Control Concept: Control Exercise

[ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

950

Lesson Summary

Six Sigma Black Belt | Control Summary: Lesson Summary

Once the improvements have been selected and implemented, the Control phase provides tools to continue measuring the process and evaluating the results using: • statistical process control (SPC). • advanced statistical process control (SPC). • lean tools • measurement system re-analysis A successful project is one in which the solutions are implemented and monitored to prevent the process from reverting to the previous pre-improvement state. The goal of the control phase is to "sustain the gain."  

951

Lesson Bibliography

Six Sigma Black Belt | Control Concept: Lesson Bibliography

Bibliography American Society for Quality. ASQ’s Foundations in Quality Learning Series: Certified Quality Engineer. Milwaukee, WI: ASQ, 2000. American Society for Quality. Six Sigma Green Belt Certification Preparation Course, Version 1 (web-based course). Milwaukee, WI, 2006. American Society for Quality. Quality Process Analyst Certification Preparation Course, Version 1 (web-based course). Milwaukee, WI, 2006. ASQ Statistics Division. Kittlitz, Rudy, editor. Glossary and Tables for Statistical Quality Control. 4th ed. Milwaukee, WI: ASQ Quality Press, 2005. Benbow, Donald, Roger Berger, Ahmad Elshennawy, and H. Fred Walker, editors.The Certified Quality Engineer Handbook. Milwaukee, WI: ASQ Quality Press, 2002. Benbow, Donald W. and T.M. Kubiak. The Certified Six Sigma Black Belt Handbook. Milwaukee, WI: ASQ Quality Press, 2005. Breyfogle, Forrest W. III. Implementing Six Sigma: Smarter Solutions® Using Statistical Methods. 2nd ed. Hoboken, NJ: John Wiley & Sons, Inc., 2003. Montgomery, Douglas C. Introduction to Statistical Quality Control. 5th ed. Hoboken, NJ: John Wiley & Sons, Inc., 2005. Pries, Kim H. Six Sigma for the Next Millennium: A CSSBB Guidebook. Milwaukee, WI: ASQ Quality Press, 2006. Pyzdek, Thomas. The Quality Engineering Handbook. 2nded. Boca Raton, FL: Taylor & Francis Group, 2003. Pyzdek, Thomas. The Six Sigma Handbook: A Complete Guide for Green Belts, Black Belts, and Managers at All Levels, 2nded. New York: McGraw-Hill, 2003. Wheeler, Donald J. Advanced Topics in Statistical Process Control. Knoxville,TN: SPC Press, 1995.

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Six Sigma Black Belt Lean Enterprise

Lesson Introduction

Six Sigma Black Belt | Lean Enterprise Introduction: Lesson Introduction

As you have learned, DMAIC is the primary methodology for Six Sigma. However, other process improvement methodologies have been adapted into the Six Sigma process. Lean enterprise, also called "lean manufacturing," is one of these additional methodologies. While Six Sigma focuses on reduction of variation, lean enterprise focuses on elimination of waste. Waste is defined as any activity that consumes resources, but creates no value. In addition to waste elimination, lean enterprise examines the entire process to ensure more efficient flow. The concept of lean enterprise is based on two assumptions: Elimination of waste improves performance and many minor improvements can lead to perfection. To better understand this concept, the ASQ Body of Knowledge provides the following topics: Lean concepts • Describe the theory of constraints. • Describe concepts such as value, value chain, flow, pull and perfection. • Describe the CFM concept. • Identify these activities in terms inventory, space, test inspection, rework, transportation and storage. • Describe how cycle -time reduction can be used to identify defects and non-value-added activities using kaizen type methods to reduce waste of space, inventory, labor and distance. Lean tools • Define, select, and apply tools such as visual factory, kanban, poka-yoke, standard work and SMED in areas outside of DMAIC-Control. Total productive maintenance (TPM) • Understand the concept of TPM.

954

Lesson Overview

Six Sigma Black Belt | Lean Enterprise Introduction: Lesson Overview

The tools and objectives of the Lean Enterprise lesson are illustrated below.

 

955

Six Sigma Black Belt Lean Enterprise Lean Concepts

Learning Objectives

Six Sigma Black Belt | Lean Enterprise | Lean Concepts Concept: Learning Objectives

At the end of this Lean Enterprise topic, all learners will be able to: • describe the theory of constraints. • describe lean-thinking concepts such as value, value chain, flow, pull and perfection. • describe the continuous flow manufacturing (CFM) concept. • identify non-value-added activities in terms inventory, space, test inspection, rework, transportation and storage. • describe how cycle-time reduction can be used to identify defects and non-value-added activities using kaizen type methods to reduce waste of space, inventory, labor and distance.

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Theory of Constraints

Six Sigma Black Belt | Lean Enterprise | Lean Concepts Task: Theory of Constraints

In contrast to variation reduction (Six Sigma) or waste removal (Lean), the theory of constraints (TOC) focuses on increasing overall system throughput by first paying attention to the "weakest link" of the system. A constraint is any limitation that prevents an organization from moving toward its goal. A constraint may be physical and internal (a machine, facility or policy) or non-physical and external (market conditions or demand for a product). According to H. William Dettmer in Goldratt's Theory of Constraints, "This is the beginning of the prescriptive part of the Theory of Constraints. Goldratt has developed five sequential steps to concentrate improvement efforts on the component that is capable of producing the most positive impact on the system." Click each step below to learn more. 1. Identify the system constraint Dettmer asks: " What part of the system constitutes the weakest link? Is it physical or is it a policy? " 2. Decide how to exploit the constraint. Dettmer states: " By "exploit," Goldratt means we should wring every bit of capability out of the constraining component as it currently exists. In other words, "What can we do to get the most out of this constraint without committing to potentially expensive changes or upgrades?" " 3. Subordinate everything else Dettmer continues: " Once the constraint is identified (Step 1) and we've decided what to do about it (Step 2), we adjust the rest of the system to a "setting" that will enable the constraint to operate at maximum effectiveness. We may have to "de-tune" some parts of the system, while "revving up" others. Once we've done this, we must evaluate the results of our actions: Is the constraint still constraining the system's performance? If not, we've eliminated the constraint, and we skip ahead to Step 5. If it is, we still have the constraint--and we continue with Step 4. "

958

Theory of Constraints

Six Sigma Black Belt | Lean Enterprise | Lean Concepts Task: Theory of Constraints

4. Elevate the constraint Dettmer further notes: " If we're doing this, it means that Steps 2 and 3 weren't sufficient to eliminate the constraint and we have to do something more. It's not until this step that we entertain the idea of major changes to the existing system--reorganization, divestiture, capital improvements, or other substantial system modifications. This step can involve considerable investments in time, energy, money, or other resources, so we must be sure we aren't able to break the constraint in the first three steps. "Elevating" the constraint means that we take whatever action is required to eliminate the constraint. When this step is completed the constraint is broken. " 5. Go back to Step 1, but beware of "inertia" In this final step, Dettmer states: " If, at Steps 3 or 4, a constraint is broken, we must go back to Step 1 and begin the cycle again, looking for the next thing constraining our performance. The caution about inertia reminds us that we must not become complacent; the cycle never ends. We keep on looking for constraints, and we keep breaking them. And we never forget that because of interdependency and variation, each subsequent change we make to our system will have new effects on those constraints we've already broken. We may have to revisit and update them, too. " H. William Dettmer summarizes by noting: " The Five Focusing Steps have a direct relationship with the three management questions pertaining to change: what to change, what to change to, and how to cause change. They tell us how to answer those questions. To determine what to change, we look for the constraint. To determine what to change to, we decide how to exploit the constraint and subordinate the rest of the system to that decision. It that doesn't do the complete job, we elevate the constraint. The subordinate and elevate steps also answer the question "how to cause the change." "

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TOC Metrics

Six Sigma Black Belt | Lean Enterprise | Lean Concepts Concept: TOC Metrics

TOC defines three operational measures to determine whether an organization is moving toward its goal: • Increased throughput (selling price cost of raw materials) • Decreased inventory • Decreased operating expenses   The following four measurements are used to identify results for the overall organization: • Net profit (NP) = throughput operating expense (T-OE) • Return on investment = net profit / inventory (NP/I) • Productivity = throughput / operating expense (T/OE) • Turnover = throughput / inventory (T/I)  

960

Lean Thinking

Six Sigma Black Belt | Lean Enterprise | Lean Concepts Task: Lean Thinking

As mentioned earlier, Six Sigma uses the DMAIC methodology to reduce variation and defects; lean enterprise thinking uses the methodology below. Click each step below to learn more. Define value Defining value is the first step to creating a lean enterprise. Ultimately, value must be determined by the customer. The customer wants the right product, with the right capabilities, for the right price. Therefore, it is important to talk to the customers to find out what they really want. Identify the value stream (value chain) The second step to creating a lean enterprise is identifying the value stream for the product. Use value-stream mapping to concentrate on the set of activities (both value-added and non-value-added) that link a process together. Enhance value flow Flow focuses on the object of value. In other words, the design of the product or the efficiencies and conveniences of the services are created for the customer. The goal is to eliminate any breaks in the flow so the product or service moves smoothly and continuously to the customer. Maximize customer pull Rather than creating products in response to sales forecasts, create the product when the customer requests it. Maximizing customer pull can result in a reduction in cycle-time, finished inventories and work-in-process (WIP). Customer pull can also result in stabilized customer ordering and pricing. Optimize the process The continuous pursuit of perfection in lean enterprise means that there are endless opportunities for improvement. The systematic elimination of waste will reduce the operating costs and fulfill the customer's desire for maximum value at the lowest price. While perfection may never be achieved, its pursuit is a goal worth striving for because it helps maintain constant vigilance against wasteful practices.  

961

Value Stream Mapping

Six Sigma Black Belt | Lean Enterprise | Lean Concepts Concept: Value Stream Mapping

Value Stream Mapping compared to Process Mapping Value Stream Map • •

• • •

"As-is" condition Time-based ° Cycle-time ° Wait time ° Change over time ° Value-add time

Process Map • "As-is" condition • Input - output based ° ° •

Process parameters Product parameters

Control methods

Inventory Operators Scheduling information

Roll over Page Resources to see an example of a value stream map and frequently used mapping symbols.

Value Stream Mapping Steps 1. 2. 3. 4.

5. 6. 7. 8.

Identify the deliverable product or service. (What is it?) Who is the ultimate customer? How does the ultimate customer define value for this product? Chart the flow of production for this product/service. Begin and end with the customer. (How did the product get to the customer? What are the steps? Why this product?) Add metrics and observations. Validate the map of the current state. Develop a future state. Prioritize a work plan.

962

Continuous Flow Manufacturing

Six Sigma Black Belt | Lean Enterprise | Lean Concepts Concept: Continuous Flow Manufacturing

Continuous flow manufacturing, also referred to as "1-piece flow" or "CFM", is a technique used to manufacture components in a cellular environment. A cell is a group of workstations, machines or equipment. The cell is arranged so a product can be processed progressively from one workstation to another without having to wait for a batch to be completed and without additional handling between operations.

CFM Goals • • •

To make one part at a time, correctly, all the time To do so without unplanned interruptions To do so without lengthy queue times

CFM Concepts • • • •

•

Tasks are reduced to their simplest components. Opportunities for machine- or operator-error are reduced. Done correctly, there is a continuous flow of activity between shop operators and the manufactured product. CFM is a generative manufacturing method created to continuously increase output, improve quality and grow sales and profits, without the need for constantly enlarging production or support staff. 1-piece flow is an extremely efficient way to manufacture goods, provided the correct physical structures have been set up to support its particular needs.

963

CFM Compared to Batch Production

Six Sigma Black Belt | Lean Enterprise | Lean Concepts Concept: CFM Compared to Batch Production

The opposite of continuous flow manufacturing is mass production or batch production. Although many companies produce goods in large lots or batches, this approach to production builds delays into the process. Items cannot move on to the next process until all the items in the lot have been processed. The larger the lot, the longer the items sit and wait between processes. Batch production can lower a company's profitability in several ways: • The lead time between customer orders and product delivery is lengthened. • Labor, energy and space are required to store and transport products. • The chances for product damage and/or deterioration are increased.

Benefits of 1-piece flow production • • •

Customers can receive a flow of products with fewer delays. Risks for damage, deterioration or obsolescence are lowered. 1-piece flow allows for the discovery of other problems that need to be addressed. [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

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Non-Value-Added Activities

Six Sigma Black Belt | Lean Enterprise | Lean Concepts Task: Non-Value-Added Activities

Non-value-added describes an action or activity in a process, procedure or service that does not add value to the customer. Keep in mind that some non-value-added activities cannot be avoided. Examples may include federal regulations, safety standards and quality control processes. Although these activities do not increase customer-defined value, they may be required business necessities. The goal behind creating a lean enterprise is the elimination of non-value-added activities (wastes) in every area of production including customer relations, product design, supplier networks and factory management. Waste is defined as any activity that consumes resources (time, space, materials) but does not add value to a product or service. Essentially, waste is anything that the customer is not willing to pay for. Nearly every bit of waste in the production process can fit into at least one of the following categories. Likewise, the presence of some waste can lead to other wastes. Click each of the waste producers below to learn more. Overproduction Overproduction is visible as storage of material: producing more than demanded or producing it before it is needed. Overproduction is the result of producing to anticipated demand: making more, making earlier or making faster than is required by the next process. What are some causes of overproduction waste? • Just-in-case logic • Misuse of automation • Long process setup-up times • Unleveled scheduling • Unbalanced work load • Redundant inspections Waiting (Queuing) Periods of inactivity in a downstream process occur because an upstream activity does not take place or deliver on time. For example, waiting occurs when a worker is ready for the next operation, but remains idle due to machine downtime, lack of parts or line stoppages. What are some causes of waiting waste? • Delayed shipments • Unbalanced work load • Unplanned maintenance • Long process set-up times • Misuse of automation • Upstream quality problems • Unleveled scheduling

965

Non-Value-Added Activities

Six Sigma Black Belt | Lean Enterprise | Lean Concepts Task: Non-Value-Added Activities

Inventory Inventory consists of excess materials not directly required for current customer orders. Examples are parts, raw materials, work-in-process (WIP), supplies and finished goods. Inventory is considered waste since it does not add value to the product. Costs are incurred for environmental control, record keeping, storage and retrieval. Although some inventory may be necessary, excess inventory will run the risk of gathering dust, deteriorating, becoming obsolete, getting wet or being damaged in handling. What are some causes of inventory waste? • Protecting the company from inefficiencies and unexpected problems • Product complexity • Unleveled scheduling • Poor market forecast • Unbalanced workload • Unreliable shipments by suppliers • Misunderstood communications Processing Processing waste is due to additional steps or unnecessary activities in a process, such as rework, reprocessing or rehandling. Processing wastes should be minimized by asking why a specific step is needed and why a specific product is produced. All unnecessary processing steps should be eliminated. What are some causes of processing waste? • Product changes without process changes • Just-in-case logic • Undefined customer requirements • Over-processing to accommodate downtime • Lack of communication • Redundant approvals • Extra copies/excessive information Transportation Transportation waste involves unnecessary movement of materials, such as the movement of "Work in Process" from one operation to another. Such examples involve the use of forklifts, conveyors and trucks in inefficient ways, making production more costly and complex. What are some causes of transportation waste? • Poor plant layout • Poor understanding of the process flow for production • Large batch sizes • Long lead times • Large storage areas   966

Non-Value-Added Activities

Six Sigma Black Belt | Lean Enterprise | Lean Concepts Task: Non-Value-Added Activities

Motion Motion waste is the inefficient and unnecessary movement of workers and machines. Workers should not have to walk excessively, lift heavy loads, bend abnormally, reach awkwardly or repeat motions when using machinery. What are some causes of motion waste? • Poor people/machine effectiveness • Inconsistent work methods • Unfavorable facility or cell layout • Poor workplace organization and housekeeping • Extra "busy" movements while waiting   Defective products This waste involves products or aspects of your service that do not meet customer expectations or requirements, resulting in refund, rework or repair. What are some causes of defective products? • Weak process control • Poor quality • Poor equipment maintenance • Inadequate training/work instructions • Poor product design • Misunderstood customer needs Underutilized workers This waste occurs when workers' abilities are not used effectively. What are some causes of underutilized workers? • The business culture • Poor hiring practices • Low or no investment in training • Low pay, high turnover strategy  

967

Cycle-Time Reduction

Six Sigma Black Belt | Lean Enterprise | Lean Concepts Concept: Cycle-Time Reduction

Cycle-time is the amount of time needed to complete a single task or activity for the product or service. Cycle-times may vary by task; therefore, it is beneficial to show a range and average on the value stream map. If cycle-time variation can be reduced, the process becomes more predictable. Often, cycle-time can be reduced by breaking down a single task and analyzing the amount of time that it takes to complete each sub-activity of that task. After this breakdown, it is easier to tell which sub-activities may be contributing to a slower cycle-time. Ultimately, non-value-added activities can be eliminated and value-added activities can be performed more quickly and efficiently. Kaizen is a Japanese term that is translated to mean "continuous improvement." Many companies have successfully used workshops called kaizen "events" or "blitzes" to drive dramatic improvements in cycle-times, inventory levels, changeover times and overall quality. Successful kaizen workshops require three key components: • Selecting the right project and boundaries • Empowering the proper team • Planning for follow-up

968

Kaizen Blitz

Six Sigma Black Belt | Lean Enterprise | Lean Concepts Concept: Kaizen Blitz

A kaizen blitz starts with a specific problem to solve. The focus area is best defined through a value stream mapping process. Any process might be a target for a kaizen blitz, but it is best to start with one having great customer impact or one with frustrated workers. Once an area for improvement is targeted, upper management - often with the help of a trained kaizen facilitator - initiates the blitz. Management gives the kaizen team a mandate to change a process or to create and test a new one, along with the power to make any necessary decisions along the way. Depending on the kaizen's scope, a cross-functional team with 5-10 representatives is ideal. Team members should include the key people who are closest to the work and live with the process. It is also just as important to include people who do not work or live with the process every day: like representatives from finance, design engineering, marketing and other areas in the company. Outside eyes can often more easily question existing methods and provide a fresh and objective view of too familiar problems. Together, the team observes the activity and raises questions or challenges the overall process. Typically, the team's goals will include: • Reducing cycle-time • Meet Takt Time • Reducing space • Reducing inventory • Maintaining a safe work environment The kaizen activity usually results in incremental improvements that are easily sustainable. In many cases, the team implements a change and studies the results before making a recommendation.

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Takt Time versus Cycle Time

Six Sigma Black Belt | Lean Enterprise | Lean Concepts Concept: Takt Time versus Cycle Time

Takt is the German word for metronome. Takt Time enables your organization to balance the pace of its production outputs with the rate of customer demand. The term Takt Time, is used to indicate the desired rhythm of the process. The formula for Takt Time is: Takt Time = available resources (hours) / demand (units) For example, if a product has a demand of 64 units per day, and the work day consists of two shifts (16 hours), then the Takt Time to produce each unit is 15 minutes. To meet this demand, the combined cycle-time for each activity within a process must be equal to, or less than, the Takt Time.

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Six Sigma Black Belt Lean Enterprise Lean Tools

Learning Objectives

Six Sigma Black Belt | Lean Enterprise | Lean Tools Concept: Learning Objectives

At the end of this Lean Enterprise topic, all learners will be able to define, select and apply lean tools such as visual factory, kanban, poka-yoke, standard work and SMED in areas outside of DMAIC-Control.

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Visual Factory

Six Sigma Black Belt | Lean Enterprise | Lean Tools Concept: Visual Factory

Several tools can be used during the DMAIC process to help build a lean enterprise. One such tool is a visual factory. The intention is to set up the workplace with signs, labels, color-coded markings, etc., to increase the awareness of the workers in terms of: • Daily production • Maintenance items • Goals • Quality metrics • Processes and procedures Visual applications help keep things running as efficiently as they were designed to run.

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Visual Factory Benefits

Six Sigma Black Belt | Lean Enterprise | Lean Tools Concept: Visual Factory Benefits

Benefits of a Visual Factory • • •

Visual techniques express information in a way that can be understood quickly by everyone. Sharing information through visual tools helps keep production running smoothly and safely. Visual information can also help prevent mistakes (poka-yoke). Color coding is a form of visual display often used to prevent errors. Shaded "pie slices" on a dial gauge instantly tell the viewer when the needle is out of the safe range. Matching color marks is another approach to help people use the right tool or assemble the right part.

Examples of a Visual Factory • • • • • •

Work group display boards with charts, metrics, procedures, etc. Color-coded pipes and wires Painted floor areas for good stock, scrap, trash, etc. Shadow boards for parts and tools Production status boards Directional flow indicators

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Visual Factory Exercise

Six Sigma Black Belt | Lean Enterprise | Lean Tools Concept: Visual Factory Exercise

Based on the information you learned about visual factories, place each tool in its correct location on the tool board. In this example, what are the benefits to having a specified spot for each tool? Roll over Page Resources, and click Possible Visual Factory Answers. [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

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Possible Visual Factory Answers

Six Sigma Black Belt | Lean Enterprise | Lean Tools | Visual Factory Exercise Example: Possible Visual Factory Answers

Possible Answers • Since the arrangement is defined, all tools will fit easily on the board at the end of the day. • Each worker will know exactly where to find a particular tool when it is needed. • Workers will be able to tell easily if a tool is missing or broken as they are always on display.

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Kanban

Six Sigma Black Belt | Lean Enterprise | Lean Tools Concept: Kanban

Another tool used to create a lean enterprise is a kanban system. Kanban is a system of a continuous supply of components, parts and supplies so that workers have what they need, where they need it and when they need it. Kanban is a Japanese term: kan meaning "card", ban meaning "signal." The kanban system works by signaling the need to replenish stock or materials or to produce more of an item. Kanban can be done using cards as the signaling component. In a simple kanban system, an empty box, container or pallet can signal the need for more supplies. The supplier or warehouse should only deliver components to the production line when signaled. [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

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Kanban Benefits

Six Sigma Black Belt | Lean Enterprise | Lean Tools Concept: Kanban Benefits

Benefits of a Kanban System • • • • •

Reduced inventories Predictable flow of materials Simplified scheduling Visual "pull" system at the point of production Improved productivity

Since kanban is a chain process in which orders flow from one process to another, the production or delivery of components is pulled to the production line. This method is in contrast to the traditional forecast-oriented method where parts are pushed to the line. An example and illustration are provided on the next page.

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Kanban Example

Six Sigma Black Belt | Lean Enterprise | Lean Tools Concept: Kanban Example

In a plant that manufactures widgets, a 42" stem-bolt is needed. The stem-bolts arrive on pallets (each pallet holding 100 stem-bolts). When the pallet is empty, the person assembling the widgets takes the card attached to the pallet and sends it to the stem-bolt manufacturing area as an order to manufacture and send another pallet of stem-bolts. A new pallet of stem-bolts is not made until the card is received. This is kanban in its simplest form. A more realistic example would involve two pallets. The widget assembler would start working from the second pallet while new stem-bolts were being made to refill the first pallet. [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

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Poka-Yoke

Six Sigma Black Belt | Lean Enterprise | Lean Tools Concept: Poka-Yoke

Because people can make mistakes even in inspection, mistake-proofing often relies on a sensing mechanism called poka-yoke. Poka-yoke is a Japanese term that means "to avoid inadvertent errors." A poka-yoke device is one that prevents incorrect parts from being made, assembled or identifies a flaw or error. Often referred to as "error-proofing", poka-yoke is actually the first step in error-proofing a system. Error-proofing is a manufacturing technique of preventing errors by designing the manufacturing process, equipment and tools so that an operation literally cannot be performed incorrectly.

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Poka-Yoke Examples

Six Sigma Black Belt | Lean Enterprise | Lean Tools Concept: Poka-Yoke Examples

Examples of Poka-Yoke Error-proofing is the practice of striving for zero defects using techniques, standards and devices that prevent errors from being made. Examples of preventative measures include:  • Childproof caps on prescription medicine bottles • Different size fuel dispensing nozzles to prevent cross-fueling • Design of parts so that they cannot be exchanged by mistake • Color-coded parts

Error-proofing also uses shutdowns, controls or warnings to detect errors and stop them before they become defects. Examples of detection measures include: • Automatic shutoff on coffee pots and other small appliances • Smoke and carbon monoxide detectors • Warning buzzer when blood pressure drops below acceptable levels during surgery The key to effective error-proofing is determining when and where defect-causing conditions arise and then figuring out how to detect or prevent these conditions every time.

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5S

Six Sigma Black Belt | Lean Enterprise | Lean Tools Task: 5S

Another tool that can be applied in a lean enterprise is the 5S structure. Originated in Japan, 5S stands for five "s" words, that assist in work place organization and the standardization of work procedures. Click each step below to learn about the five methods and see examples of each. The words in parentheses are the original Japanese terms. Sort (Seiri) Eliminate unnecessary items from the workplace. Method: Tag items believed to be unnecessary are moved to a central location and reused or eliminated. Example: In a bank, each teller station is stocked with a working supply of commonly used forms, such as deposit tickets and savings account withdrawal forms. Extra forms are stored in the supply closet. Set in Order (Seiton) Store items efficiently and effectively. Method: "A place for everything, and everything in its place." Example: In a copying/printing center, all paper is properly stored and labeled according to size, color and weight. Shine (Seiso) Clean and maintain Method: "Clean thoroughly, clean often." Establish a daily cleaning routine. Identify maintenance issues along the way. Example: In any corporation, conference rooms are cleaned and straightened after each meeting so the rooms are immediately ready for the next scheduled meeting. All AV equipment is checked for maintenance needs. Standardize (Seiketsu) Establish best practices. Method: Establish a routine, identify ownership and solicit the input of employees who are doing the work. Example: In a hospital, the responsibility of nurse scheduling is given to the senior nurse who best understands the needs of each department balanced with the need to retain quality nurses. Sustain (Shitsuke) Continue the improvement over the life of the company. Method: Change the culture of clutter. Establish a new status quo of workplace organization and reward accordingly. Example: A company implements a program to instill a continuous improvement mindset and rewards employee suggestions that reduce waste or enhance profitability.

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Standard Operations (Work)

Six Sigma Black Belt | Lean Enterprise | Lean Tools Concept: Standard Operations (Work)

The lean concept standard work maintains that each activity should be performed the same way every time. Standard work is the term used to systematize how a part is processed, and includes man-machine interactions and studies of human motion. Standard work operations are most efficiently and safely completed with all tasks organized in the best known sequence, using the most effective combination of these resources: • Man • Materials • Methods • Machines • Mother Nature • Measurements Within standard work, each operation is broken down into small pieces and analyzed. Each worker is then given all the tools to make the part quickly, with the highest quality. The process is documented in writing and with photographs. Charts and posters at the work area are often used to reinforce the methods. To have the greatest impact, standardization must occur not only within the area but also across the entire company. Standardization includes paint and color standards for safety elements, equipment operation instructions, floor markings, interior and exterior building markings, material labeling, etc. By creating standards and defining procedures, we achieve commonality across the entire organization.

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Standard Operations (Work) Benefits

Six Sigma Black Belt | Lean Enterprise | Lean Tools Concept: Standard Operations (Work) Benefits

Benefits of Standard Work • • • • • • •

Can eliminate errors that waste time and money Helps ensure reproducibility from operator-to-operator Helps reduce variation in cycle-time Helps produce a more consistent product or service Can simplify down-stream activities Helps assure a high quality product, proud workers, satisfied customers and workplace safety Leads to remarkable productivity improvements, with reduced variation in the shop floor environment

984

SMED

Six Sigma Black Belt | Lean Enterprise | Lean Tools Concept: SMED

Single minute exchange of dies (SMED) is a system used to reduce changeover time and improve timely response to demand. Developed by Toyota, SMED, is also referred to as the "Toyota Production System." SMED involves a set of procedures to be followed for a successful exchange of dies. The goal of SMED should be to develop a production system that gets as close as possible to making only what the customer wants, when the customer wants it, throughout the production chain. The resulting production system becomes a strong, flexible operation adaptable to changes. According to Donald W. Benbow and T.M. Kubiak in The Certified Six Sigma Black Belt Handbook, "it was common practice in metal-forming industries to produce thousands of one part before changing the machine's dies and then producing thousands of another part. This practice often produced vast inventories of work in process and associated waste. These procedures were justified because changing machine dies took several hours." Many companies produce goods in large lots simply because long changeover times make it costly for products to change frequently. However, when methods are in place to accommodate quick changeover, setups can be done as often as needed. Quick changeovers mean that products can be made cost effectively in smaller lots. Before a setup operation can be improved, it is best to analyze how it is currently performed. Three preliminary steps involved in a setup analysis include: • Videotaping the entire setup operation • Asking setup personnel to talk about what they do • Studying the time and motions involved in each step of the setup

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Using SMED

Six Sigma Black Belt | Lean Enterprise | Lean Tools Concept: Using SMED

Setup improvement activities can be implemented in three stages: • Distinguish between internal and external setups. ° ° •

•

External setups are those items that can be performed before a machine or process is stopped. Internal setups are those tasks that must be done after the machine or process has stopped.

Convert internal setups to external setups. Look at each task within the changeover process to determine how current internal setups can be converted to external setups. Streamline all aspects of the setup operation. Once new processes are in place, practice the process continually and analyze it for improvements.

Benefits of a SMED System • • •

•

Flexibility: Changing customer needs can be met without the expense of excess inventory. Quicker delivery: Small-lot production means reduced lead time and reduced customer waiting time. Better quality: Less inventory storage means fewer storage-related defects. Quick changeover methods lower defects by reducing setup errors and eliminating trial runs of the new product. Higher productivity: Shorter changeovers reduce downtime, resulting in a higher equipment productivity rate.

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Six Sigma Black Belt Lean Enterprise Total Productive Maintenance

Learning Objectives

Six Sigma Black Belt | Lean Enterprise | Total Productive Maintenance Concept: Learning Objectives

At the end of this Lean Enterprise topic, all learners will be able to understand the concept of total productive maintenance (TPM).

988

Total Productive Maintenance

Six Sigma Black Belt | Lean Enterprise | Total Productive Maintenance Concept: Total Productive Maintenance

Total productive maintenance (TPM) is an initiative for optimizing the effectiveness of manufacturing equipment. TPM addresses the production operation with a comprehensive, team-based management program that is proactive instead of reactive. The goal of TPM is to eliminate losses, whether from breakdowns, defects or accidents. TPM helps identify and eliminate the "six big losses" that contribute negatively to equipment effectiveness: • Breakdowns • Setup and adjustment loss • Idling and minor stoppages • Reduced speed • Defects and rework • Startup yield loss TPM implementation starts with measuring and analyzing overall equipment effectiveness (OEE). This analysis will help diagnose problems and will become the measurement to determine how successful TPM efforts are. As stated in the Control lesson, OEE is a combination of the uptime, cycle-time efficiency and quality output of the equipment: Uptime% x Speed% x Quality% = O.E.E. %

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TPM Pillars

Six Sigma Black Belt | Lean Enterprise | Total Productive Maintenance Task: TPM Pillars

The following seven strategies are the most common for implementing TPM effectively. They form the pillars to foundation of any TPM effort. It is not necessary to implement all these strategies at once. The company must decide which of these strategies will have the most positive and immediate results. Click each strategy below to learn more. Focused Improvement (Kaizen) To make equipment more efficient, examine its effectiveness by identifying and analyzing all losses caused by downtime, speed and defects. Make continual improvements. Autonomous Maintenance Allow machine operators to take responsibility for routine maintenance tasks, freeing up skilled maintenance workers to work on other TPM initiatives. The result is more knowledgeable machine operators who can effectively communicate equipment problems to maintenance staff. Planned Maintenance Have a systematic approach to all maintenance activities. This involves identifying the preventive maintenance required for each piece of equipment, creating standards for condition-based maintenance, and setting responsibilities for operating and maintenance staff. Technical Training Train staff to improve their skills. This includes training on maintenance, operations and troubleshooting. In addition, make certain the staff understand why these skills are important. Quality Maintenance Focus on eliminating non-conformances in a systematic manner, much like focused improvement. Understand what parts of the equipment affect product quality in order to eliminate current and potential quality concerns. Office TPM The goal is to improve productivity and efficiency in the administrative functions and identify and eliminate losses. Analyze processes and procedures to determine opportunities for increasing office automation. Safety/Environmental Management Focus on creating a safe workplace that is not endangered by the processes or procedures. The goal is zero accidents, zero health damage and zero fires.

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TPM Benefits

Six Sigma Black Belt | Lean Enterprise | Total Productive Maintenance Concept: TPM Benefits

Benefits of Total Productive Maintenance (TPM) • • • • • •

Improved machine reliability Extended machine life Increased capacity without the purchase of additional machines or sacrifice of additional floor space Improved teamwork between machine operators and maintenance workers Improved safety Increased ability to reallocate skilled workforce to more technical duties by having machine operators perform daily and routine maintenance

 

991

Lean Enterprise Pyramid Game

Six Sigma Black Belt | Lean Enterprise Concept: Lean Enterprise Pyramid Game

[ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

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Lesson Summary

Six Sigma Black Belt | Lean Enterprise Summary: Lesson Summary

The primary focus of a lean enterprise is to eliminate waste. As you have learned, waste is defined as any activity that consumes resources, but creates no value. The emphasis is on making the entire process flow more efficiently rather than improving specific sub-processes. This lesson emphasized the following concepts and tools as a knowledge base to use for creating a lean enterprise: Lean concepts Theory of constraints (TOC) focuses on increasing overall system throughput by first paying attention to the "weakest link" of the system. Lean thinking describes the methodology for creating a lean enterprise and includes the following steps: • Define value • Identify the value stream • Enhance value flow • Maximize customer pull • Optimize the process Continuous flow manufacturing (CFM) is a technique used to manufacture components in a cellular environment. The cell is a group of workstations, machines or equipment arranged such that a product can be processed progressively from one workstation to another without having to wait for a batch to be completed and without additional handling between operations. Non-value-added activities describe an action in a process, procedure or service that does not add value to the customer. Non-value-added activities are typically described in terms of waste producers that fall into the following eight categories: • Overproduction • Waiting • Inventory • Processing • Transportation • Motion • Defective products • Underutilized workers Cycle-time is the amount of time needed to complete a single task or activity for the product or service. If cycle-time variation can be reduced, the process becomes more predictable. Lean tools Several lean tools can be used during the DMAIC process that can help build a lean enterprise. • Visual factory • Kanban • Poka-yoke • Standard work • SMED

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Lesson Summary

Six Sigma Black Belt | Lean Enterprise Summary: Lesson Summary

Total productive maintenance (TPM) is an initiative for optimizing the effectiveness of manufacturing equipment. The goal of TPM is to eliminate losses, whether from breakdowns, defects or accidents.

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Lesson Bibliography

Six Sigma Black Belt | Lean Enterprise Concept: Lesson Bibliography

Bibliography American Society for Quality. Six Sigma Green Belt Certification Preparation Course, Version 1 (web-based course). Milwaukee, WI, 2006. Benbow, Donald W. and T.M. Kubiak. The Certified Six Sigma Black Belt Handbook. Milwaukee, WI: ASQ Quality Press, 2005. Dettmer, H. William. Goldratt's Theory of Constraints: A System's Approach to Continuous Improvement. Milwaukee, WI: ASQ Quality Press, 1997. MacInnes, Richard L. The Lean Enterprise Memory JoggerTM. Salem, NH: Goal/QPC, 2002.

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Six Sigma Black Belt Design for Six Sigma

Lesson Introduction

Six Sigma Black Belt | Design for Six Sigma Introduction: Lesson Introduction

Design for Six Sigma (DFSS) strives to prevent defects by transforming customer wants and perceptions into reliable, defect-free product or process. DFSS provides a process and structure for delivering Six Sigma quality products to the customer. To better understand this concept, the ASQ Body of Knowledge provides the following topics: DFSS Introduction • Introduce the purpose of DFSS. Quality function deployment (QFD) • Demonstrate a quality function deployment tool for analyzing the customer’s needs and linking to the technical requirements needed to satisfy the customer. Robust design and process • Understand the role functional requirements have within design. • Examine strategies for incorporating robust design concepts into the design process; especially strategies for reducing noise. • Understand the concepts of tolerance design and statistical tolerancing. • Calculate tolerances using process capability data. Failure mode and effects analysis (FMEA) • Understand the terminology, purpose and use of scale criteria (including risk priority number (RPN)) for FMEA and apply to processes, products or services. • Understand the distinction between and interpret data associated with design FMEA (DFMEA) and process FMEA (PFMEA). Design for X (DFX) • Understand design constraints such as design for cost, design for manufacturability and producibility, design for test and design for maintainability. Special design tools • Understand the concept of special design tools such as the theory of inventive problem-solving (TRIZ) and axiomatic design (conceptual structure robustness).

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Lesson Overview

Six Sigma Black Belt | Design for Six Sigma Introduction: Lesson Overview

The tools and objectives of the DFSS lesson are illustrated below.

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Six Sigma Black Belt Design for Six Sigma Overview

Introducing DFSS

Six Sigma Black Belt | Design for Six Sigma | Overview Concept: Introducing DFSS

Some organizations have a history of long-term success with development, launch, and integration of new products. With roots in the Department of Defense and NASA, Design for Six Sigma (DFSS) seeks to understand the customer’s perceptions, needs, and expectations that are critical to ensure a successful product. DFSS is a proactive, rigorous, systematic method using tools, training, and measurements for integrating customer requirements into the product development process. DFSS strives to prevent defects by transforming customer wants and expectations to what can be produced, whereas the Six Sigma DMAIC model focuses on eliminating defects by reducing operational variability. The DFSS customer focus increases the probability of success much earlier by applying systematic and scientific methods such as quality functional deployment (QFD), failure modes and effects analysis (FMEA), and robust design optimization (RDO). • QFD approaches develop an understanding of the customer’s needs and translate these into engineering and manufacturing requirements. • Through FMEA, analyzing failures and their effects influence design perimeters. • RDO deals with integrating design of experiments (DOE) to find optimal and robust solutions early in the development.

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Committing to DFSS

Six Sigma Black Belt | Design for Six Sigma | Overview Concept: Committing to DFSS

By designing for producibility, reliability, performance, and maintainability, DFSS projects offer solutions that meet or exceed customer needs. However, achieving quality performance through any set of tools also requires preparation and commitment to change. For a list of tools involved in DFSS, roll over each gear below. [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

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DFSS and Six Sigma

Six Sigma Black Belt | Design for Six Sigma | Overview Concept: DFSS and Six Sigma

Six Sigma aims to improve an existing process by reducing variation or centering the mean. After organizations introduce new designs, Six Sigma professionals return to solve problems similar to the previous process. To generate the right product at the right time at the right cost, DFSS incorporates the Six Sigma problem-solving technique into the design process. DFSS is the practice of designing any product, service or process to satisfy customer and internal business requirements at a Six Sigma level of performance.

1002

DFSS and ROI

Six Sigma Black Belt | Design for Six Sigma | Overview Concept: DFSS and ROI

Because quality experts regard 70-80% of quality problems as design-related, engineers and other process designers have the best opportunity to improve product quality and save costs. As a process moves through the phases of concept to design, prototyping and production, the cost of eliminating quality problems increases. DFSS effects on cost-savings are proportional to the initial investment. The greater the initial investment to eliminate design issues, the lower the life cycle costs associated with the process. Since process improvement after start-up is more costly, a well-developed DFSS project development plan will help to ensure success and maximize the return on investment. DFSS Addresses Business Challenges • Customers demanding product/process excellence • Managing variability • Improving predictability and capability • Reducing costs and increasing profitability • Increasing development effectiveness • Managing development costs • Meeting customer requirements

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Using DFSS

Six Sigma Black Belt | Design for Six Sigma | Overview Concept: Using DFSS

Black Belts use DMAIC to address problems to reduce costs and improve quality by reducing variability or shifting the mean. Even then, a process (given its design) has a maximum level of performance. Entitlement refers to the best performance level for a process, product, service, or transaction. What happens if future customer requirements exceed the current process capability? Since customers desire more performance and the process is operating at entitlement, process redesign is necessary; thus the need for DFSS arises. In the interaction below, click Next Step to learn about a process link between DMAIC and DFSS. [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

1004

DMADV

Six Sigma Black Belt | Design for Six Sigma | Overview Concept: DMADV

As DMAIC guides the Six Sigma Black Belt through an existing process, the stages for DFSS are: Define-Measure-Analyze-Design-Verify (DMADV). Used when designing a new process, product, service or transaction, DMADV works closely with obtaining information and analyzing the voice of the customer in order to meet customer requirements. DFSS contains such a large body of knowledge for each stage that DFSS is a course in itself. The purpose of this lesson is to provide an overview of DFSS.

1005

DFSS Teaming

Six Sigma Black Belt | Design for Six Sigma | Overview Concept: DFSS Teaming

When your team develops a new design from start to finish, engineering should not be the only department involved. From inputs such as learning training needs from human resources, patent infringement advice from the legal department or money matters from the finance department, your team can benefit and derive important information. Using cross-functional team members from other departments is critical to the smooth operation and the success of DFSS. On the product design side, DFSS projects include: • Subject matter experts (SMEs). • Six Sigma Black Belts and Green Belts as team leaders. • Master Black Belts as mentors and trainers. • Project champions as process owners and roadblock breakers.

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DFSS or Six Sigma

Six Sigma Black Belt | Design for Six Sigma | Overview Concept: DFSS or Six Sigma

For each situation listed below, select the best approach for dealing with that situation. After clicking a box, either a check mark will display (correct answer) or an X (incorrect answer). [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

1007

Six Sigma Black Belt Design for Six Sigma Quality Function Deployment

Learning Objectives

Six Sigma Black Belt | Design for Six Sigma | Quality Function Deployment Concept: Learning Objectives

At the end of this DFSS topic, all learners will be able to analyze a completed quality function deployment (QFD) matrix.

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Customer Input

Six Sigma Black Belt | Design for Six Sigma | Quality Function Deployment Concept: Customer Input

Organizations today realize the importance of giving allegiance to their customers. Paradigms have shifted from "product-centered" to "customer-centered." Meeting customer requirements is a core principle of quality because delivering what the customer needs and values gives purpose and direction to all work processes. Quality, delivery, and cost are important considerations that influence customer satisfaction. DFSS influences customer satisfaction by developing and planning the product to meet the customer’s needs and ensuring those requirements carry through to manufacturing and field operations. Therefore, all processes and organizations must be thoroughly grounded in customer-defined requirements. Customer satisfaction is a value judgment made by the customer regarding their total experience with the product or service. Quality is an important factor (but not the only factor) influencing customer satisfaction. Listening to and integrating your process with the voice of the customer is critical to remaining competitive.

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QFD Principles

Six Sigma Black Belt | Design for Six Sigma | Quality Function Deployment Concept: QFD Principles

Securing customer input helps prepare a list of customer concerns/wants. Quality function deployment (QFD) is a methodology that organizations often use to incorporate the voice of the customer throughout a product or service development life cycle. For this reason, some quality experts call QFD “customer-driven engineering” or “listening to the voice of the customer.” QFD Principles • Start with the “voice of the customer” at the concept stage (e.g., surveys isolate which benefits customers feel are important). • Carry through to manufacturing with highly detailed instructions (e.g., instructions for production process control or for how front-line employees will provide a service). • Employ a series of matrices and charts (e.g., tools that rank features by significance, identify possible problems, and provide well-defined engineering specifications).  

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QFD Overview

Six Sigma Black Belt | Design for Six Sigma | Quality Function Deployment Task: QFD Overview

As a tool for use by the whole organization, QFD is a course in itself. QFD links VOC to existing quality. QFD is a methodology translating customer needs and requirements (voice of the customer) into the production of yourproducts and services. Introduced by Yoji Akao (1966), QFD is a structured, disciplined methodology and qualitative tool used to identify the customers' quality requirements and translate them into important design targets. Benefits • Creates a customer-driven environment • Establishes priorities and improves quality and customer value • Prioritizes process improvements • Forces early communication, planning, and decision-making • Involves the entire company and bridges departments • Provides documentation for the decision-making process Use When • Analyzing customer requirements • Developing a new product, process, service or transaction • Improving a product, process, service or transaction • Interpreting customer requirements into organizational methodology  

1012

House of Quality

Six Sigma Black Belt | Design for Six Sigma | Quality Function Deployment Concept: House of Quality

The House of Quality (named for its house-shaped matrix appearance) is one of the most important matrices in QFD. Early in the planning phase, the House of Quality clarifies the relationship between customer needs and product features. It helps correlate market or customer requirements and analyses of competitive products with higher-level technical and product characteristics to identify the strong and weak relationships. The House of Quality diagram makes it possible to bring together several factors into a single figure.

1013

Left Wing and Attic Matrix

Six Sigma Black Belt | Design for Six Sigma | Quality Function Deployment Concept: Left Wing and Attic Matrix

The left wing, the starting point for constructing the House of Quality, serves as the voice of the customer by listing previously identified customers' needs and requirements. Included is a scale to rate the importance of each need and serve as a multiplying factor when determining rankings. Use a 1-10 scale, where: • 10 = extremely important or critical to the customer. • 1 = not very important to the customer. Note: Not all customer needs merit a 10. The attic, serving as the voice of the company, lists the engineering characteristics (technical requirements) designers believe are required to meet the customer’s specific needs. The center is a matrix identifying the interrelationships between the customer needs and the technical requirements. For example, how significant is size if the product is small and light weight? Designers evaluate the interrelationships by a variety of methods, including point values as 10-to-0 and 9-3-1, or symbols. The example below uses symbols to designate the significances.

1014

The Roof

Six Sigma Black Belt | Design for Six Sigma | Quality Function Deployment Concept: The Roof

After identifying the technical requirements and completing the matrix between the requirements and the needs, the roof provides an area for designers to rate the requirements to each other. This analysis identifies the key points where improvement in the technical requirement could benefit the product. The analysis revolves around a key question: Does improving one requirement automatically improve or deteriorate another requirement? For instance, note the following relationships from the matrix below: • Improving yield has a strongly positive relationship with improving process capability. • Improving yield has a strongly negative relationship with improving rate. • Improving yield has no effect on the cost to maintain.

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The Basement

Six Sigma Black Belt | Design for Six Sigma | Quality Function Deployment Concept: The Basement

The basement provides several opportunities: • Records weighted scores for each engineering characteristic as it supports customer needs • Records engineering targets for each technical requirement The weight score provides a numerical value on how each technical requirement rates against the customer requirement. This technique forms a weighted rating: a rating linked to the most important customer requirement that is determined by multiplying the individual rating and the customer importance value. The sum of the products then provides the rating for the characteristic. For example, calculate the weighted scale for the Weight design requirement: • The weight design requirement has a weak or possible relationship to the customer need of low cost: (1 * 10). • The weight design requirement has a strong relationship to the customer need of small, lightweight: (9 * 8). • (1 * 10) + (9 * 8) = 82. The designer then uses the Key Design Requirements row to identify the engineering requirements that most strongly meet the customer’s requirements. Notice the large difference between those marked with an X and those unmarked. Some matrices may also include a competitive analysis of each engineering requirement with the competition (benchmarking results). The target values row records the specific engineering targets for each technical requirement. Since targets need to be precise, do not use a range. Based on information analyzed in the House of Quality, target values may change.

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The Basement

Six Sigma Black Belt | Design for Six Sigma | Quality Function Deployment Concept: The Basement

1017

Right Wing: Customer and the Competition

Six Sigma Black Belt | Design for Six Sigma | Quality Function Deployment Concept: Right Wing: Customer and the Competition

The right wing allows designers to compare their product to the competition in terms of the customer’s requirements. For instance, note the following comparison between UsDot relative to the positioning of the competition (G-Wiz and J-co Com). • UsDot rates below both competitors in terms of reproducibility and the ability to verify; both of which are of maximum importance to the customer. • UsDot’s ability to verify rating is significantly lower than both competitors are, and the customer highly values this characteristic. • UsDot product has the highest reliability.

1018

Analyzing

Six Sigma Black Belt | Design for Six Sigma | Quality Function Deployment Concept: Analyzing

The matrix is actually examining two relationships. In the graphic below, the lower grid shows the relationship between the individual customer requirements and each engineering characteristic. Some professionals and organizations create a matrix using a series of symbols. Whether circles, diamonds, triangles, circles of different colors, pluses and minuses, the house of quality shows the relationship between the customer needs and the technical requirements. Within the roof, however, the grid is showing the relationships between the engineering characteristics. Regardless of the recording technique: • A positive relationship shows both technical requirements can be improved at the same time. • A negative relationship means that as one requirement improves, the other worsens. • A blank means that a change has no effect. To practice analyzing a house of quality matrix, roll over Page Resources, and then click House of Quality Exercise. To check your answers, close the House of Quality Exercise window, roll over Page Resources, and click House of Quality Answers.

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House of Quality Exercise

Six Sigma Black Belt | Design for Six Sigma | Quality Function Deployment | Analyzing Example: House of Quality Exercise

Study the matrix below to answer the following questions. To check your answers, close this window, roll over Page Resources, and click Answers. 1. 2. 3. 4. 5. 6.

What is the relationship between Easy to Click and Button Resistance? What is the relationship between Easy to Clean and Product Dimensions? What is the relationship between Energy Needed to Move and Sealed Ball? Which customer requirement does the company believe they are the best at in their field? Compared to their main competitor, which customer requirement is the company worst at? How does this company compare with its competition in terms of its products being Easy to Clean?

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House of Quality Answers

Six Sigma Black Belt | Design for Six Sigma | Quality Function Deployment | Analyzing Example: House of Quality Answers

1. 2. 3. 4. 5.

6.

What is the relationship between Easy to Click and Button Resistance? Strong positive relationship. What is the relationship between Easy to Clean and Product Dimensions? No relationship. What is the relationship between Button Resistance and Sealed Ball? Negative relationship. Which customer requirement does the company believe they are the best at in their field? Contouring the mouse to the hand. Compared to their main competitor, which customer requirement is the company worst at? Mouse does not jam (thus implying their mouse has problems jamming). How does this company compare with its competition in terms of their products being Easy to Clean? In the middle: better than B, but not as good as A (who is the best).

 

1021

Numerical Scoring

Six Sigma Black Belt | Design for Six Sigma | Quality Function Deployment Concept: Numerical Scoring

In order to quantify ratings, some quality professionals use values instead of symbols. The preferred scale depends on the individual and the organization. Common scales include 5-to-0, 10-to-0, 5-3-1, and 9-3-1. In the below QFD matrix, the Few Errors characteristic has been calculated for you as an example (rating of 46). Given the information on this QFD matrix, calculate the weighted rating for each characteristic, and then prioritize the customer’s needs. To check your work, roll over Page Resources and click QFD Answer.

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QFD Answer

Six Sigma Black Belt | Design for Six Sigma | Quality Function Deployment | Numerical Scoring Example: QFD Answer

To determine the weighted rating of a column, multiply the value by the customer importance value, and then add the column. The weighted ratings are 65, 21, 36, 46, 35, 53, and 70. Sample calculation: Adaptable Content: 65 = (5 * 4) + (0 * 2) + (4 * 5) + (0 * 4) + ( 5 * 5) Prioritize Characteristics: Current BoK (70), Adaptable Content (65), Moveable Sections (53), Few Errors (46), Compact Size (36), Low Price (35), and Durability (21)

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Houses of Quality in DFSS

Six Sigma Black Belt | Design for Six Sigma | Quality Function Deployment Concept: Houses of Quality in DFSS

Since using the QFD process is important to completing the design from customer requirements to manufacturing characteristics, designers generally use a series of matrices. When progressing from one matrix to another, you will notice the features along the roof of the previous matrix become a side feature of the next matrix. For example, see the location of Technical Characteristics in the first and second images. By continually narrowing the process and fine-tuning the choices, you will integratecustomer expectations into product design, process planning and eventually to process control.

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Tips

Six Sigma Black Belt | Design for Six Sigma | Quality Function Deployment Task: Tips

Whereas brainstorming helps develop a list of characteristics, a House of Quality with too many characteristics can be overwhelming. Use affinity diagrams and tree diagrams to develop details about the characteristics before making the House of Quality. Each grouping in the affinity diagram may warrant its own House of Quality. Detailed examples of affinity and tree diagrams were presented in the Project Management lesson of this course. Click each item below for a list of directions for completing a House of Quality, user tips, and analysis tips. Steps 1. 2. 3. 4. 5. 6. 7.

Capture the voice of the customer (customer requirements). Determine the relative importance of each customer requirement. Establish the relationship between the design requirements and the customer requirements. Determine the relative importance of each design requirement. Compare self to the competition regarding each customer requirement. Compare the design requirements to each other. Add target values and specifications for each requirement.

User Tips • Refer to the following information in this course: matrix diagrams, House of Quality matrix, customer data collection tools • QFD requires an opening share of information • Using a cross-functional team brings together different people with knowledge about the customer, product, process, service, and/or transaction • Customer data may exist within the organization, but not communicated to those needing the information • Avoid the “we know better than the customer” attitude • For each characteristic, set a specific target, not a range • Trade offs between characteristics may lead to unmet customer requirements, delayed development, increased cost, and/or poor quality • Use specialized software to develop a complex matrix

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Tips

Six Sigma Black Belt | Design for Six Sigma | Quality Function Deployment Task: Tips

Analysis Tips • Odd patterns in the center of the matrix may indicate problems. • If there is an empty row, no characteristic meets the customer requirement. Therefore, identify a new characteristic. • If there is an empty column, a customer requirement was missed or the characteristic is not needed. • Rows with no strong relationships – Having at least one strong relationship helps meet customer requirements. If there is not a strong relationship, look for one. • Column with no strong relationships – Each characteristic should have at least one strong relationship. If there is not a strong relationship, rethink the characteristic. • Row or column with many relationships – This may be a cost, reliability or safety issue. Remove the relationship from the house and analyze it separately.

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Six Sigma Black Belt Design for Six Sigma Robust Design and Process

Learning Objectives

Six Sigma Black Belt | Design for Six Sigma | Robust Design and Process Concept: Learning Objectives

At the end of this DFSS topic, all learners will be able to: • understand functional requirements of a design. • develop a robust design using noise strategies. • understand the concepts of tolerance design and statistical tolerancing. • calculate tolerances using process capability data.

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Introduction

Six Sigma Black Belt | Design for Six Sigma | Robust Design and Process Concept: Introduction

Known for developing quality-engineering methodology to improve quality and reduce waste, Dr. Genichi Taguchi’s work improves engineering productivity to achieve high-quality and low-cost solutions. Many companies in diverse industries around the world use the Taguchi Methods to save millions of dollars. Vested companies aim at reducing waste during design, manufacturing, and operations, thus affecting costs and the bottom line. This topic includes the following Taguchi Methods: • Robust design • Functional requirements • Noise factors This topic also includes the following important concepts: • Tolerance design • Tolerance and process capability Note: The Improve lesson of this course also touched upon the concept of "Taguchi robustness."

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Taguchi Methods

Six Sigma Black Belt | Design for Six Sigma | Robust Design and Process Concept: Taguchi Methods

Competition pressures organizations to examine their products, processes, and services in order to improve efficiency, decrease costs, improve quality, increase production volume, reduce cycle times, and improve customer satisfaction. Consider what Madhav S. Phadke writes in Introduction to Robust Design (Taguchi Methods). ITT reported the following about development: • Design influences more than 70% of the product life cycle cost. • Companies with high product development effectiveness have earned 3 times the average earnings of their competition. • Companies with high product development effectiveness have revenue growth 2 times the industry's average revenue growth. While Genichi Taguchi refers to quality engineering techniques, other terms include Taguchi Methods, robust design, robust engineering, or robust DOE. Robust design is an efficient and systematic methodology that applies statistical experimental design for improving product and manufacturing process design, thus aiming to design a more reliable product or process. For example, many statistical control charts are quite robust in regards to the assumption of normality (i.e., somewhat skewed or bimodal populations can still provide us with control charts that detect changes in mean or variability). Furthermore, many statistical methods can give us valid results with some marked departure from normality.

1030

Robust Design

Six Sigma Black Belt | Design for Six Sigma | Robust Design and Process Concept: Robust Design

Defining the ideal state of the basic function that is performing perfectly is the key to robust design. To achieve this, Taguchi suggests the following guidelines for robust design: • Identify the ideal function for the product or process. • Select quality characteristics that are continuous variables. • Select characteristics that add quality. • Quality characteristics should cover all aspects of the ideal function. • Quality characteristics should be easy to measure. Robust design aims to produce a reliable design by controlling parameters so random noise does not cause failure. Since DOE techniques help determine the best design concepts used for tolerance design, a robust DOE strategy helps create a design that improves the product parameters, process parameters, and desired performance characteristics. A product or process is controlled by three primary factors: noise, signal, and control. To learn more about each, roll over each label in the diagram below. [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

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Moving Needs Through Design

Six Sigma Black Belt | Design for Six Sigma | Robust Design and Process Concept: Moving Needs Through Design

The voice of the customer (VOC) describes the customer’s needs. VOC helps to align design and improvement efforts, identify areas to enhance, identify critical features and identify key drivers of customer satisfaction. VOC occurs throughout DFSS by using the needs established during Define to focus the development process through delivery. Customers typically state their needs in common language, but designers must transform the requirements into precise, technical terms and requirements in order to meet the customer’s needs. After defining the VOC, designers need to create critical-to-quality (CTQ) requirements. To develop the CTQs, designers do the following: 1. 2. 3.

Select several quality characteristics for each customer need Develop measures to quantify each need Set targets and specifications to exceed the competition

Designers convert the CTQs into the functional requirements (FRs) that serve as a transition between the CTQs and the critical-to-process (CTP) features documented at the process level. The process of transforming the VOC into CTPs is required to ensure robustness. Functional robustness is the ability to withstand variation in input conditions and still achieve desired performance capabilities and produce the desired result at the lowest possible cost.

1032

Functional Requirements

Six Sigma Black Belt | Design for Six Sigma | Robust Design and Process Concept: Functional Requirements

Customers only like surprises when requirements are exceeded. Otherwise, customers are disappointed or disgruntled. Functional requirements (FRs) are the requirement the product or process must possess to satisfy the customer’s requirements. The FRs need to be understood early in the design process in order to establish criteria for selecting a design based on the quality level and development costs that enable the product to survive in a competitive marketplace. Along with establishing the functional requirement early in the process, the FRs must yield accurate information. Misinformation about the FRs can delay the development cycle. Therefore, to meet the objective of their business strategy, the customer’s business requirements serve as the foundation of the VOC. The customer's requirements must transition into quality characteristics, target values and measurement techniques. Thus detailed requirements and specifications are developed, and constraints involved in the product or process are identified. Examples of Functional Requirement • Car must average 35 miles/gallon (highway driving). • Manual must be written in active voice. • A warning signal must activate when the temperature exceeds 30oC. • Inside diameter must be 0.2500 inches.

• • • • • •

Benefits of Functional Requirements Promotes partnership with the customer Establishes a baseline for requirements Emphasizes quality to reduce rework Increases time efficiency by reducing implementation of unnecessary items Reduces maintenance Increases reliability

  [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

1033

Robustness and Cost

Six Sigma Black Belt | Design for Six Sigma | Robust Design and Process Concept: Robustness and Cost

Customers always have expectations of the product or process. Since satisfactory performance depends on the interdependencies of different components, the product with components within tolerance intervals may not satisfactorily perform. For example, if the car door’s size is near its upper tolerance limit and the size of the doorframe is near its lower tolerance limit, the door may not close properly. A product performs best when all product parameters are at their ideal values. A large number of product failures and the resulting cost of poor quality (COPQ) are a result of neglecting uncontrollable factors causing variation during the early design stages. Robust design involves deciding the best values for the controllable factors in the presence of the uncontrollable factors. Therefore, a robust design is less sensitive to variation due to the uncontrollable factors. Process and product design largely determine both the product’s cost and variations. Increasing process controls can reduce variations, but these controls may be costly. Therefore, designers focusing on reducing both variations and the need for process controls will reduce costs.

1034

Noise Factors

Six Sigma Black Belt | Design for Six Sigma | Robust Design and Process Concept: Noise Factors

Noise factors are all the uncontrolled sources producing variation throughout the product’s life and across production units, except variables in design parameters. There are two types of noise factors: external and internal. External noise sources are variables that are external to the product affecting its performance. Internal noise sources are the product’s deviations from its nominal settings, including worker/machine and environmental conditions. In baking, the use of sugar, butter, eggs, milk, and flour are controllable factors, whereas the conditions inside the oven such as humidity and temperature are not controllable. Motor vehicle tires encounter external noise through exposure to a variety of conditions such as surface conditions due to weather (damp, wet, snow, ice), different temperature, and different road types (concrete, asphalt, gravel, dirt, and off road). The ability of tires to provide a smooth ride and responsive stopping regardless of the conditions is an example of robustness. For more examples of noise factors, roll over Page Resources, and click Noise Examples.

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Noise Examples

Six Sigma Black Belt | Design for Six Sigma | Robust Design and Process | Noise Factors Example: Noise Examples

Examples of Noise Factors   General • Weather • Temperature • Humidity Raw Materials • Material constraints • Moisture content Mechanical • Machine type • Machine age Electronics • Motor interfaces • Electrical isolation • Circuit board fabrication

  • • •   • •   • •   • • • •

Vibration Shift Operator

  • •

Operating Environment Use

Supplier Date produced

  • •

Material properties Lot number

Cleanliness Machine number

  • •

Tool wear Tool design

  • • •

Circuit board thickness Wait time Material thickness

Oxidation Component density Water temperature Component type

 

1036

Controlling Noise Factors

Six Sigma Black Belt | Design for Six Sigma | Robust Design and Process Concept: Controlling Noise Factors

Noise factors are difficult, expensive, or impossible to control. In the past, many engineers approached noise problems by attempting to control the noise factors themselves. Because of the expense, Dr. Taguchi suggests designers should only use this type of control action as a last resort, and he recommends an experimental approach to seek the design parameters to minimize the impact of the noise factors on variation. This approach drives the designer to select the appropriate control settings that will make the product unaffected by noise factors, thus robust. Remember, the goal of robustness strategies is to achieve a given target with minimal variation. Lack of robustness is synonymous with excessive variation, resulting in quality loss. Ignoring noise factors during the early design stages can result in product failures and unanticipated costs; therefore addressing noise factors early in the process through robust design minimizes these problems.

1037

Control Methodology

Six Sigma Black Belt | Design for Six Sigma | Robust Design and Process Concept: Control Methodology

To layout a robust design strategy, the product development team must first identify the inputs, outputs, cost-effective controllable factors and uncontrollable factors. Then designers use well-planned experimental design to gather data for analysis to provide valid and objective information about the design. Well-planned experimental design maximizes the amount of information obtained for a given amount of effort. DOE, previously covered in the Improve lesson, is an efficient procedure for planning experiments to obtain data for analysis for yielding valid and objective information.

1038

DFSS and Orthogonality

Six Sigma Black Belt | Design for Six Sigma | Robust Design and Process Concept: DFSS and Orthogonality

The goal of setting noise factors is to simulate worst-case conditions that could occur. Once the design team identifies the ideal function and corresponding noise and control factors, the team begins to develop the experimental plan. Traditionally, if an experiments involves 5 control factors and 3 noise factors using an 8-run design and a 4-run experiment, 32 trials are required. As you have learned in the lmprove lesson of this course, Taguchi’s approach uses orthogonality, an approach studying each factor independently. To accomplish this, the plan consists of two orthogonal arrays – the inner array and the outer array. The inner array consists of control factors and the outer array consists of noise and signal factors. To summarize the orthogonal array information from the Improve lesson, the matrix for each the three noise factors allows the designer to use a 2-factor noise interaction. Thus, the designer runs all noise factors against each control factor, and then analyzes the data by computing the signal-to-noise ratio to summarize the results at each control factor setting. Another way for determining the effects of noise factors involves performing the experiment with the best combination and the worst combination of noise level settings. By making the product or process perform robustly at these two extremes, then the process will be robust at any combination of noise factor settings in between.

1039

Tolerance

Six Sigma Black Belt | Design for Six Sigma | Robust Design and Process Concept: Tolerance

Tolerance is a permissible limit of variation in a parameter's dimension or value. Dimensions and parameters may vary within certain limits without significantly affecting the equipment’s function. Designers specify tolerances with a target and specification limits (upper and lower) to meet customer requirements. The tolerance range, the difference between those limits, is the permissible limit of variation. Systems are made of components, and components are made of materials. Realistically, not all components are made of the same materials. Designers must determine the tolerances for all system components. Different methods exist for determining tolerance specifications; a conventional method depends on the designer’s experience and perception, and a loss function method is based on the COPQ.

1040

Statistical Tolerance

Six Sigma Black Belt | Design for Six Sigma | Robust Design and Process Concept: Statistical Tolerance

Parts work together, fit into one another, interact together and bond together. Since each part has its own tolerance, statistical tolerance is a way to determine the tolerance of an assembly of parts. By using sample data from the process, statistical tolerance defines the amount of variance in the process. Statistical tolerance is based on the relationship between the variances of independent causes and the variance of the overall results. Tolerence intervals were also covered in the Point and Interval Estimation section of the Analyze Lesson.

Example: Given a 12-piece sample from a process with a mean of 14.591 and a standard deviation of 0.025, find the tolerance interval so that there is a 0.95 confidence that it will contain 99% of the population. From the table, K = 4.150.

 

1041

Stack Tolerance

Six Sigma Black Belt | Design for Six Sigma | Robust Design and Process Concept: Stack Tolerance

Sometimes parts are stacked together. Depending on the application, the parts may be the same or quite different. In these cases, tolerance levels must be determined for the entire stack. • Sum the minimal heights for the lower tolerance limit. • Sum the maximum heights for the upper tolerance limit. Assuming the processes producing each part are capable and within normal distribution, the tolerances of the parts are not additive, but are instead related to the variance.

 

1042

Statistical Tolerancing

Six Sigma Black Belt | Design for Six Sigma | Robust Design and Process Concept: Statistical Tolerancing

According to Thomas Pyzdek in The Six Sigma Handbook, " Engineering tolerances are usually set without knowing which manufacturing process will be used to manufacture the part, so the actual variances are not known. However, a worst case scenario would be where the process was just barely able to meet the engineering requirement. This situation occurs when the engineering tolerance is 6 standard deviations wide (± 3 standard deviations). Thus, we can write the equation as:

" "In other words," Pyzdek asserts, "instead of simple addition of tolerances, the squares of the tolerances are added to determine the square of the tolerance for the overall result." Pyzdek goes on to say, "The result of the statistical approach is a dramatic increase in the allowable tolerances for the individual piece parts." This is an important concept in terms of tolerance because now the parts can have a greater tolerance for each part. An example is provided on the next page.    

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Statistical Tolerancing Example

Six Sigma Black Belt | Design for Six Sigma | Robust Design and Process Concept: Statistical Tolerancing Example

The following example is taken from The Six Sigma Handbook by Thomas Pyzdek. Consider a shaft and bearing assembly where the shaft is specified to be 0.997 ± 0.001 and the bearing is specified to be 1.000 ± 0.0001. In this example, the minimum clearance between the two is 0.001 inches and the maximum clearance is 0.005 inches. Pyzdek notes: " Thus, the assembly tolerance can be computed as: Tassembly = 0.005" - 0.001" = 0.004" The statistical tolerancing approach is used here in the same way as it was used above. Namely,

If we assume equal tolerances for the bearing and the shaft to tolerance for each becomes:

Which nearly triples the tolerances for each part. "

1044

Statistical Tolerancing Assumptions

Six Sigma Black Belt | Design for Six Sigma | Robust Design and Process Concept: Statistical Tolerancing Assumptions

In concluding the discussion of statistical tolerancing, Pyzdek uses the following assumptions from the formula used on the previous page: " • • •

The component dimensions are independent and the components are assembled randomly. This assumption is usually met in practice. Each component dimension should be approximately normally distributed. The actual average for each component is equal to the nominal value stated in the specification.

"

1045

Tolerance Design

Six Sigma Black Belt | Design for Six Sigma | Robust Design and Process Concept: Tolerance Design

Tolerance design establishes metrics allowing designers to identify the tolerances that can be loosened or tightened to meet customer needs while producing a cost-effective product. Tolerance design goes a step beyond parameter design by considering tolerance decisions as economic decisions just as spending additional money buys better materials or equipment. Besides economics, tolerance design also considers other factors such as constraints due to material’s properties, engineering design choice and safety factors. By enhancing the understanding of the relationship between product parameters, process parameters, and desired performance characteristics, designers use DOE to identify what is significant and move the process or product to the ideal function. The following formulas are important in tolerance design: Tolerance Specifications

Functional Limit

Need functional limit and the safety limit to calculate DOE establishes upper and lower functional limits

Economic Safety Factor

Taguchi uses the point where th product fails 50% of the time (L 50)

 

1046

Tolerance Design Example

Six Sigma Black Belt | Design for Six Sigma | Robust Design and Process Concept: Tolerance Design Example

The following tolerance design problem involves the power supply to televisions. • Functional limits at +/- 25% of output voltage • The average quality loss (A0) after shipping a bad TV = $300 •

In-house power supply adjustment before shipping = $1.00

1047

Tolerance Design and Process Capability

Six Sigma Black Belt | Design for Six Sigma | Robust Design and Process Concept: Tolerance Design and Process Capability

Customers always have requirements. To meet those requirements, we assign products and processes certain specifications and a target. As the products deviate from the target, quality losses grow. Functional requirements (FRs) are the requirement the product or process must have to satisfy the customer. Tolerance is a permissible limit of variation in a dimension or value of the parameter. Linking tolerance and process capability is about linking functional requirements and tolerances to the economic safety factor. Three situations are forthcoming: nominal-is-best, smaller-is-better, and larger-is-better. Nominal-is-Best and Smaller-is-Better

 

A manufacturer of doors received 2 formulas a special order from a major builder for 40 inches doors. The functional limits for the door order are +/- 0.5 inches. The economic loss due to a poor door is $45, and the average manufacturing cost is $8. Determine the tolerance for the order to satisfy the economic safety factor.

Larger-is-Better The wire used to hold ceiling planters has a cross-sectional area of 0.5 in2. The wire is supposed to hold at least 30 pounds of plants. The cost of producing the wire is $3 while the failure cost of the wire is $100. Determine the tolerance needed for the wire required to satisfy the economic safety factor.

 

To satisfy the economical safety factor, the customer should receive doors with a tolerance of 40 inches +/- 0.211.

 

To satisfy the economic safety factor, the wire should be 5.77 times the functional limit (30 lbs.) or 173.1 lbs.

 

1048

Six Sigma Black Belt Design for Six Sigma Failure Mode Effects Analysis

Learning Objectives

Six Sigma Black Belt | Design for Six Sigma | Failure Mode Effects Analysis Concept: Learning Objectives

At the end of this DFSS topic, all learners will be able to: • understand the terminology, purpose, and use of scale criteria (including risk priority number (RPN)) for failure mode and effects analysis (FMEA) and apply to processes, products or services. • understand the distinction between and interpret data associated with design FMEA (DFMEA) and process FMEA (PFMEA).  

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Purpose

Six Sigma Black Belt | Design for Six Sigma | Failure Mode Effects Analysis Concept: Purpose

Both customer satisfaction and dissatisfaction are keys to identifying critical-to-quality (CTQ) characteristics. CTQ are the select few, measurable key characteristics of a specific product, process, service, or transaction that must be in statistical control to guarantee customer satisfaction. As QFD is a vehicle for identifying key elements driving customer satisfaction, failure modes and effects analysis (FMEA) is an up-front process for reducing the impact on customer dissatisfiers. As a cost-efficient safety and reliability improvement tool used during product development, FMEA is a systematic group of activities intended to: • document the process. • recognize and evaluate a failure and the effects that failure has on the system. • identify actions that could eliminate the failure, reduce the probability the failure occurs, or reduce the criticality of the failure on the system or its users. First used by the U.S. military in the 1940s and then by industry in the 1960s, FMEA is a systematic problem-prevention tool. FMEA helps quality professionals find the potential critical failures of a system and then eliminate or control them. A critical failure is any failure affecting user safety or causing a total system shutdown. While it is impossible to eliminate all possible failures, the FMEA process provides an opportunity to consider and document all the failures that are most damaging to a system or to its users’ safety.

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Overview

Six Sigma Black Belt | Design for Six Sigma | Failure Mode Effects Analysis Task: Overview

FMEA consists of three processes: identify, prioritize, and focus. By identifying critical product characteristics and process variables, the team is able to prioritize product and process deficiencies to focus on prevention of the most significant product and process problems. Click each item below to learn more. Benefits • Ranks possible failures by their effect on the customer • Prioritizes deficiencies to focus improvement efforts • Documents information about risks of failure and risk reduction • Emphasizes prevention • Reduces product development time and cost • Improves reliability and quality • Reduces the amount of rework, repair and scrap • Stimulates team discussion Use When • Identifying possible failures • Designing/redesigning a process, product or service • Evaluating a product for robustness (functionality, producibility, reliability) • Identifying causes during early stages of defect reduction efforts • Identifying key process/product parameters and evaluating methods for controlling them • Considering a change to the product’s/process’s design, application, environment, material, manufacturing or assembly process • Following a team brainstorm about the problem Input Sources • Customer requirements • Design specifications • DOE • Failure and rework data • Prior FMEAs • Warranty, rework and service data • For DFMEA, the product or service; for PFMEA, the process

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Overview

Six Sigma Black Belt | Design for Six Sigma | Failure Mode Effects Analysis Task: Overview

Quality Tools with FMEA Other tools to gather information or ideas for the FMEA process: • Fishbone diagrams • Histograms • Pareto charts • Process decision program charts • Process maps • Run charts • Tree diagrams • Checklists • Brainstorming • Affinity diagrams • Scatter diagrams • Statistical analysis Expected Results • Learn to identify critical product/process parameters • Achieve consensus on solutions and methods of implementation • Understand detailed product/process Types of FMEA Covered in Body of Knowledge: • Design FMEA - To improve system design • Process FMEA - To improve the manufacturing process Others not in Body of Knowledge: • System FMEA - To improve linking multiple processes • Functional FMEA - To improve performance • Defect FMEA - To identify root causes of defects

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Risk Priority Number

Six Sigma Black Belt | Design for Six Sigma | Failure Mode Effects Analysis Concept: Risk Priority Number

Before returning to the individual types of FMEA, one must also understand a tool within FMEA. Risk priority number (RPN) is the dimensionless index used to rank and evaluate the combined degree of severity, frequency of occurrence, and the ability to detect specific defects. Generated by multiplying the severity, occurrence, and detection for each defect, the RPN statistic reduces the number of possible failures to investigate. To help the team narrow its focus on possible root causes, address the failures with the highest RPN and any failure with a severity ranking of 10.

User Tips • •

Think of RPN as a risk factor The higher the RPN value, the higher the risk

In the sample below, consider the scoring criteria as a suggestion rather than absolute. Also, note that the detection scale is the reverse of the severity and occurrence scales.

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Design FMEA

Six Sigma Black Belt | Design for Six Sigma | Failure Mode Effects Analysis Task: Design FMEA

A vital part of the “up-front” engineering disciplines, design failure mode and effects analysis (DFMEA) is a proactive approach documenting weaknesses in product design that may cause system failures while a product is in service, thus eliminating unsafe conditions that might result from a failure. Click each topic to learn more. Benefits Completed when designing new products or changing existing products, DFMEA: • helps identify potential product failure modes early in the product development cycle. • identifies characteristics requiring special controls as well as highlighting areas of improvement. • increases the likelihood that all potential failure modes and their effects on assemblies will be considered. • assists in evaluating product design requirements and test methods. • establishes a priority for design improvement. • documents the rationale behind design changes and helps guide future development projects. • improves system safety by eliminating unsafe conditions that might result from a failure. Teams Beginning its investigation by identifying the lowest system level for analysis, cross-functional teams, including representation from all engineering functions, should complete the following tasks: • Analyze product design • Recommend design changes • Follow through on recommended actions The engineering functions may include, but are not limited to: • Reliability • Product design • Quality • Manufacturing • Test • Field service • Logistics Improvement DFMEA often leads to design changes that improve a product’s reliability in one of two ways: • A reduction in the failure rate during useful life • An increase in the duration of useful life through elimination of an early wear-out failure mode

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Design FMEA

Six Sigma Black Belt | Design for Six Sigma | Failure Mode Effects Analysis Task: Design FMEA

Worksheet To see a sample DFMEA worksheet, roll over Page Resources, and then click DFMEA Worksheet.

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DFMEA Worksheet

Six Sigma Black Belt | Design for Six Sigma | Failure Mode Effects Analysis | Design FMEA Resources: DFMEA Worksheet

 

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Process FMEA

Six Sigma Black Belt | Design for Six Sigma | Failure Mode Effects Analysis Task: Process FMEA

Process failure mode and effects analysis (PFMEA) is a proactive approach to identify potential process deficiencies early in the process planning cycle. This enables engineers to focus on controls that reduce nonconforming product and increase detection capability well before production begins. It also provides an organized, systematic approach to process change and helps prioritize process improvement actions. Click each topic to learn more. Benefits • Helps analyze products and processes to reduce the occurrence and improve the detection of defects • Assists in the development of process control plans • Establishes a priority for improvement activities • Documents the rationale behind process changes • Guides future process improvement plans • Helps identify potential Six Sigma projects Compared to DFMEA Similarities to DFMEA: • Uses cross-functional teams • Follows same general steps • Uses similar worksheet Differences from DFMEA: • PFMEA does not rely on product design changes to overcome process weaknesses • Team must consider design characteristics relative to the manufacturing process to ensure that the product meets expectations Worksheet To see a PFMEA worksheet, roll over Page Resources, and then click PFMEA Worksheet.

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PFMEA Worksheet

Six Sigma Black Belt | Design for Six Sigma | Failure Mode Effects Analysis | Process FMEA Concept: PFMEA Worksheet

 

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Procedure and Tips

Six Sigma Black Belt | Design for Six Sigma | Failure Mode Effects Analysis Concept: Procedure and Tips

Procedure The FMEA team begins by identifying the lowest system level for analysis (e.g. parts or components). After selecting the appropriate system level, the team completes the following steps: 1. 2. 3.

Identify the design/process/service and construct a process map. Identify the potential failures. For each failure, identify the possible consequences/effects. a.

4.

For each consequence, assign a level of severity (S). a. b.

5. 6.

8.

Use a 1-to-10 scoring scale. Insignificant = 1, Catastrophic = 10

For each failure, determine the potential root causes by listing all the possible causes. For each cause, determine the occurrence rating (O). a. b.

7.

Failure Effects – The outcome of the failure mode’s occurrence on the process (identifying the impact on the customer’s experience).

Use 1-to-10 scoring scale. Extremely unlikely = 1, Inevitable = 10

For each cause, identify the current process control: the tests and/or procedures reducing the possibility of the failure reaching the customer. For each process control, assign a detection rating (D). a. b.

Use a 1-to-10 scoring scale. Most certain to detect = 1, Most certain not to detect = 10

9. 10. 11. 12.

Calculate the risk priority number (RPN) by multiplying S x O x D. Calculate criticality by multiplying S x O. Prioritize by RPN and criticality by sorting the RPN column. Develop a corrective action plan based on the causes found and determine actions to minimize the effect of each cause. 13. Implement corrective actions and reevaluate risk. 14. Repeat the analysis until all potential failures pose an “acceptable” risk level. 15. Document all changes and results.

User Tips • • • • • • •

Helpful until during the Define Phase in DMADV and both the Define and Improve Phases in DMAIC. Creating FMEA results requires disciplined cause-and-effect thinking. Use the broad knowledge within a cross-functional team to correctly assess the risk. Use flowchart and process maps to identify the system to be analyzed. SIPOC (Suppliers-Inputs-Process-Outputs-Customers) analysis can be helpful. Document the known cause-and-effect relationships in a fishbone diagram before starting FMEA analysis. Use the scoring guidelines table as a ratings guide.

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Procedure and Tips

Six Sigma Black Belt | Design for Six Sigma | Failure Mode Effects Analysis Concept: Procedure and Tips

• • • •

Criticality and RPN calculations provide guidance for rank ordering potential failures. The higher the RPN, the more urgent the necessary improvement. The detection level in a PFMEA must be determined for the process step at hand; thus not based on the end of the process or any other step. The same failure mode, the same effect and the same cause can occur more than once over different process steps. More specifically, the same cause can occur more than once with different effects within the same failure mode. Therefore, do not duplicate their severity, occurrence and detection ratings because each rating is independent of every other rating.

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FMEA Exercise

Six Sigma Black Belt | Design for Six Sigma | Failure Mode Effects Analysis Concept: FMEA Exercise

Given the information on the chart, rank the failures associated with obtaining the wrong part in order (from highest to lowest) by RPN. To check your answer, roll over Page Resources, and then click FMEA Answer.

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FMEA Answer

Six Sigma Black Belt | Design for Six Sigma | Failure Mode Effects Analysis | FMEA Exercise Example: FMEA Answer

Answer 1. 2. 3. 4. 5. 6.

Fails test (400) Can’t build parts: Supplier error (192) Defective parts shipped: Inadequate test procedure (160) Can’t build parts: Supplier error (128) Defective parts shipped: Wrong parameter (80) Defective parts shipped: Test malfunction (40)

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Six Sigma Black Belt Design for Six Sigma Design for X

Learning Objectives

Six Sigma Black Belt | Design for Six Sigma | Design for X Concept: Learning Objectives

At the end of this DFSS topic, all learners will be able to understand design constraints such as design for cost, design for manufacturability and producibility, design for test and design for maintainability.

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DFX Introduction

Six Sigma Black Belt | Design for Six Sigma | Design for X Concept: DFX Introduction

Design for X (DFX) is an approach for designing products and services that meet customer requirements. As a cross-functional team design activity involving manufacturing, distribution and service organizations, DFX strategy reviews design continually to find ways to improve product. For instance, when considering serviceability, maintenance and service personnel are involved to note their requirements and concerns. Due to its use of cross-functional teams and the nature of continual review, DFX is needed within concurrent engineering (simultaneous engineering) as an approach to improve new product development where the product and associated processes develop in parallel.

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Concepts for DFX

Six Sigma Black Belt | Design for Six Sigma | Design for X Task: Concepts for DFX

The DFX toolbox contains numerous techniques for addressing product and process design. Although importance varies from industry to industry and from product to product, each technique has many applications. Click each to learn more.

Design for Cost • Also called value engineering • Designers must consider price limitations Design for Manufacturability Goal: To design products and processes in such a way that they result in fewer problems during manufacturing. • Emphasize robustness rather than ideal performance • Reduce the probability of mistakes by reducing complexity • Design preventative mechanisms for likely errors • Reduce the number of parts • Reduce the number of manufacturing operations

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Concepts for DFX

Six Sigma Black Belt | Design for Six Sigma | Design for X Task: Concepts for DFX

Design for Assembly • Simplify the product into fewer parts • Make the product easy to assemble • Reduce service, decrease time to market, and reduce repair time Sometimes Design for Manufacturability and Design for Assembly are combined (DFM/A). Benefits of Integrating DFM and DFA • Simpler designs • Fewer parts • Reduced assembly time • Reduced production cost • Fewer errors • Fewer suppliers • Easier to test and maintain Design for Producibility Goal: By influencing design and concurrent engineering, DFP is a key metric of the success of product design. • Identifies the needs of innovative manufacturing • Ensures proposed process will satisfy design requirement • Decreases cost • Reduces concept-to-build cycle times • Reduces risk Design for Test • Important during development, production, and use • Makes access points easily assessable • Creates built-in test points • Uses standard connections and interfaces • Tests with standard equipment • Develops a build-in self test

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Concepts for DFX

Six Sigma Black Belt | Design for Six Sigma | Design for X Task: Concepts for DFX

Design for Maintainability (Serviceability) • Important to the customer • Designs easy service • Makes access points simple, yet secure • Assures reliability of individual components • Balances reliability and cost with the product’s intended use and life • Reduces downtime for maintenance • Reduces the number of maintenance tasks • When applicable, uses disposable parts instead of parts requiring repair • Eliminates or reduces the need for adjustment • Uses mistake-proof fasteners and connectors Design for Safety • Eliminates potential failure elements that may occur during operation • Emphasizes safety throughout the product life: safe to manufacture, safe to sell, safe to use, and safe to dispose Others • Design for user friendliness • Design for ergonomics • Design for appearance • Design for packaging • Design for features • Design for time to market • Design for environment

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Reliability

Six Sigma Black Belt | Design for Six Sigma | Design for X Task: Reliability

Failure is a real and important concept whether it is software, sensitive medical equipment, a complex machine for an industrial process, or a household toaster. How long will the product work? How many failures will occur within so-many years? How do different environmental conditions affect performance? Since successful performance is important to customers, producers must have a useful method for determining the probability of the product's ability to perform successfully for a specified time under specified conditions. Within the engineering field, reliability is the probability that a product will perform as stated, under specified operating conditions, for a given time period. This definition contains four concepts: probability, successful performance, operating conditions, and time. Click each below to learn more. Probability • The chances that something will happen • A calculated, numerical value • Previously covered probability theory provides the mathematical foundation Successful Performance • A specifically defined set of criteria for goodness or failure • A unit's conditions for each must be clearly defined; failure could mean total inoperativeness or diminished performance • To calculate reliability, a product (or unit) exists in 1 of 2 states: successful performance or failure Operating Conditions • Operating conditions specify the environmental and use limits for operating the • •

unit (Ex.) This medicine must be stored in a dry room between 56 oF and 87 oF. Customers have a responsibility to use a unit within these limits, but this is by no means a guarantee Product designers must anticipate and design for stress conditions above those proper use conditions

Time • Within the context of reliability, the time period involved must be specified • Times could be hours, years, miles, cycles, or some other measure tied to duration or amount of use

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Bathtub Curve Introduction

Six Sigma Black Belt | Design for Six Sigma | Design for X Concept: Bathtub Curve Introduction

Before examining each distribution, it is important to understand how the pattern of product failure can change with time. The bathtub curve, so named for its distinctive shape, is the model used to describe failure patterns of a population over the entire life of the product. The bathtub curve is a plot of failure rate vs. time and shows how fast product failures are taking place and if the failure rate is increasing, decreasing or staying the same. The curve is divided into three regions, as seen in the illustration below. The bathtub curve is not a perfect model. The graph is not in proportion and was never intended to show the exact shape of the ends of the curve. The left and right ends of the bathtub curve show only the general trends of the population failure rate as the product ages. However, it is useful for describing failure patterns for a population of well-designed, mature products. In addition, because each proportion of the bathtub curve has a corresponding distribution that provides the appropriate failure rate change, the bathtub curve often determines the distribution selected for a reliability analysis. Given the connection between distributions and the bathtub curve, the discussion to follow is framed in terms of the three bathtub curve regions. For ease of explanation, it begins with the wearout period and proceeds to the left. Test your understanding of the bathtub curve, roll over Page Resources, and click Test. [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

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Test

Six Sigma Black Belt | Design for Six Sigma | Design for X | Bathtub Curve Introduction Fact: Test

Test your understanding of the bathtub curve, by dragging each label on the left to the appropriate box representing each region on the right. [ This page in the e-Learning course contains an animation or activity that cannot be printed. See the online version to view this content. ]

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Wearout Period – Normal Distribution

Six Sigma Black Belt | Design for Six Sigma | Design for X Concept: Wearout Period – Normal Distribution

The right side of the bathtub curve has an increasing failure rate, signifying that: • probability of failure is increasing. • age is a factor in the probability of failure. This makes sense, as most items become more likely to fail with age due to accumulated wear. The normal distribution can be used to model a product’s times to failure in the wearout period. This is because the normal distribution has an increasing failure rate corresponding with that of the wearout period. Both are shown below.

Rollover Page Resources, and then click Reliability Calculations to see how to calculate reliability using the normal distribution.

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Reliability Calculations

Six Sigma Black Belt | Design for Six Sigma | Design for X | Wearout Period – Normal Distribution Fact: Reliability Calculations

To calculate reliability using the normal distribution, you must know or be able to estimate the mean and the standard deviation. Use the normal distribution to calculate a product’s reliability. The reliability itself is found in normal probability tables. In order to use the tables, it is necessary to use the translation equation (z):

The beginning of the wearout region is often assumed to be 3.5 to 4.5 standard deviations to the left of the mean. The exact figure is determined by the amount of wearout failure risk that product designers are willing to assume.  

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Useful Life Period - Exponential Distribution

Six Sigma Black Belt | Design for Six Sigma | Design for X Concept: Useful Life Period - Exponential Distribution

The useful life period (center of the bathtub curve) has several distinct characteristics: • Period of intended product use • Customer use is the highest • Most reliability calculations and predictions done • Constant failure rate • Age of the product does not affect the probability of failure • Low failure rate if reliability is high • Exponential distribution can be used to model a product’s times to failure The exponential distribution has a constant failure rate, corresponding with that of the useful life period as seen in the illustration below. To view the mathematical formulas in detail roll over Page Resources, and click Formulas.

 

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Formulas

Six Sigma Black Belt | Design for Six Sigma | Design for X | Useful Life Period - Exponential Distribution Fact: Formulas

The mean of the exponential distribution is symbolized by Theta (Θ). If a product can be repaired, Θ is referred to as the mean time between failures (MTBF). If a product cannot be repaired, Θ is referred to as the mean time to failure (MTTF). The mean of the exponential distribution is an indicator of reliability during the useful life region of the bathtub curve and should not be confused with the end of useful life or the beginning of wearout. For reliability to be high, the MTBF (MTTF) must be high compared to the mission time. The formula for the exponential distribution is:

 

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Early Life Period

Six Sigma Black Belt | Design for Six Sigma | Design for X Concept: Early Life Period

The final portion of the bathtub curve, that which is furthest to the left shows a decreasing failure rate. Failures during this period are referred to as early life failures. Systems in this phase of lifecycle are deemed unsuitable for routine operation or delivery to customers.  The failures are caused by nonconformities introduced into a product by the production process. Common sources of early life failures include: • Inadequate materials • Improper use • Handling damage • Over-stressed components • Improper setup or installation • Power surges The early life period is sometimes called the burn-in period. Roll over Page Resources, and click Burn-In to reveal more details. Even though virtually all new products experience early life failures, the failures are generally not used to make reliability predictions.

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Burn-In

Six Sigma Black Belt | Design for Six Sigma | Design for X | Early Life Period Fact: Burn-In

Burn-in refers to the practice of running the system under conditions that simulate an operating environment for a period of time sufficient to allow the failure rate to stabilize. For many types of product, burn-in is performed at normal operating conditions. For others, burn-in is performed at higher-than-normal stress levels such as increased temperatures, vibration levels, etc. During burn-in, many of the units containing nonconformities fail and are removed from the population. This improves the reliability of units delivered to the customer and reduces the likelihood that a unit will fail in customer hands because of an early life cause. Unfortunately, the burn-in approach to ensuring high reliability is also very costly and can be less than 100% effective.

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Reliability Indicators

Six Sigma Black Belt | Design for Six Sigma | Design for X Concept: Reliability Indicators

Mean time to failure (MTTF), mean time to repair (MTTR), and mean time between failures (MTBF) are indicators of a unit's reliability. While none of these measure useful life length (they measure reliability during life), MTTF and MTBF differ by being a measure of reliability for nonrepairable and repairable units respectively. The greater the MTTF and MTBF, the less likely a unit is to fail and the higher the reliability. MTTR is the total corrective maintenance time divided by the total number of corrective maintenance actions during a given period. MTTR is the average time it takes to do a repair (corrective maintenance) once a unit has failed.

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Six Sigma Black Belt Design for Six Sigma Special Design Tools

Learning Objectives

Six Sigma Black Belt | Design for Six Sigma | Special Design Tools Concept: Learning Objectives

At the end of this DFSS topic, all learners will be able to understand the concept of special design tools such as the theory of inventive problem-solving (TRIZ) and axiomatic design (conceptual structure robustness).

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TRIZ

Six Sigma Black Belt | Design for Six Sigma | Special Design Tools Concept: TRIZ

This course previously covered the importance and benefits of using Taguchi Methods for performing robust design. TRIZ and axiomatic design (AD) are tworelatively new approaches to enhancing robust design. Both approaches aid the design decision-making and problem-solving processes during the Design phase of DMADV. TRIZ is an acronym for the Russian phrase Teorija Rezbenija Izobretaltelshih Zadach, meaning “theory of inventive problem solving.” Genrich Altshuller (1926-1998), a Russian mechanical engineer, created TRIZ as a set of problem-solving design tools and techniques. After studying over 400,000 patents looking for inventive problem-solving methods, Altshuller noticed patterns across different industries. Traditionally, inventive problem-solving is linked to psychology; however, TRIZ is based on a systematic view of the technological world. Altshuller realized that people, including specialists, have difficulty thinking outside of their field of reference. Given a problem (P) within their specialty, many people will only limit their search for a solution (S) to their area of specialty. What happens if the known solution to the problem could be found in another knowledge area? For an example of a solution found in a seemingly unrelated area, roll over Page Resources, and click Diamonds.

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Diamonds

Six Sigma Black Belt | Design for Six Sigma | Special Design Tools | TRIZ Example: Diamonds

Traditional diamond-cutting methods cut diamonds along natural fractures, but often result in new fractures that go undetected until using the diamond. Rather than improving the existing process, cutters needed a new process. The key in establishing the new method was a pressurized process in the food canning industry used to split green peppers and remove the seeds. A similar technique applied to diamond cutting resulted in cuts without additional damage.

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Solutions and Knowledge

Six Sigma Black Belt | Design for Six Sigma | Special Design Tools Concept: Solutions and Knowledge

Altshuller classifies problems into two types: those with known solutions and those with unknown solutions. Books, journals, subject matter experts and personal knowledge provide answers to known solutions for 99% of problems. Altshuller also classified solutions by levels of inventiveness. The concept of employee creativity is often tied to breakthroughs: an improvement to unprecedented levels of performance. Since breakthroughs comprise only 1% of solutions, TRIZ helps designers avoid the trial-and-error approach and guides them to a better design because 99% of the problems have been solved somewhere before.

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Parameters and Principles

Six Sigma Black Belt | Design for Six Sigma | Special Design Tools Concept: Parameters and Principles

The ideal solution is one with only benefits and no harmful or negative effects. Unfortunately, problem-solvers often resort to trade-offs and compromise, thus not achieving the ideal solution. An inventive problem is a problem in which the solutions cause other problems to appear. For example, an increase in metal’s strength also increases the weight. This solution creates a dilemna because the increased weight is a negative outcome and not cost-effective. Through his study of many patents, Altshuller identified 39 fundamental engineering parameters and 40 inventive principles. His solution involved using contradictory engineering parameters that created undesirable results to identify the inventive principles to use for a solution.

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Table of Contradictions

Six Sigma Black Belt | Design for Six Sigma | Special Design Tools Concept: Table of Contradictions

In order to help designers identify solutions, Altshuller also created a table of contradictions. The table is a very large grid listing the 39 fundamental engineering parameters along both axes. However, the y-axis is the feature to improve and the x-axis is the undesirable result. The intersecting cells contain numbers corresponding to the inventive principle to use for a solution. For example, the conflicting engineering parameters for a beverage can are the length of a moving object and stress. To improve the can wall thickness, the length of a non-moving object is the feature to improve, and stress is the undesired effect. Finding the intersection of these two parameters on the table identifies the appropriate inventive principles; in this case 1, 14, and 35. Closer examination within each of these principles could • change the shape of the wall (#1). • change the material used (#14). • change the method of welding the lid to the can (#35).

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TRIZ and DFSS

Six Sigma Black Belt | Design for Six Sigma | Special Design Tools Concept: TRIZ and DFSS

By providing a methodology to think and look outside the box and avoiding contradictions, TRIZ can help engineers, designers, developers, researchers and quality professional solve problems and find new ideas leading to new product development. Some links to DFSS and Six Sigma include: • Solving bottlenecks • Eliminating contradictions discovered in the House of Quality roof • Determining target values • Identifying potential failure modes • Lowering costs • Improving serviceability

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Axiomatic Design

Six Sigma Black Belt | Design for Six Sigma | Special Design Tools Concept: Axiomatic Design

In order to transform inputs into outputs, axiomatic design (AD) is a series of activity steps to analyze systematically the transformation of customer needs into functional requirements, design parameters and process variables. Originally developed by Nam Suh at MIT, AD helps designers understand and structure design problems by facilitating the analysis and synthesis of design requirements, solutions and processes in both manufacturing and nonmanufacturing environments. AD identifies four domains within design: customer, functional, physical and process. Designers create solution alternatives by mapping the requirements specified in a domain to a set of characteristic parameters in an adjacent domain. The mapping between the customer and functional domains is defined as concept design; the mapping between functional and physical domains is product design; the mapping between the physical and process domains corresponds to process design. Identifying the customer’s needs and requirements also known as customer domain serves as the AD’s foundation. The functional domain consists of the requirements of what the product must do to meet the customer requirements, while the physical domain consists of the design parameters necessary to meet the functional requirements. Thus, the process domain consists of the requirements to produce the product to meet the physical domain.

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Axioms and Domain

Six Sigma Black Belt | Design for Six Sigma | Special Design Tools Concept: Axioms and Domain

An axiom is a self-evident truth upon which other knowledge must rest, thus serveing as a starting point for deducing other truths. In this sense, an axiom can be known before knowing any of the other propositions. Fundamental Axioms of Axiomatic Design • The functional requirements are independent of each other. • Good designs are less complex. General Steps for Axiomatic Design 1. 2. 3. 4.

Establish design objectives. Generate ideas for solutions. Analyze the solution’s alternatives. Implement the selected design.

After converting the customer needs into functional requirements, the designer breaks down the high-level functional requirements (FR) into lower-level FRs until implementing the design. At the same time, the designer moves between adjacent domains. This zigzag movement ultimately links the entire design.

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Lesson Summary

Six Sigma Black Belt | Design for Six Sigma Summary: Lesson Summary

DFSS is a proactive methodology for integrating information from the voice of the customer into a design process to produce a defect-free process/product for the customer. The purpose of this lesson is to emphasize some of the primary DFSS tools. • QFD is a methodology for determining the VOC and using the information to drive development. • The House of Quality is a QFD tool linking the customer to the technical requirements. Moving the information through a series of matrices integrates the customer needs into required processes and their controls. • Robust design is a series of tools and concepts aiming to reduce the effect of noise so the design does not fail. Tolerance design links components, their specifications, and their interdependence with other components. • FMEA is a proactive tool aimed at dissatisfiers by examining potential causes of failure to prevent failure for the customer. • DFX addresses design by focusing on specific aspects of cost, manufacturing, assembly, test, safety and maintainability. • Axiomatic design is another tool for transforming the customer’s needs throughout the design process. • TRIZ provides a methodology for thinking outside the box to problem solve during design.

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Lesson Bibliography

Six Sigma Black Belt | Design for Six Sigma Concept: Lesson Bibliography

Bibliography American Society for Quality. ASQ’s Foundations in Quality Learning Series: Certified Manager of Quality/Organizational Excellence. Milwaukee, WI: ASQ. 2005. American Society for Quality. ASQ’s Foundations in Quality Learning Series: Certified Quality Engineer. Milwaukee, WI: ASQ. 2000. American Society for Quality. Six Sigma Green Belt Certification Preparation Course, Version 1 (an online course). Milwaukee, WI, 2006. ASQ Statistics Division. Rudy Kittlitz, editor. Glossary and Tables for Statistical Quality Control, 4th ed. Milwaukee, WI: ASQ Quality Press. 2005. Benbow, Donald and T.M. Kubiak. The Certified Six Sigma Black Belt Handbook. Milwaukee, WI: ASQ Quality Press, 2005. Breyfogle, Forrest W. III. Implementing Six Sigma: Smarter Solutions® Using Statistical Methods. 2nd ed. Hoboken, NJ: John Wiley & Sons, Inc., 2003. Pries, Kim H.Six Sigma for the Next Millennium: A CSSBB Guidebook. Milwaukee, WI: ASQ Quality Press, 2006. Pyzdek, Thomas. The Six Sigma Handbook: A Complete Guide for Green Belts, Black Belts, and Managers at All Levels, 2nded. New York: McGraw-Hill, 2003. Taguchi, Genichi. Taguchi on Robust Technology Development. New York, NY: ASME Press, 1993. Tague, Nancy.The Quality Toolbox, 2nd ed. Milwaukee, WI: ASQ Quality Press, 2005.

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Six Sigma Black Belt Next Steps

Post-Assessment

Six Sigma Black Belt | Next Steps Introduction: Post-Assessment

Now that you have completed the web-based Six Sigma Black Belt certification preparation course, the following learning option is available to you: 1.

2. 3.

Take the course post-assessment. Here are 150 questions from each section of the ASQ Body of Knowledge. You may repeat this assessment as many times as needed until you reach a passing score of 80%. The questions are in a randomized bank of approximately 500; the assessment will pose different queries each time you take it. If you select an incorrect answer, you will receive feedback as to which course topic/lesson covers that question. Once you reach or exceed the passing score

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Practice Test

Six Sigma Black Belt | Next Steps Introduction: Practice Test

Now that you have completed the web-based Six Sigma Black Belt certification preparation course, the following learning option is available to you: 1. 2. 3.

Use the Practice Test to check your knowledge and continue your certification exam preparation. This test may be taken as many times as you choose. There are 150 randomized questions from all of the topics/sections of the Body of Knowledge. If you select an incorrect answer, you will receive feedback as to which course topic/lesson addresses that question.

 

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Printer-friendly Version of Course

Six Sigma Black Belt | Next Steps Summary: Printer-friendly Version of Course

Use the link below to generate an Adobe Acrobat file (PDF) of this entire course (minus any interactivity) for you to print or save. There are approximately 1,000 pages in this course so be sure you have an adequate paper supply.   Click here for a printer-friendly file.  

 

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Course Evaluation

Six Sigma Black Belt | Next Steps Introduction: Course Evaluation

As part of our internal process of continual improvement, we solicit feedback from all students who take our web-based training. We invite you to complete the attached course evaluation and share your appraisal with us. Click the link below to open the Adobe Acrobat PDF file. Use the Zoom feature to view this file at 100%. Once you are done, select the email button to forward your critique to ASQ. Click here to start the course evaluation.

We appreciate your feedback. Thank you.  

 

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