Dmaic - Book of Knowledge - Green Belt11ea60e023f

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Classroom Session Agenda–Day 1

1

Total Min

Topic

Step

60

Introductions and Expectations

N/A

20

Meeting Skills

N/A

20

Define A,B and C Review and CAP

A,B,C

10

Break

10

Measure Overview

1,2,3

90

Measure 1 Review CTQ Tools

1

60

Measure 1–CTQ Tools continued

1

10

Break

45

Measure 2–Performance Standards

5

Break

120

Minitab Tutorial and Graphical Analysis

2

various

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Classroom Session Agenda–Day 2*

2

Total Topic Min

Step

30

Day 1–General Review and Homework

A,B,C,1,2

30

Minitab–continued

various

15

Measure 3–Overview

3

15

Break

45

Measure 3–Data Collection Plan

3

75

Measure 3–Sampling

3

60

Measurement System Analysis (MSA)

3

15

Break

15

Analyze Overview

4,5,6

150

Analyze 4–Establish Process Capability

4

* Elevator Speeches will be shared throughout the day

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Classroom Session Agenda–Day 3*

3

Total Topic Min

Step

30

Day 2–General Review

various

15

Analyze 5–Define Performance Objective 5

15

Break

150

Analyze 6–Identify Variation Sources

6

30

Analyze 6–continued

6

15

Improve Preview

7,8,9

30

Improve 7 and 8–Design Of Experiment

7,8

15

Break

30

Improve 9–Statistical Tolerancing

9

15

Control Preview

10,11,12

60

Control 12–Control Charts

12

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Assessment Strategy Introductions

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The Learning Objectives are divided in 3 categories: 1. Classroom 2. Project, and 3. Test It is expected that a Green Belt be proficient in all learning objectives, however, only those designated Test represent the content of the certification exam. Each phase of the DMAIC cycle is listed below and the learning objectives have classified into the 3 categories within each phase.

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Overview–Classroom Learning Objectives

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1 Explain the benefits of Six Sigma to GE’s business. Compare and contrast Six Sigma’s process improvement approach to quality with traditional defect prevention strategies (i.e., inspection and testing). Identify the “vital few” CTQs that apply to all GE customers: responsiveness; marketplace competitiveness; on time, accurate and complete deliverables; and product/service technical performance. Explain the relationship between increasing levels of process complexity and quality improvement results. 2 Describe the Six Sigma Methodology for quality improvement. Define the term “sigma” (standard deviation) as it relates to the sigma capability (z value) of a business or manufacturing process. Recognize a Six Sigma level of quality (i.e., 99.99966% probability that defects will not be passed on to the customer). Define key Six Sigma terms and acronyms, including CTQ, opportunity, defect, DPMO, and Six Sigma capability (Z value). Explain the Master Back Belt (MBB), Black Belt (BB) and Green Belt (GB) roles in Six Sigma. Describe Six Sigma’s focus on repeatable processes. Describe Six Sigma’s focus on inputs (X’s) over outputs (Y’s) using the formula Y=f (X). Describe the statistical objective of Six Sigma (i.e., reduce process variation). Describe the relationship between DPMO and process capability (i.e., as DPMO goes down, process capability goes up. Describe the financial benefits of Six Sigma to GE.

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Overview–Project Learning Objectives

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1. Determine if DMAIC is the right strategy by identifying the conditions under which the DFSS methodology would be more appropriate. Compare and contrast the DFSS design methodologies to DMAIC.

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Overview–Test Learning Objectives

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1 Describe the 5 phases of DMAIC, including the purpose, tools, and outputs for each phase.

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Define–Project Learning Objectives

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1 Identify project CTQs. Define “CTQ” (Critical to Quality Characteristic). Identify customer(s) in a quantifiable way. – Recognize the components of a process (i.e., supplier, input(s), subprocess, output(s), customer(s). – Distinguish between internal and external customers.

Compile and evaluate customer CTQ data. – – – – – –

Distinguish between customer driven CTQs and process driven CTQs. Recognize sources of existing customer data. Assess customer requirements and expectations. Recall the vital few customer CTQs. Analyze the voice of the customer and it’s impact on CTQ data. Translate customer needs into requirements (CTQs).

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Define–Project Learning Objectives (continued)

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2 Use a process/product drill-down tree to: define the limits of a project (project bounding); clarify what the project is and is not; identify other areas for improvement. Create a process/product drill-down tree. Integrate measurements to clarify areas needing improvement. Given an example of a process/product drill down tree, identify viable Six Sigma projects.

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Define–Project Learning Objectives (continued)

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3 Develop a team charter. Describe the purpose of a charter. Identify the five major elements of a charter. Define the business case for a project in terms of its potential benefits, the consequences of not doing it, its relationship to other activities, and its fit with business initiatives/target. Develop a problem statement. Describe the customer’s pain. Identify key considerations and potential pitfalls to consider when developing a problem statement. Develop a SMART goal statement (specific, measurable, attainable, relevant, time bound). Assess the scope of the project. Identify the 8 steps for bounding a project. Define project milestones. Select a project team and define team roles. Identify team roles and responsibilities. Evaluate a proposed Six Sigma project. Recognize characteristics of a “good” project. Recognize characteristics of a “bad” project.

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Define–Project Learning Objectives (continued)

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4 Map a business process. Describe the goal of process mapping. Identify the components of a process map (COPIS). Describe the steps involved in creating a process map. Define and name a process. Given a business process, use brainstorming and storyboarding techniques to: identify its outputs, customers, suppliers, and inputs; identify customer requirements for primary outputs; and identify process steps

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Define–Project Learning Objectives (continued)

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5 Obtain approval for a Six Sigma project. Identify the steps in the project approval process. Enter a project into QPT.

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Define–Test Learning Objectives

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1 Recognize the components of the 12 Step Process and how they may be applied to a Six Sigma project. 2 Describe the purpose of the define phase and it’s key deliverables: CTQs, team charter, and process map. Identify the five key objectives of the Define Phase. 3 Describe the CAP tools and their connection to Six Sigma.

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Measure1–Classroom Learning Objectives

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1 Describe and define the deliverables of Step 1.

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Measure 1–Project Learning Objectives

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1 Identify the project Y. Identify the tools that may be used to select the relevant CTQ or Y on which to focus. Explain the purpose Quality Function Deployment, Process Map, and FMEA tools have. Define performance standards for Y including specification limits as well as defect and opportunity definitions.

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Measure 1–Project Learning Objectives (continued)

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2 Select CTQ characteristics. Select the Critical to Quality (CTQ) characteristic to be improved in a project. Narrow the focus of a project to an actionable level. Establish the project team and gained consensus on the project definition. 3 Select and apply appropriate tools to narrow the focus of a Six Sigma project by identifying key areas for improvement. Identify tools that may be used to narrow the focus of a project, including Process Map, and FMEA. Recognize the purpose and benefits of each tool.

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Measure 1–Project Learning Objectives (continued)

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4 Use Process Mapping to identify potential breakdowns, rework loops, and sources of variation in a process. Use the C.O.P.I.S. model to illustrate a customer focused process. Identify the elements of a process (input, mechanism, control, output, process boundary). Identify and distinguish between internal and external process controls. Recognize the purpose and benefits of process mapping. Recognize the three types of process maps. Describe the process mapping process, including the following steps: Determine the scope. Determine the steps in the process. Arrange the steps in order. Recognize ISO 9000 standard symbols for process mapping. Validate a process map. Evaluate a process map.

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Measure 1–Project Learning Objectives (continued)

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5 Use a Failure Modes and Effects Analysis to identify the potential failure modes of a process or product. Recognize the purpose and benefits of FMEA. Describe how FEMA works. Describe FMEA, including preparation, process, and improvement steps. Define the terms “failure mode,” “cause,” and “effect,” as they relate to FMEA, and recognize examples of each. Assign degree of severity, likelihood of occurrence, and ability to detect ratings, and calculate a risk priority number (RPN). Complete an FMEA form. – Recognize when and by whom an FMEA is prepared, updated, and completed.

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Measure 1–Project Learning Objectives (continued)

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6 Conduct a test-retest study and analyze the results. Describe the purpose and procedure for conducting a testretest study. Plot and test-retest study data. Use descriptive statistics to evaluate test-retest study data. 7 Establish a Data Collection Plan for a Six Sigma project. Describe the purpose and benefits of a Data Collection Plan. Write a data collection strategy. Define a clear strategy for collecting reliable data efficiently.

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Measure–Test Learning Objectives

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1 Recall the DMAIC 12 Step process, and distinguish between characterization phases (DMA) and optimization phases (IC). Define product characterization. Define process optimization. 2 Recognize how statistics can be applied to the problem solving process. Define the terms “precision” and “accuracy” as they relate to a Six Sigma process. Relate precision/variation and accuracy/mean to quality and customer satisfaction. State the goal of Six Sigma in statistical terms. Define the term “Upper Specification Limit (USL).” Define the term “Lower Specification Limit (LSL).” Define the term “target (T).” Define “σ.”

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Measure–Test Learning Objectives

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3 Explain how statistics can be used to solve problems. Identify project variables using the formula Y = f (X1,…..,Xn ). Describe the relationship between any dependent variable (Y) and independent variables (X). Explain how the shape, mean, and standard deviation characterize a process. Express the capability of a process in terms of a standard measure (z-value). Define hidden factories and how capability impacts cycle time. 4 Identify the key deliverables of the Measure phase of DMAIC.

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Measure–Test Learning Objectives

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5 Relate and apply the Quality Function Deployment (QFD) process to Six Sigma. Explain the purpose of QFD. Describe the phases of QFD. Explain QFD flowdown for product and service applications. Generate/build a House of Quality (Product Planning Chart). Identify what the customer wants (the “what’s”). Identify the functions or processes that impact customer wants (the how’s). Evaluate the impact of each function/process on customer wants. Calculate the overall magnitude of the impact each function/process has on customer wants (prioritize actions). Analyze and diagnose a completed House of Quality. Describe other QFD applications. Determine when QFD is appropriate to use. Recognize QFD pitfalls. Describe an example of QFD from GE Medical Systems. 6 Describe and define the deliverables of Step 2.

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Measure–Test Learning Objectives

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7 Define Performance Standards for a Six Sigma project. Describe the purpose and characteristics of a performance standard. Describe the purpose and characteristics of an operational definition. Define the term “defect.” Given an example of a problem or process, write an operational definition. Describe and distinguish between continuous and discrete data. Recognize the components of a performance standard, including product/process characteristic, measure, target value, specification limits, and defect. Given a CTQ type, identify performance standard sources and discrete/continuous data measurement methods. Given an example, define the measurable characteristic, determine whether it is continuous or discrete, determine the specification limit if applicable, identify a defect. 8 Describe and define the deliverables of Step 3.

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Measure–Test Learning Objectives

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9 Establish the accuracy of the measurement system and the data (Analyze the measurement system). Describe measurement as a process that includes Measurement, Analysis, Improvement, and Control phases. Describe measurement as a system that includes operators, gages, and environment. Define the terms “(gage) resolution,” “precision,” “accuracy,” and “bias” as used in Measurements System Analysis (MSA). Using the MSA checklist, document the existing measurement system. Recognize the sources of variation in a measurement system.

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Measure–Test Learning Objectives

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10 Conduct a Gage R&R study and analyze the results. Develop and implement a Data Collection Plan to collect Gage R&R study data. Describe equipment and appraiser sources of variation. Describe the total R&R variation in terms of Reproducibility (AV) and Repeatability (EV). Set up, collect, and enter data into a Minitab data sheet. Calculate both the appraiser variation (reproducibility) and equipment variation (repeatability). Describe the concepts of stability and linearity in gage studies. Compare R&R variation to the tolerance (specification window). Create graphs and charts (ANOVA method) to analyze study results. Recall and apply rules of thumb (guidelines) for analyzing R&R study results.

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Measure–Test Learning Objectives

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11 Describe and define the use of gage R& R for discrete data. Describe the use of the attribute R & R spreadsheet for discrete data. 12 Recall and list the deliverables of the Measure phase of DMAIC.

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Analyze–Classroom Learning Objectives

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1 Perform hypothesis testing for a continuous Y and discrete X. Determine process stability with run charts and other tools Determine the data shape with histograms, normal probability plots, and Anderson-Darling tests. Select and use the appropriate tool to determine the p-value. Determine whether or not to accept the null hypothesis or the alternative hypothesis. 2 Perform hypothesis testing for a discrete Y and discrete X. Use chi-square testing to determine the goodness-of-fit and as a test of independence. Based on the chi-square test, determine whether or not to accept the null hypothesis or the alternative hypothesis.

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Analyze–Classroom Learning Objective (continued)

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3 Perform hypothesis testing for a continuous Y and continuous X. Use a scatterplot to determine correlations between variables. Use a linear regression analysis to quantify correlations and predict values. Determine process stability with run charts and other tools. Determine whether or not to accept the null hypothesis or the alternative hypothesis. Describe the use of multiple regression for this type of data. Describe the implications of multiple regression in statistical analysis.

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Analyze–Project Learning Objectives

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1 Use benchmarking to assist in developing project goals. Describe the purpose of benchmarking. Describe the uses of five different types of benchmarking, including competitive benchmarking, product benchmarking, process benchmarking, best practices benchmarking, strategic benchmarking, and parameter benchmarking. Apply benchmarking methodology to a variety of situations. List potential sources of benchmarking data and how to access such sources. Describe the advantages and disadvantages of Internal, Competitive, and Functional benchmarking and their relationship to Best Practices. 2 Set realistic and achievable defect reduction goals based on current baseline, GE guidelines, benchmarking results, and the process entitlement. Describe the methods used to set project goals. Use GE Standards for defect reduction in combination with benchmark results to determine project goals. Use the process entitlement to validate the achievability of the project goals.

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Analyze–Test Learning Objectives

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3 Develop consensus within a project team on the acceptability of the project goals. Use a Cause & Effect (Fishbone) diagram to identify Xs that may impact the Y that is important in a project and provide a visual display of all possible causes of a specific problem. Recognize the purpose and benefits of a Cause & Effect diagram. Write a problem statement. Brainstorm categories appropriate to a problem. Recognize the 4 Ps: policies, procedures, people and plant. Brainstorm and analyze causes for each category to identify the most likely cause(s) of a problem. Determine which causes need to be verified with data.

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Analyze–Test Learning Objectives

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4 Use a Pareto Chart to separate the vital few from the trivial many in a process to determine where to focus improvement efforts. Recognize the purpose and benefits of a Pareto Chart. Describe the Pareto Principle. Describe the steps involved in building a Pareto Chart: Collect data. Total results and arrange data in descending order. Draw and label a Pareto Chart. Analyze results. Compare before and after Pareto Chart to evaluate improvement effectiveness. 5 Describe process map analysis. Describe value added/ non-value added analysis.

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Analyze–Test Learning Objectives

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6 Identify variation sources. Brainstorm a list of potential vital X’s. Use a histogram to aid in determining variation, center, and shape of a process. Use a dot plot to aid in determining variation, center, and shape of a process. Use a box plot to aid in determining variation, center, and shape of a process. Use a run chart to determine process stability. Define the terms population and sample and relate the two to each other. Use statistical tests to validate sampling techniques. Define the theoretical framework for hypothesis testing. Define and follow the hypothesis testing protocol. Define the terms null hypothesis and alternative hypothesis. Develop the null hypothesis for your project. Develop the alternative hypothesis for your project. Define type I and type II errors in relation to hypothesis testing. Define the relationship between the confidence interval and the p-value.

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Analyze–Test Learning Objectives

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1 Describe and define the deliverables of Step 4. 2 Apply statistical principles of the Standard Normal Probability Distribution to predict the probability of a defect and process capability. Use continuous data to describe a process by its average, standard deviation, and normal curve. Define the term “random variable.” Interpret uniform, triangular, normal, and exponential distributions. Relate probability to distribution curves. Define the terms “mean” and “standard deviation” as they relates to a normal distribution curve. Recognize and distinguish between population and sample computational equations. Use Minitab to calculate a mean and standard deviation. Recognize the Descriptive Statistics tool as a method for validating calculations. Calculate statistical measures of variation, including range, deviation, sum-of-square, standard deviation, and coefficient of variation. Calculate capability (Z value). Perform basic statistic calculations using Minitab. Describe the purpose and characteristics of Descriptive Statistics tools, including Histogram, Dot Plot, Box and Whisker Plot, Run Chart. Be able to distinguish a normal distribution from other common non-normal distributions.

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Analyze–Test Learning Objectives (continued)

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3 Characterize a process using discrete data. Define the terms unit (U), opportunity (OP), and defect (D). Recognize formulas for DPU, TOP, DPO, and DPMO. Use Z tables to convert DPMO to “Z”. Run and interpret a Minitab Product Report. Compare and contrast Classical Yield (Yc), Throughput Yield (YTP), and Rolled Yield (YRT). Calculation the distribution of defects for a given DPU. Calculate submitted, observed, and escaping defect levels. Recall DPU application rules. Determine how DPU controls Throughput Yield (YTP). Explain how complexity impacts quality.

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Analyze–Test Learning Objectives (continued)

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4 Use Process Centering strategies to perform a capabilities analysis. Explain the concept of Process Centering. Distinguish between special (assignable) and common (random) cause variation. Choose rational subgroups for proper sampling and analysis. Differentiate between entitlement, short term process capability, and long term process capability. Interpret Minitab “hand calculations,” histogram, and box plots. Calculate the long and short term standard deviation and Z-values. Explain the general long term 1.5 Z shift. Use Minitab Six Sigma Process Report to obtain short and long term process capability measures - ZST, ZLT, ZbenchLT, Zshift, DPMOST, DPMOLT. Using capability measures and a 2x2 matrix, determine if there is a control problem or a technology problem.

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Analyze–Test Learning Objectives (continued)

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5 Determine process capability. Define the term “process entitlement” as it relates to process capability. Define and provide examples of common cause and special cause variation. Define and use rational subgrouping of data. Define shift and drift of a process. Describe the components of variation. Calculate variation for a given process. Calculate the standard deviation for a process. Calculate process capability. Define the difference between long term and short term capability and their uses in a six sigma project. Define the use of the sum of squares and the standard deviation. Use the universal equation for Z to calculate Z scores. Define, derive, and use the Z-Bench for a process. Relate and convert between the Z score and Defects per Million Opportunities. Use data collected in the Measure phase to generate a process capability chart for a process. Interpret the results generated by the process capability report to determine the short term and long term process capability of a process. Use process capabilities to compare your process with a benchmark process. Determine whether the deficiencies in a process are due to control problems or technology problems.

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Analyze–Test Learning Objectives (continued)

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6 Describe and define the deliverables of Step 5. 7 Describe and define the deliverables of Step 6. 8 Describe the statistical analysis tools and process for normal/non-normal data. Describe the use of the normality test. Describe the use of Mood’s median for non-normal data.

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Improve–Project Learning Objectives

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1 Characterize X’s as either operating parameters or critical elements. 2 Develop a strategy for those X’s identified as operating parameters. Develop a mathematical model of a proposed solution. Determine the best configuration or combination of X’s 3 Develop a strategy for those X’s identified as critical elements. Optimize process flow issues. Standardize the process. Develop a practical solution. Explain the needs and process to do screening experiments. The implications for this in DOE is described.

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Improve–Project Learning Objectives

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4 Perform optimizing experiments in order to develop a proposed solution. Identify factors for optimization experiments. Identify factor levels for optimizing experiments. Design optimizing experiment to include randomization and replication. Perform experiments and collect data. Analyze data with various tools including regression analysis.

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Improve–Project Learning Objectives

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5 Develop a proposed solution. Interpret the outputs of various tools to determine the optimum solution. Determine if the optimum solution will meet project goals. Present the proposed solution to management. Use statistical tolerancing to define the control mechanisms for implementation.

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Improve–Project Learning Objectives

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6 Establish operating tolerances. Describe the concept of tolerances and describe an example of this concept. Describe the use of simulation and the use of Crystal Ball. Describe and show an example of Crystal Ball. 7 Pilot the proposed solution.

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Improve–Test Learning Objectives

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1 Describe and define the deliverables of Steps 7 and 8 in Six Sigma. 2 Describe and define the deliverables of Step 9 in Six Sigma.

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Control–Project Learning Objectives

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1 Develop/modify and implement Quality Plans. Describe the purpose and characteristics of a Quality Plan. Recognize the components of a Quality Plan. Plan ongoing process controls, including monitoring and auditing strategies. Explain the benefits of monitoring as compared to First Article Inspection (FAI) and Information Management methods. Determine what to monitor for a given process. Determine the appropriate amount of monitoring data to collect, and how frequently the monitoring should occur. Recognize methods for detecting changes in a process. Recognize the steps that should be taken if a process change is detected. Explain the purpose of auditing. Describe guidelines for effective auditing. Compare and contrast manufacturing control methods. Explain the purpose and process of variable data charting (SPC). Explain the purpose and process of process management charting.

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Control–Project Learning Objectives

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2 Develop and implement risk management strategies. Explain the value of a risk management process. Define the terms “risk” and “risk management” as they relate to DMAIC/Six Sigma. Determine when to use risk management. Recognize different types of risks. Recognize the steps involved in risk management, including identifying risks, rating risks, abating risks, and executing risk management plans. Recognize methods for identifying risks. Describe methods and tools for rating risks. Using the Probability of Occurrence Rating guide and Consequence of Occurrence/Risk Impact chart, prioritize risks according to risk factor score. Determine when and how to implement a Risk Abatement plan. Integrate lessons learned from prior risk management efforts. Describe the formal risk review process. Explain the criticality of tracking and executing risk abatement plans.

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Control–Project Learning Objectives

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3 Develop and implement mistake proofing strategies. Recognize examples of mistake proofing. Describe principles underlying the process of mistake proofing. Recognize the difference between errors and defects. Explain how defects originate. Identify ten types of human error. Recognize human error-provoking conditions. Identify the three key mistake proofing techniques: shutdown, control, and warning. Distinguish between prediction/prevention and detection methods of mistake proofing. Recognize typical mistake proofing tools. Describe the 5 steps involved in mistake proofing, including identifying problems, prioritizing problems, finding the root cause, creating solutions, and measuring results. Recognize the advantages of mistake proofing as a proactive tool. Explain how mistake proofing fits into the Six Sigma process.

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Control–Project Learning Objectives

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4 Select and apply the appropriate Control Chart. Recall and explain SPC Concepts, including controlled variation, uncontrolled variation, common causes, and special causes. Recognize the five main uses of control charts. Distinguish between variable, attribute, and process focused control charts. Determine control limits. Distinguish between control limits and specification limits. Recognize the four states of a process.

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Control–Test Learning Objectives

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1 Describe and define the deliverables of Steps 10 and 11 in Six Sigma. 2 Describe and define the deliverables of Step 12 in Six Sigma. 3 Develop and implement Variable Control Charts. Describe the purpose of Statistical Process Control Charts. Given a control chart, recognize when a special cause is acting on a process. Recognize other types of variable control charts, including X Bar Chart, R Chart, Individuals Chart, and Moving Range Chart. State the five main uses of control charts. Describe data collection and sampling techniques. Establish and maintain control limits. Select the appropriate Variable Control Chart. Distinguish between control limits and specification limits. Determine whether a process is “in control” or “out of control.” Recognize Western Electric rules for identifying an out of control process. Recognize and apply Minitab rules. Build an Individuals and Moving Range chart. Use knowledge of the process to eliminate or reduce assignable/special causes.

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Control–Test Learning Objectives

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4 Develop and implement Attribute Control Charts. Describe the purpose of Attribute Control Charts. Define and relate the terms “a defect” and “a defective.” Recognize types of Attribute Control Charts, including CCharts, U-Charts, P-Charts, NP Charts. Select the appropriate Attribute Control Chart. Use Minitab to generate each type of Attribute Control Chart. Determine the appropriate Attribute Chart subgroup size.

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Glossary And Minitab Primer

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1 Define the typical terms used in Six Sigma methodologies. 2 Describe the use of the Minitab software program.

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Introduction Exercise (60 Minutes)

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Introductions

Desired Outcome: Introduction of Classmates and CD Rom Learnings What

How

Who

Timing

Team Preparation

Go around your tables and introduce yourself to your table-team members (name and business only, at this time.)

All

2 mins.

Exercise

Discuss the importance of the DMAIC Step that your team has been assigned.

All

7 mins.

Create a list of items that describe the deliverables for the step and why this step is important in the DMAIC cycle. Use your knowledge from your CD Rom Learnings. Close Exercise

Choose a spokesperson to report out

1 min.

Report Out

When asked by the instructor, each team member will introduce themselves: – Name – How long you’ve been with GE – Your Title and what you do – Previous Quality Experience – What Phase your project is in After last team member has introduced himself/herself, the spokesperson will discuss the deliverables of the abovementioned exercise.

1 min.

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Classroom Session–Objectives

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Share and get feedback on project deliverables for Define and Measure phases Review Define phase Review Measure phase Learn how to apply CTQ tools in the Measure phase of a project Learn how to use Minitab for statistical and graphical analysis during a project Learn knowledge and skills in Analyze phase and apply to Capital Logistics case Preview Improve phase Learn how to apply Design of Experiment (DOE) in the Improve phase of a project Preview Control phase Learn how to apply control charts in the Control phase of a project

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Iterative Process

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Steps A,B,C

Steps 10,11,12

Steps 1,2,3

Steps 7,8,9

The Phases of the 12-Step Process Phase 1 (Define). This phase defines the project. It identifies customer CTQ’s and ties them to business needs. Further, it defines a project charter and the business process bounded by the project. Phase 2 (Measure). This phase is concerned with selecting one or more product characteristics; i.e., dependent variables, mapping the respective process, making sure the measurement system is valid, making the necessary measurements, and recording the results. Phase 3 (Analyze). This phase entails estimating the short and long-term process capabilities and benchmarking the key product performance metrics. Following this, a gap analysis is often undertaken to identify the common factors of successful performance; i.e., what factors explain best-in-class performance.

Steps 4,5,6

Phase 4 (Improvement). This phase is usually initiated by selecting those product performance characteristics which must be improved to achieve the goal. Once this is done, the characteristics are diagnosed to reveal the major sources of variation. Next, the key process variables are identified by way of statistically designed experiments. For each process variable which proves to be significant, performance specifications are established. Phase 5 (Control). This phase is related to ensuring that the new process conditions are documented and monitored via statistical process control methods. After a “settling in” period, the process capability would be reassessed. Depending upon the outcomes of such a follow-up analysis, it may be necessary to revisit one or more of the preceding phases.

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Statistical Thinking

D M Practical Problem

4

A Statistical Problem

Statistical Solution

Characterize the Root cause process analysis – Stability – Critical X’s – Shape Measure the influence of the – Center critical X’s on – Variation Data Integrity the mean and variability – MSA Capability – Test – Brainstorm – ZBench ST & LT potential X’s – Model – Sampling plan – Estimate

Problem statement – Project Y – Magnitude – Impact

I C Practical Solution

Verify critical X’s and ƒ(x) Change process Control the gains – Risk analysis – Control plans

Collect data The Practical-To-Statistical-To-Practical Transformation Process

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The 12-Step Process

Step Define

Description

5

Focus Tools

Deliverables

A

Identify Project CTQ’s

Project CTQ’s

B

Develop Team Charter

Approved Charter

C

Define Process Map

High Level Process Map

Measure 1 2 3

Select CTQ Characteristics Define Performance Standards Measurement System Analysis

Analyze 4 Establish Process Capabilities 5 Define Performance Objectives 6 Identify Variation Sources

Improve 7 Screen Potential Causes 8 Discover Variable Relationships 9 Establish Operating Tolerances Control 10 Define & Validate Measurement System on X’s in Actual Application 11 Determine Process Capability 12 Implement Process Control

Y Y Y

Customer, QFD, FMEA Project Y Customer, Blueprints Performance Standard for Project Y Continuous Gage R&R, Data Collection Plan & MSA test/Retest, Attribute Data for Project Y R&R

Y

Capability Indices

Y

Team, Benchmarking

X

Process Analysis, Graphical Analysis, Hypothesis Tests

X X

DOE-Screening Factorial Designs

Y, X Simulation

Process Capability for Project Y Improvement Goal for Project Y Prioritized List of all X’s

List of Vital Few X’s Proposed Solution Piloted Solution

Y, X Continuous Gage R&R, MSA Test/Retest, Attribute R&R Y, X Capability Indices Process Capability Y, X X

Control Charts, Mistake Sustained Solution, Proofing, FMEA Documentation © GE Capital, Inc., 2000

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The “Basics” For Effective Meetings

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DMAIC is a powerful methodology which will allow teams to significantly improve the processes on which they are working. However, in order for teams to efficiently use the tools and techniques associated with DMAIC, they must be able to work together effectively. Although not the focus of this class, we will briefly focus on the minimum requirements for effective meetings. Further training in effective meeting skills is provided in “Facilitating Teams through Change Projects” Training

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Meeting Skills

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The “Basics” For Effective Meetings Roles:

Leader or Facilitator Timekeeper Scribe Note Taker

Tools:

Agenda Desired Outcomes Ground Rules Decision-Making Process Brainstorming

Define These Roles For A Meeting Or Any Team During this training, you will practice these roles so that you can use them in your project team meetings to improve meeting effectiveness.

Rules Of Brainstorming:

No judgment of ideas

Record all ideas

No discussion of ideas during brainstorming

The effectiveness of any meeting can be improved simply by having an agenda. That effectiveness can be improved even further by including the desired outcomes. Desired outcomes, or the goals you hope to achieve during the meeting, provide additional focus and give clear purpose for your meeting. Ground rules, or the “code of conduct,” further increase the effectiveness of your meeting by specifying the behavior that is expected from all participants. For ongoing teams, such as DMAIC teams, ground rules should be established and agreed upon by all team members early in the project. © GE Capital, Inc., 2000 DMAIC GB C TX PG

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Practice Meeting (5 minutes)

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Desired Outcome: Name your team What

How

Team Preparation

Choose a facilitator, timekeeper and scribe

Determine Team Name

Brainstorm a list of possible team names

Who

Timing

All

30 secs.

Facilitator

4 mins.

All

30 secs.

Using N/3*, prioritize your brainstormed list Identify your top name

Close Exercise

Choose a spokesperson to report out

* N/3 is a prioritization technique used to narrow a large list down to the top priorities. The number of ideas (N) is divided by 3 (N/3) and team members get that number of votes to identify their top choices. All votes should not be put on one choice.

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Define Review Module Objectives

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Define Review Objectives

Review CAP Tools Review steps in Define phase Review and get feedback on Green Belt project deliverables for Define phase

Review Steps in Define phase

Review

and get feedback on Greenbelt project deliverables for Define phase

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First Things First (10 minutes) Desired Outcome: Learning the components for successful change What

How

Who

Timing

Team Preparation

Think of a change initiative that you have experienced in the past in which the change was unsuccessful. Why did the change initiative fail?

Each Team Member

5 mins.

Prepare List

On a flip chart, list your group’s ideas for why change initiatives fail. What are the common themes? Be prepared to report findings.

Facilitator

5 mins.

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Change Acceleration Process (CAP)

3

Techn ical St ra

te g y egy

rat nal St o i t a z i an al/Org Cultur

Change Initiative (Target)

CAP Complements Technical Strategy With Cultural Tools To Achieve The Change Initiative

Change can be depicted via the equation: Q x A = E Q = Quality of solution to be implemented A = Acceptance of solution to be implemented E = Effectiveness of the implemented solution It is as important to have a strategy for developing acceptance as it is to have a plan for implementing the solution. A Technical Strategy and a Cultural/Organizational Strategy are both necessary in order to effectively achieve your change target. CAP gives us tools to develop the Cultural/Organizational or Influence Strategy. © GE Capital, Inc., 2000 DMAIC GB D TX PG

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Cap Model

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Leading Change Creating Creating A A Shared Shared Need Need Shaping A Vision Mobilizing Mobilizing Commitment Commitment Current State

Transition State

Improved State

Making Making Change Change Last Last Monitoring Progress

Changing Systems And Structures

Leading Change

All implementation projects require a Champion who sponsors the change if they are to be successful.

Creating A Shared Need

The reason to change, whether driven by threat or opportunity, is instilled within the organization and widely shared through data, demonstration, demand, or diagnosis. The need for change must exceed the resistance to change.

Shaping A Vision

The desired outcome of change is clear, legitimate, widely understood, and shared.

Mobilizing Commitment

Making Change Last

Once change is started, it endures and flourishes, and learnings are transferred throughout the organization.

Monitoring Progress

Progress is real; benchmarks are set and realized; indicators are established to guarantee accountability.

Changing Systems And Structures

Management practices are used to complement and reinforce change.

Did the themes that you’ve developed in your last exercise align with our CAP Model? This CAP Model helps us to focus on the organizational changes aspect of projects.

There is a strong commitment from key constituents to invest in the change, make it work, and demand and receive management attention.

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Cap Tools And Six Sigma

Creating A Shared Need Define

SIPOC Threat vs. Opportunity Matrix Project Scope Contract

Shaping A Vision

5

Mobilizing Commitment

Making Change Last

Monitoring Progress

In Frame / Out Threat vs. Of Frame

Opportunity Matrix

GRPI ARMI

Measure

Analyze

Improve

Making Change

Making Change

Last Checklist Control Pans Measures And Rewards

Control Pans Measures And

Last Checklist

Rewards

Control

The above-mentioned tools are covered in the Tools Section of the Self-Paced Workbook. For further training, you can attend the week-long course sponsored by Learning Services.

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Homework

6

Desired Outcome: Identify Cap Tools which you will use in your project What Prepare a plan for CAP Tools

How Identify at least one CAP Tool that you have used in your project thus far

Who

Timing

Each Student

As Homework

If you have not used any CAP Tools, then identify a CAP Tool that you could, in retrospect, have used For tomorrow, be prepared to share with the class which tool you used, how you used it, and how it helped you with your project

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Define Phase Flowchart

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A

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DEFINE PHASE OVERVIEW

Define A: Identify Project CTQ’s

Define B: Develop Team Charter

Define C: Define Process Map

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Define Phase Overview

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What is the Define phase? The Define phase is when your team identifies: Who your customers are and what their requirements are for your products and services The reason for doing the project and project boundaries The project team members and how they will work together What process you are trying to improve and what the process map looks like

Why is the Define phase important? This phase is important because it clearly and precisely describes the goals of the project, aligns the project with organizational priorities and lays the groundwork that will allow the team to remain focused. Steps involved in the Define phase: Define A: Identify Project CTQ’s Define B: Develop Team Charter Define C: Define Process Map

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Define A–Identify Project CTQ’s

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What does it mean to Identify Project CTQ’s? Critical to Quality Characteristics, CTQ’s, are the key measurable characteristics of a project or process whose performance standards must be met in order to satisfy the customer. Green Belt improvement projects typically focus on one or two CTQ’s of a process or product. Why is it important to Identify Project CTQ’s? Project CTQ’s are important because they ensure that the improvement team is solving problems that are both critical to your customer and aligned with your business strategy. If project CTQ’s are not identified and validated in this manner, valuable resources may be wasted on counterproductive projects that neither increase customer satisfaction nor add value to the business. What are the project tasks for completing Define A? A.1: Identify Customer A.2: Collect Voice of the Customer data to identify customer CTQ A.3: Build a process/product drill-down tree to identify project CTQ’s

DEFINE STEP OVERVIEW

Define A: Identify Project CTQ’s

Define B: Develop Team Charter

Define C: Define Process Map

A.1 Identify Customer A.2 Collect Voice of the Customer data to Identify Project CTQ’s A.3 Build a process/product drill-down tree to Identify Project CTQ’s

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Define B–Define Team Charter

What does it mean to Develop a Team Charter? A charter is a document that establishes a purpose and plan for the project. It contains a statement of the problem, the scope of the project (including the process to be improved), and an improvement goal, a plan and schedule for the project, estimated financial benefits, and a list of team members and their roles. The charter becomes the blueprint for the project when key stakeholders approve it. Why is it important to Develop a Team Charter? The charter documents the expectations, boundaries, and business case for your project and can help you identify necessary resources. It is also a key communication tool that can help your team stay focused and help you share information about your project with each other and with the business. An approved charter ensures that your team, sponsor, and stakeholders agree up front on what is being done and that your project will have a beneficial impact on the business. What are the project tasks for completing Define B? B.1 Define the business case B.2 Develop problem statement B.3 Develop goal statement B.4 Assess project scope B.5 Select project team and define roles B.6 Develop charter B.7 Get sign-off for team charter

DEFINE STEP OVERVIEW

Define A: Identify Project CTQ’s

B.1 Define the business case B.2 Develop problem statement B.3 Develop goal statement B.4 Assess project scope

Define B: Develop Team Charter

Define C: Define Process Map

B.5 Select project team and define roles B.6 Develop charter B.7 Get sign-off for team charter

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Define C–Define Process Map

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What does it mean to Define a Process Map? A high-level process map is a chronological display of the most significant four to five steps, events, and operations in a process. It provides a structure for defining a process in a simplified, visual manner. The high-level map gives you an overall view of an entire process and lays the foundation for thinking about the process in more detail. Why is it important to Define a Process Map? A high-level (COPIS) map will help you understand the process and validate your project scope. It is a bridge between the problem and scope statements in your charter and the more detailed maps you will develop to help you improve the process. A highlevel map provides focus for the team and helps you identify areas that are within (as well as beyond) your control. In addition, process mapping serves as a communication tool that helps you to clarify the process to others, both internally and externally to the business. What are the project tasks for completing Define C? C.1 Develop high-level Process Map

DEFINE STEP OVERVIEW

Define A: Identify Project CTQ’s

Define B: Develop Team Charter

Define C: Define Process Map

C.1 Develop high-level Process Map

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Elevator Speech–Homework Activity*

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Desired Outcome: Share elevator speech for the project with members of your team What

How

Who

Preparation

Develop an elevator speech for your project.

All

Elevator Speech

Each team member shares the elevator speech for their project. (See the description of an elevator speech on the following page.)

Each Team Member

Feedback

Make a note of any feedback you receive from your class members. Did your elevator speech provide a clear understanding of your project?

All

Elevator speeches will be shared with the entire class throughout the 3-day workshop. * For additional information on elevator speeches, see the Self-Paced Workbook, pp 197-198

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Elevator Speech

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Here is what our project is about (describe the problem or issue) Here is why it’s important to you (describe the benefit of doing the project) Here is what success will look like (describe the goal of the project and where we currently are)

What is it?

Why use it?

This is a tool that helps the team members put together a short “sell” pitch for the project. Being able to clearly and simply state the need for change and describe the future state is essential for rallying the support and commitment of key constituents.

It helps the team link the need for change with the vision of the future. All the team members will be using a common “sell” pitch. For teams that have thoroughly debated and documented both the need and vision, this is the synthesis event whereby they distill the essence of the project. For teams struggling to get started in terms of need and vision, it can be the place to begin to bring some focus to the team’s more rambling discussion of need and/or vision.

The metaphor of the elevator is useful in challenging the team to be clear, precise and simple. Imagine a chance meeting of a team member and a key stakeholder in an empty elevator with a 90-second ride. Describe the need for change and the vision of the new state, as one might respond to the question, “Why are we doing this project?”

The elevator speech should be able to deal with the questions that will arise once the project is announced to the broader constituent base.

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DMAIC Checklist–Define A

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A.1 Identify customer Have you considered both internal and external customers? Have you focused on the most important customer segment(s)?

A.2 Collect voice of the customer data to identify customer CTQ’s Have you collected data to understand customer requirements? Have you coordinated your data collection with others who are collecting similar data, so as not to overwhelm the customer? Have you validated the customer CTQ’s (Big Y) with the customer? Have you verified a VOC Research method that you’ve selected that reflects the true VOC?

A.3 Build a process/product drill-down tree to identify project CTQ’s Is your project CTQ focused on what’s most important to the customer? If you have multiple CTQ’s, have you used the appropriate tool to prioritize them?

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DMAIC Checklist–Define B

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B.1 Define the business case Is the business case compelling to the team? Does this business case illustrate why this project needs to be done now ? Have I considered intellectual infringements?

B.2 Develop problem statement Does your problem statement identify a problem and not prejudge a root cause or attempt to solve a problem? Is the problem statement linked to the project CTQ? Is the problem statement based on facts not assumptions? Has another Improvement Team tried to solve this or a similar problem? What can you learn from their effort?

B.3 Develop goal statement Is your goal statement SMART (Specific, Measurable, Attainable, Relevant, Timebound)? Does your goal statement focus on what needs to be improved, and without predetermining a solution? How will you know the team is successful?

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DMAIC Checklist–Define B (continued)

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B.4 Project scope Does your team agree on the project scope? Is your project scope within the team’s control?

B.5 Roles Are all functions represented? Does each team member fully represent their manager’s input on the project?

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DMAIC Checklist–Define C

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C.1 Develop high-level process map Does the COPIS scope (start and stop) match the scope definition in your team charter? Have you mapped the process from your customer's perspective? Is this the “As-Is” process? Was the map validated with the people who actually do the process

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Forms Of Intellectual Property

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Patent Best Protection against independent development by others Gives right to exclude others from making, using selling, the invention of 20 years from filing Can wait 2-3 years for patent to issue Right granted by the government for new, useful, non-obvious inventions Trade Secret Rights exist only so long as actually kept secret Protects against theft or misappropriation, not independent development Does not require inventiveness in the patent sense Copyright Protects original works of authorship fixed in a tangible medium Does not protect against independent development Trademark Defines sources of goods or services Arbitrary, fanciful marks get stronger protection

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Intellectual Property Assessment in Chartering Phase

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Throughout the project consider implications to Intellectual Property Policies and Procedures through the following: Commercial benefit for licensing–consider this in the cost/benefit Infringement Avoidance–GE has a policy covering avoiding infringing on other’s IP-Assure no infringement Identify and Capture IP–Throughout this project consider whether IP is developed and take actions to capture and protect Note: When writing your Business Case be certain to consider and include IP issues. Consult the business’ IP Business Champion and IP Designer with questions, and for guidance

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Measure Module Objectives

1

Review steps in Measure phase Start work on Green Belt project deliverables for Measure phase

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Measure Phase Flowchart

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MEASURE PHASE OVERVIEW

Measure 1: Select CTQ Characteristic

Measure 2: Define Performance Standards

Measure 3: Establish Data Collection Plan, Validate Measurement System, & Collect Data

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The12-Step Process Step Define

Description

Focus Tools

Deliverables

A

Identify Project CTQ’s

Project CTQ’s

B

Develop Team Charter

Approved Charter

C

Define Process Map

High Level Process Map

Measure 1 2 3

Select CTQ Characteristics Define Performance Standards Measurement System Analysis

Analyze 4 Establish Process Capabilities 5 Define Performance Objectives 6 Identify Variation Sources

Improve 7 Screen Potential Causes 8 Discover Variable Relationships 9 Establish Operating Tolerances Control 10 Define & Validate Measurement System on X’s in Actual Application 11 Determine Process Capability 12 Implement Process Control

Y Y Y

Customer, QFD, FMEA Project Y Customer, Blueprints Performance Standard for Project Y Continuous Gage R&R, Data Collection Plan & MSA test/Retest, Attribute Data for Project Y R&R

Y

Capability Indices

Y

Team, Benchmarking

X

Process Analysis, Graphical Analysis, Hypothesis Tests

X X

DOE-Screening Factorial Designs

Y, X Simulation

Process Capability for Project Y Improvement Goal for Project Y Prioritized List of all X’s

List of Vital Few X’s Proposed Solution Piloted Solution

Y, X Continuous Gage R&R, MSA Test/Retest, Attribute R&R Y, X Capability Indices Process Capability Y, X X

Control Charts, Mistake Sustained Solution, Proofing, FMEA Documentation © GE Capital, Inc., 2000

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Measure Phase Overview

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What is the Measure phase? This phase is concerned with selecting one or more product characteristics to measure, defining how the characteristics will be measured, planning data collection, and collecting data. Why is the Measure phase important? This phase is important because it ensures that accurate and reliable data is collected to measure current process performance related to the customer CTQ. Steps involved in the Measure phase: Measure 1: Select CTQ Characteristic Measure 2: Define Performance Standards Measure 3: Establish Data Collection Plan, Validate Measurement System & Collect Data

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Mapping Tools To Generation Of CTQ Components Define A

Output Output Unit Unit C-O-P-I-S C-O-P-I-S

Output Output Characteristic Characteristic

High Level Need (VOC)

Project Project YY Operational Operational Definition Definition

CTQ CTQ

Project Project YY Measure Measure

Specification Specification Limits Limits

Define A C-O-P-I-S C-O-P-I-S

Measure 1 QFD QFD C&E C&E C-O-P-I-S C-O-P-I-S

QFD QFD Process ProcessMap Map C&E C&E Pareto Pareto

Measure 2 VOC VOC QFD QFD

Target Target

QFD QFD Pareto Pareto VOC VOC

Defect Defect

FMEA FMEA C&E C&E

##of ofDefect Defect Opportunities Opportunities Per Per Unit Unit

Measure 1

FMEA FMEA Process ProcessMap Map

Measure 2

Measure 2

Measure 2

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Statistical Thinking

D M Practical Problem Problem statement – Project Y – Magnitude – Impact

6

A Statistical Problem Characterize the process – Stability – Shape – Center – Variation

Data Integrity – MSA Capability – Brainstorm – ZBench ST & LT potential X’s – Sampling plan

I C Practical Solution

Statistical Solution

Verify critical X’s and ƒ(x) Change process Control the gains – Risk analysis – Control plans

Collect data The Practical-To-Statistical-To-Practical Transformation Process

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Measure 1–Select CTQ Characteristics

What does it mean to Select a CTQ Characteristic? The goal for this step is to drill-down from what you learned in Define to identify the specific sub-process or system characteristic that will be the subject of your Green Belt project. In the Measure phase, you need to further narrow the scope by focusing on one particular factor that impacts the CTQ. Remember that every project is different, and the level that you need to drill-down to depends on how broad in scope you want your project to be. By the end of this step, you should have identified exactly what aspect of the product/service you will measure for your project. Why is it important to Select a CTQ Characteristic? It is important to manage the scope of your project. By drilling-down to a sub-process or sub-system, if necessary, you keep the connection to the high-level customer CTQ while, at the same time, keeping the project scope manageable. What are the project tasks for completing Measure 1? 1.1 Identify the measurable CTQ characteristic that will be improved (Project Y).

MEASURE STEP OVERVIEW

Measure 1: Select CTQ Characteristic

Measure 2: Define Performance Standards

Measure 3: Establish Data Collection, Validate MSA

1.1 Identify measurable CTQ characteristics that will be improved (Project Y).

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Mapping Tools To Generation Of CTQ Components Define A

Output Output Unit Unit C-O-P-I-S C-O-P-I-S

Define A

Output Output Characteristic Characteristic

High Level Need (VOC)

Project Project YY Operational Operational Definition Definition

CTQ CTQ

Project Project YY Measure Measure

Specification Specification Limits Limits

Target Target

Defect Defect

##of ofDefect Defect Opportunities Opportunities Per Per Unit Unit

C-O-P-I-S C-O-P-I-S

Measure 1 QFD QFD C&E C&E C-O-P-I-S C-O-P-I-S

QFD QFD Process ProcessMap Map C&E C&E Pareto Pareto

Measure 1

Measure 2 VOC VOC QFD QFD

QFD QFD Pareto Pareto VOC VOC

Measure 2

Measure 2 FMEA FMEA C&E C&E

Measure 2 FMEA FMEA Process ProcessMap Map

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CTQ Tools Module Objectives Learn how to apply a variety of CTQ tools to help prioritize & define CTQ elements to be improved If you don’t already know your Project Y, then one or more of these tools can help you: – – – – –

Process Mapping Cause & Effect (Fishbone) Failure Modes and Effects Analysis (FMEA) Pareto Charts Quality Function Deployment (QFD)

This group of CTQ tools can be used to do some preliminary analysis of your process in order to identify the sub-processes that contribute most to satisfying the customer CTQ requirement. Most likely, you will use 1 or 2 of these tools to gather your Project Y (Measure, Step 1 deliverable). Note: FMEA’s and Pareto Charts can also be used in other DMAIC phases and will be covered in detail in later sections of the program.

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Process Mapping

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Process Mapping–CTQ Tool #1

A Graphical Representation of Steps, Events, Operations, and Relationships of Resources Within a Process

Applications

Techniques for examining a process to determine where and why major breakdowns occur

Graphically displays steps, events, operations and relationships of resources

Used to design an improved process

Benefits

Provides a structure for breaking down a complex process

Uncovers problem spots

Determines what data to collect.Targets selected improvements.

Enables group to see the entire process as a team Magnifies normally overlooked areas and displays their relevancy

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Levels Of A Process

Acquire New Business

Core

Obtain Request to Buy Service

COPIS/SIPOC

S

Conduct Underwriting

Establish Terms

Prepare Contract

Prepare Docs

Negotiate Contract

Initialize Customer Service

Close Deal

C Customer/ Customer Service

Underwriters

Detailed Subprocess Map Tasks

Earlier in Define, you developed a high-level or COPIS process map. By looking at a process from a “big picture” perspective, you evaluated customer needs and supplier inputs, and determined initial measurement objectives. Now, you will look in more detail at the subprocesses defined in the COPIS map. Subprocess maps provide specifics on the process flow that you can then analyze using several useful techniques. Choose what to subprocess map by determining which of the major steps in the COPIS have the biggest impact on the output (Y’s). The block (or blocks) selected is the one on which you create a subprocess map–using it to understand how and why it impacts the output.

Procedures

If the Project Y is a cost measure, which of the blocks adds the most cost? If the Project Y is a function measure, which block has the most errors or problems? Like working with a puzzle, you begin to assemble the pieces of an area on which it makes sense to focus our efforts.

If the Project Y is a time measure, which of the blocks consumes the largest portion of total time, or which one has the most variation or delays? © GE Capital, Inc., 2000 DMAIC GB G TX PG

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Versions Of A Process

What You Think It Is...

What It Really Is..

Subprocess mapping is simply drawing a picture of the process–documenting the flow of the process. But, there are at least four major versions of a process map that you can draw. First, you can document what individuals who touch the process think it is. Certainly with the daily contact, you would expect people to know how the process works. But many people can easily explain how things work when things go right. You need to know how the process works in all conditions, so you need to go further.

What It Should Be...

What It Could Be...

Reconciling the map requires your team to observe the process–making sure you have recorded all the existing steps. As the team moves forward and does process analysis and problem-solving, eventually you will move toward the third version of the process map–the “should be” map created as part of their Improvement plan. At this point, a check must be made as to whether customer CTQ’s have been met or exceeded.

Reconciling what the process map is, into what it really is, is a second version of the process. These first two versions of the process constitute what is referred to as the “as is” process map. A thorough “as is” process map is one of the short-term goals of good process mapping and a deliverable for the Analyze phase. © GE Capital, Inc., 2000 DMAIC GB G TX PG

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Outside-In Focus

6

Does your process overlap with the customer’s? Should the customer’s process be mapped? Should you partner with the customer to assess the processes?

Continue to keep focused on the customer’s perspective.

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Subprocess Mapping Techniques

7

Process flowchart Alternate path method Deployment or cross-functional map/flowchart

There are a number of ways to draw a subprocess map. Your team can choose the approach or approaches most appropriate (or comfortable) for your use. Whatever type of subprocess map is chosen, make sure that it accurately reflects your process as it currently exists.

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Process Mapping Symbols

8

These symbols represent the standard symbols for process mapping. Most projects use the simplified symbol sets shown on the following page.

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Process Flowchart

Automated System Answers

Customer Calls

TouchTone Phone

Yes

Customer Chooses Routing Option

Call Placed In Criteria Que, On Met? Hold

Customer Prepare LoanWaits? Offer

Yes

Rep Answers Phone

No

Call Gets Routed To Voice-Activated System

No

Call Ends

Key:

Start End

Task

Review Or Decision

Direction

The business process map most people are familiar with uses four simple symbols: oval, rectangle, diamond, and arrow. It is generally used when the process is fairly small and simple, or when documenting the work done by a single person or group.

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Alternate Path Flowchart

Automated System Answers

Customer Calls

TouchTone Phone

85 Yes

Customer Chooses Routing Option

Call Placed In Criteria Que, On Met? Hold

Customer Prepare LoanWaits? Offer

80 Yes

Rep Answers Phone

15 No

Call Gets Routed To Voice-Activated System

20 No

Call Ends

Key: 60 40 Task

Direction Percentages

Decision

The “alternate path” process map method arose from reengineering efforts, where the mapping of very large processes made “decision diamonds” more of a hindrance than a help. In this technique, diverging or alternate “paths” are noted by split arrows. Teams can then note relative percentages of times/incidences the process follows each path. Process mapping software tools also make it easier to add “icons” showing the tools or methods employed at different points in the process. Showing the alternate path allows us to identify sources of variation which maybe adding complexity to our process.

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Deployment Or Cross-Functional Flowchart

Customer

Contract Admin.

Initiate Call

Attorney

Review Contract

Dealer

Write Contract

Who

Sign Contract

Negotiate

Negotiate

Revise Contract

Revise Contract

File Contract

File Contract

Review Contract

File Contract

PROCESS FLOW

This approach to process mapping emphasizes who performs which tasks and which steps are done concurrently. It provides a clear visual perspective of the hand-offs and relationships between groups involved in the process. (Note: Either of the mapping techniques described on the previous pages can be placed on this type of map.) Always include the process customer and key suppliers as “bands” on this type of map. (Because customers are visible at the top, some people refer to this as a “Service Blueprint.”)

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Steps In Deployment Mapping 1. Identify the participants of the process from start-to-top point. Place the customer at the upper left corner. 2. Identify the “trigger” or initial step and identify the “final” step 3. Identify who receives the output of the initial step and what activity they perform 4. Repeat by identifying who receives the output from the second step and what activity they perform 5. Continue identifying steps and align vertically with participants

For Your Process/Subprocess: 1. Identify the participants involved in the process, write their names on cards, and pin or tape the cards in a vertical column on the wall with the customer at the top of the column. 2. Identify the action that initiates the process, write it on a card, and place it next to the appropriate participant card. In many instances,the process is initiated by the customer but it is not always the case. Also, identify the final step in the process and place in the appropriate row at the end of the map. Here again, the last step may be the customer’s action.

3. Next, identify who receives the output of the second step and what activity they perform. Write this activity on a card and place it to the right of the second step on the same row as the participant performing the activity. 4. Identify who receives the output of this activity and what activities that participant performs. 5. Continue to create cards and position them in the same manner until the process is complete (i.e., the customer receives the final process output).

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Tips In Subprocess Mapping Involve people who know (focus on) the “as is” Clarify process boundaries Brainstorm steps–write on Post-its® – Use verb-noun format (e.g., Prepare contract, not contracting ) – Don’t include “Who” in step description

Combine, eliminate duplicates, clarify steps Organize steps into proper “flow” and add arrows

Respect the boundaries

Don’t start “problem-solving”

Validate and refine before analyzing

Here are some guidelines on building a subprocess map. These are not absolute–but they should help you avoid some of the pitfalls of process mapping.

Focus on “As Is”–To find out why problems are occurring in a process, you need to concentrate on how it’s working now.

Clarify Boundaries–If you’re working from a welldone high-level map, this should be easy. If not, you’ll need to clarify start and stop points.

Brainstorm Steps–It’s usually much easier to identify the steps before you try to build the map. Starting each step description with a verb (e.g., “Collate Orders”; “Review Credit Data”) helps you focus on action in the process. Who does the step is best left in parentheses (or left out) –you want to avoid equating a person with the process step.

Combine and Clarify–Make sure brainstormed steps are clear and don’t overlap.

Organize in “Flow”–Creating the map is last. With all steps visible, it’s typically much easier to create a meaningful map without getting stuck on one or two minor issues.

Is the customer involved in your subprocess step? If so, how?

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Verifying CTQ Elements For Process Mapping Using Process Mapping in the Measure phase allows us to:

Select an upstream step that is generating defects Determine where to collect the data Define the output measure (a good place to begin looking is a “No Exit” out of Decision Diamonds)

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Subprocess Mapping–Breakout Activity (20 minutes) Desired Outcome: Practice creating a subprocess map What

How

Who

Timing

Team Preparation

Choose a facilitator, timekeeper, scribe and/or note taker

All

30 secs.

Prepare Subprocess Map

Prepare the subprocess map for your own project

All

19 mins.

Close Exercise

Choose a subprocess to report your results

All

30 secs.

Brainstorm the challenges of subprocess mapping on your own projects

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Cause & Effect Diagrams–CTQ Tool #2

A visual tool used by an improvement team to brainstorm and logically organize possible causes for a specific problem or effect.

Machines

Methods

Materials

Problem Statement

Potential High-Level Causes

Measurement

Mother Nature

Procedure:

People

7. As a team, determine the three to five most likely causes.

1. Draw a blank diagram on a flip chart. 2. Define your problem statement. 3. Label branches with categories appropriate to your problem. The categories shown are often used, but any categories can be used. 4. Brainstorm possible causes and attach them to appropriate branch.

8. Determine which likely causes you will need to verify with data. Alternative procedure:

Brainstorm causes independent of categories.

Use the Affinity Diagram and brainstorm items into categories.

5. For each cause ask, “Why does this happen?” 6. Analyze results; do any causes repeat?

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Cause & Effect Diagrams–Example Cause & Effect for Capital Logistics Example Of A CTQ Measurements

People Capital Truck

Dock Clock

Capital Driver or

Watches

3rd Party Carrier or

Computer Tracking

Capital Truck Lease Driver New employees

Weight of freight Temperature

Distance

48' trailers

Overnight Delivery Precipitation

Unload Delivery

Methods

Volvo Trucks Mack Trucks

Drop off & Hook up

Environment

52' trailers

Why are the deliveries not timely?

Freightliner Trucks

Machines

The C&E answers the question of “What am I going to measure?” I can now focus on weight of freight or distance or temperature, etc. (This is the output characteristic.)

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FMEA–CTQ Tool #3 An FMEA is a structured approach to: Identifying the ways in which a process can fail to meet critical customer requirements Estimating the risk of specific causes with regard to these failures Evaluating the current control plan for preventing these failures from occurring Prioritizing the actions that should be taken to improve the process

Identify Ways The Product Or Process Can Fail, Then Plan To Prevent Those Failures Purpose & Benefits of FMEA

Improves the quality, reliability, and safety of products

Helps to increase customer satisfaction

Reduces product development timing and cost

Documents and tracks actions taken to reduce risk.

Types of FMEA

System FMEA: is used to analyze systems and subsystems in the early concept and design stages. Focuses potential failure modes associated with the functions of a system caused by design.

Design FMEA: is used to analyze products before they are released to production

Process FMEA: is used to analyze manufacturing, assembly and transactional processes

FMEA’s will be covered in detail during the Improve phase of the CD Rom. This section is a brief introduction.

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Potential Failure Modes and Effects Analysis Worksheet FMEA Date: (Original) (Revised) Page:

Process/Product: Invoicing FMEA Team: Invoice Process Mgnt. Team Black Belt: E. Jones

10/15/96 5/25/97 1 of

Missing

Delayed

Rare “

9 9

Underbill

5

Wrong Ct

8

Rare

9

Wrong Price

5

“

9

576 DMAIC Team 360 to Investigate Root Causes 360 of Count & 225 Price Accessories 90 126

E. Jones 5/15/97

All DMAIC Tasks Complete

8 8

4 3

2 64 2 48

5 5

1 1

2 10 3 15

6 6

5 7

3 90 3 126

RPN

8 5

Detection

Wrong Ct Wrong Price

RPN

8

Detection

Overbill

Action Taken

Severity

Inaccurate

Potential Cause(s) Of Failure

Responsibility Recommended And Target Completion Action Date

Occurrence

Enter Amt Owed

Current Controls

Potential Effect(s) Of Failure

Severity

Item/Process Potential Step Failure Mode

Action Results Occurrence

FMEA Process

1

No Payment

6

Sale Error De Error De Error

5 7

Reviewed “

3 3

Delay

3

5 7

Reviewed “

3 3

45 63

3 3

5 7

3 45 3 63

Late Bill

3

Sale Error De Error De Error Sale “Too Busy” System Down

7

Measured

4

84

3

7

4 84

3

“

4

36

3

3

4 36

Sales Busy System Down

7 3

Measured “

4 4

168 72

6 6

7 3

4 168 4 72

Total Risk Priority Number

2,205

No Bill

6

Resulting Risk Priority Number

821

In this example,the “Wrong Ct” component of billing accuracy becomes the highest priority defect type.

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Failure Mode And Effects Analysis How it Works

Function Part/Process

Failure Mode

Effects

Controls

Severity (1-10)

Detectability (1-10)

Causes Occurrence (1-10)

RPN RPN Risk Priority Risk Priority Number Number RPN = S x O x D RPN = S x O x D == 11 to to 1000 1000

Review the product, service, or process

Assign Severity, Occurrence, and Detection Factors

Determine failure modes

List one or more potential effects for each failure mode. Answer the question: “If the failure occurs, what are the consequences?”

Calculate RPN.Prioritize RPNs from high to low. Identify the top issues, those with high RPN’s.

Determine preventive or remedial actions, especially for high-priority issues.

Identify potential causes

Recalculate RPN after actions have been implemented

List current controls

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FMEA: Calculating Risk Priority Number (RPN) RPN = Severity x Occurrence x Detection Severity Scale Rating

Bad

10

Good

Criteria – A Failure Could: Injure a customer or employee

9

Be illegal

8

Render product or service unfit for use

7 6

Cause extreme customer dissatisfaction

5

Cause a loss of performance which is likely to result in a complaint

4

Cause minor performance loss

3

Cause a minor nuisance, but be overcome with no performance loss

2 1

Result in partial malfunction

Be unnoticed and have only minor effect on performance Be unnoticed and not affect the performance

Occurrence Scale Rating

Time Period

Probability

More than once per day

> 30%

9

Once every 3-4 days

≤ 30%

8

Once per week

≤ 5%

7

Once per month

6

Once every 3 months

5

Once every 6 months

≤ 1 Per 10,000

4

Once per year

≤ 6 Per 100,000

10

≤ 1% ≤ .03%

Detection Scale Rating Definition 10 Defect caused by failure is not detectable 9 8

Occasional units are checked for defect

7

All units are manually inspected

6

Units are manually inspected with mistake-proofing modifications

Units are systematically sampled and inspected

3

Once every 1-3 years

≤ 6 Per Million

2

Once every 3-6 years

≤ 3 Per 10 Million

5

Process is monitored (SPC) and manually inspected

1

Once every 6-100 years

≤ 2 Per Billion

4

SPC is used with an immediate reaction to out-ofcontrol conditions

3

SPC as above with 100% inspection surrounding out of-control conditions

2

All units are automatically inspected

1

Defect is obvious and can be kept from affecting the customer

Total RPN is determined by multiplying all of the individual scores. Note: Occurrence, detection and severity are independent estimates of risk.

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Using A FMEA In The Measure Phase Helps to prioritize Project Y’s Helps to identify where and how a process may fail to meet a CTQ (defects)

In this process, you may uncover an issue where you need to contain a problem (e.g., regulatory, non compliance, legal). If this occurs, it raises the priority.

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Pareto Charts–CTQ Tool #4 Is there a defect that occurs frequently?

Segment data to look for a significant factor that influences the process

Frequency

C

A

E

D

B

Category of Defect

The Pareto chart is a bar chart with the bars (segmentation levels) arranged in descending order. It is an essential tool to help prioritize improvement targets by identifying the 20% of the problems that cause 80% of the poor performance (Pareto principle).

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Pareto Charts (continued) Example

April 1 – June 30

100

Number Of Units Investigated: 5,000

180

*f = frequency

160

80

f* of D+B+F

140

70

f* of D+B

Frequency

120

60 f* of D

100

Cumulative Summation Line (Cum Sum line)

90

50

80

40

60

30

40

20

20

10

Cumulative Percentage

200

LEGEND A: Illegible B: Bank Info Incomplete C: Missing Signature D: Personal Information Incomplete E: Employment History Incomplete F: Address Incomplete

0 Defect Type # Defects % Defects Cum %

D 105 50.5 50.5

B 40 19.2 69.7

F 20 9.6 79,3

A 10 4.8 84.1

C 5 2.4 86.5

E 3 1.5 88.0

Other* 25 12.0 100.0

Total 208 100

Approximately 80% of Defects from Defects D + B + F A fully documented Pareto chart will include the “Cumulative Summation line”, or Cum Sum line, which depicts the running total of the frequency of each subsequent bar (segmentation factor). The right-hand axis on the graph will show the cumulative percent of defects. By reading the Cum Sum line against the cumulative percentage, your team can determine which of the segmentation levels comprise 80% of the total for the problem, and direct their attention to those levels. In this example, I would likely focus on the ‘D” segment, and this would become my project Y. You should also create a Pareto showing $’s. This may cause your focus to change. * Other- Try to keep this category as small as possible. Find out what is in “other”. © GE Capital, Inc., 2000 DMAIC GB G TX PG

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Using Pareto Charts In The Measure Phase Quantitative tool use to determine segmented areas of focus Graphically displays most frequent occurrence of outcomes (little y’s) Helps you get from Big Y to little y

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QFD–CTQ Tool #5 Definition of QFD (Quality Function Deployment)

Structured Methodology to Identify and Translate Customer Needs and Wants Into Measurable Features and Characteristics of a Product or Service

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QFD Flowdown–Product Application

Key Functional Requirements

Key Part Characteristics

(WHAT’s)

House of Quality #3

GE Processes

Y

Process Variables (HOW’s)

(HOW’s) (WHAT’s)

House of Quality #2

Part Characteristics

Y

GE Processes

(HOW’s) (WHAT’s)

House of Quality #1

Part Characteristics

Functional Requirements

(WHAT’s)

Customer Requirements

Functional Requirements (HOW’s)

House of Quality #4 X

Key Manufacturing Processes

Key Process Variables

Product application of QFD links functional requirements to key process variables.

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QFD Flowdown–Services Application

Process Controls (HOW’s) House of Quality #2

Y Critical-to-Quality Characteristics (CTQ’s)

Key Service Processes

Service Functions/Proceses (WHAT’s)

House of Quality #1

Service Functions/Processes (HOW’s)

Service Requirements (WHAT’s)

Customer Wants (WHAT’s)

Service Requirements (HOW’s)

House of Quality #3

X Key Process Variables

Services application of QFD links project deliverables to key process tasks.

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House Of Quality Summary

Conflict Conflict Resolution Resolution 3.Characteristics/measures 3.Characteristics/measures

HOW'S HOW'S

1a. 1a. Customer Customer Needs Needs

H

How How do do you you satisfy satisfythe thewants wants??

L

WHAT'S WHAT'S

What Whatdoes doesthe the customer customer want? want? Voice Voiceof of the the Customer Customer

Competitor #2

Target Target Direction Direction Competitor #1

How How important important are arethe thecustomer customer wants wants to to the the customer? customer?

Roof Roof Correlation Correlation

Current Rating

1b. 1b. Customer Customer Importance Importance

L

H M

H

M

M

L

2. 2. Competitive Competitive Assessment Assessment

L M

M L

L

4.4.Relationships Relationships HH Strong Strong 99 MM Medium 3 Medium 3 LL Weak Weak 11

Where Whereare arewe weand and competitors competitorsrelative relativeto to customer importance? customer importance?

H M

Importance ImportanceRatings Ratings 6. 6. Target Target values values of of HOW's HOW's (units) (units) 5. 5. Competitive Competitive Benchmarks Benchmarks How How do do competitors competitors perform performrelative relative to to each each HOW? HOW?

It is not necessary to develop every room for every house of quality you build. Room 1a Customer Needs (in their language) High-level wants identified by the customer Room 1b Customer Importance Customer ranking of the wants. A typical score is 1-5. 1–least important 5–most important Room 2 Competitive Components Customer’s view of how GE compares with the competition Room 3 Characteristics/Measures Measurable attributes that can be used to indicate how well the customer’s needs are met. Room 4 Relationships Strengths of interrelation between the WHAT’S and the HOW’s. H–Strong (9) M–Medium (3) L–Weak (1)

To what extent will a HOW impact a WHAT? Using a 9, 3, and 1 scale forces a wider spread between the most important and least important items. Room 5 Competitive Benchmarks How the competition performs relative to the measures/characteristics. Room 6 Target and Specifications Target values for the HOW’S. Setting measurable targets allows the team to define what is required to achieve customer satisfaction. Roof Relationship Impact of the HOW’S on each other. ++ Strong positive + Positive - Negative -- Strong Negative Importance Ratings (IR) IR = Σ (Customer Importance X Strength Of Relationship) © GE Capital, Inc., 2000

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House Of Quality Example–Lunch Selection

PB&J Sandwich

Instant Soup

Fast Food

Cost of ingredients

Number of dishes used

M H

Time to prepare

Percent nutrition provided

H M

Percent carbohydrate provided

Weight of portion

Importance

Customer Needs

Number of measured ingredients

O = HOLD CONSTANT

Relationship High Positive Positive High Negative Negative

Product Requirement

Lunch QFD

30

H

2 3 2 2 2 2 4 2

3 3 3 1 3 2 3 3

4 2 4 4 5 4 1 4

Direction for improvement Fills us up Is nutritious Tastes good Is easy to make Is easy to clean up Sticks with us Is inexpensive Is clean

5 4 3 4 2 4 1 2

M L H

L L H M

H L

L

H H

M L

M M

M

Importance Rating

94* 52 59 48 60 10 18

Target (Obtained from VOC)

16 33 25

3

1 0.50 0

PB&J

2

33 25

3

1 0.25 0

Key

Instant Soup

8

15 10

5

3 0.50 1

H=9

Fast Food

16 40 73 10

0 3.00 0

M=3

Units Of Measure (Obtained from VOC)

oz %

$

L=1

% min

*Importance Rating For “Weight Of Portion” = 5(9) + 4(3) + 4(9) + 1(1) = 94 Roof Relationship Symbols indicate if the quality goals of the CTQ’s are conflicting. For example, if I chose to focus on “Weight of Portion” I need to be concerned about the negative impact on the “Number of Measured Ingredients”

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Analyzing A House Of Quality

L

L

H M

M

L

H

M L

L L Empty Emptyrows rowsininRoom Room33- Unaddressed customer Unaddressed customer want wantwould wouldbe beaamajor major problem problem

M

Competitor #2

Competitor #1

Strong Strong negative negative relationship relationship in roof in roof –Identify –Identify trade-offs trade-offs

Current Rating

Empty Empty columns columns in in Room Room 33 -- Perhaps Perhaps an an unnecessary unnecessary measure measure characteristic characteristic signaling signaling itit does does not not affect affect customer customer wants wants

Highest Highest score score on on competitive competitive comparison comparison -- Able Able to to lead lead the the market market with with existing existing product/service product/service

M Low Low score score on on competitive competitive comparison, comparison, but but high high score score on on competitive competitive benchmarks benchmarks -Market Market technical technical advantages advantages to to improve improve customer customer perception perception

Low Low competitive competitive benchmarks benchmarks -- Poor Poor long-term long-term market market performance performance

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C Measure 1–Select CTQ Characteristics

CTQ And Performance Standard Worksheet Output Output Unit Unit

Here’s our next step:

Output Output Characteristic Characteristic

Project Project YY Operational Operational Definition Definition

High-Level Need (VOC) Prepared Prepared Lunch Lunch

Project Project YY Measure Measure

CTQ Specification Specification Limits* Limits*

32

AA Lunch LunchPortion Portion

Define A

Define A

Healthy HealthyLunch Lunch

Measure 1

Total TotalWeight Weight In InOunces OuncesPer PerServing Serving

Measure 1

Weight Weight

LSL=14 LSL=14oz. oz. USL=18 USL=18oz. oz.

Measure 2

Measure 2

Target* Target*

You may not know Spec, Target or Defect at this time (in Step 1). If you know it now, write it down. This information will come from the VOC.

Defect Defect**

##of ofDefect Defect Opportunities Opportunities Per Per Unit Unit

16 16oz. oz.

Measure 2

18 18oz. oz.

Measure 2

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C Methodology Step: Measure 1–Select CTQ Characteristics 33

CTQ And Performance Standard Worksheet Output Output Unit Unit

Output Output Characteristic Characteristic

Project Project YY Operational Operational Definition Definition

High-Level Need (VOC)

Prepared Prepared Lunch Lunch

Project Project YY Measure Measure

CTQ

Define A

AA Lunch LunchPortion Portion

Define A

Healthy Healthy Lunch Lunch

Measure 1

% %Carbohydrate Carbohydrate Per PerServing ServingPer PerUSDA USDA

Measure 1

% %Carbohydrate CarbohydrateContent Content

Measure 2

Specification Specification Limits* Limits*

>>20% 20%

Measure 2

Target* Target*

You may not know Spec, Target or Defect at this time (in Step 1). If you know it now, write it down. This information will come from the VOC.

25% 25%

Measure 2

Defect Defect** Open Worksheet 2. Select Files of Type: Excel 3. Highlight the file to be imported 4. Double-click or click Open

Importing Data: To determine whether a file can be opened by Minitab, choose Open Worksheet from the File menu. Notice that the area labeled Files of Type contains a drop-down menu. This is indicated by the arrow (triangle) at the right of the Files of Type selection box.

When importing from Excel, an Excel file can contain only one worksheet and the information contained in Row 1 will become the titles in Minitab. Note: During import, Minitab will convert percentages, dollars, etc.

When you choose a file type from the drop-down list, only those files containing the chosen file extension are displayed in the file list. When you are importing files, it is important to choose the specific file type you are importing.

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Using Minitab: A Typical Session

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Paste data from Excel 1.In Excel: Highlight Data (and Column Names) to be copied Using Your Mouse 2.Copy the Data to the Windows Clipboard Edit > Copy (or CTRL-C on Your Keyboard) 3.Go to Minitab: ALT > Tab 4. Position the Cursor where you want the data to fill See example below. 5. Go to the Edit Menu: Edit > Paste/Insert Cells (or Ctrl-V on the keyboard)

Insertion point

Note: In order for this to work, you must make all data non-format specific in Excel before you cut-paste.

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Using Minitab: A Typical Session

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Tips for moving data back and forth: Structure the data so that each variable is in a single column Each column must have a title The column title must have fewer than 31 characters and be on a single line All data must immediately follow the column names Do not put empty rows between rows of data Columns containing dollar signs or commas cannot be transferred to Minitab using Copy or Paste, but can be imported using the import command. Reformat these numbers to include only decimal points. After movement into Minitab, check column heading type (D vs. T.)

If you want to use a file in both Minitab and Excel, keep these points in mind.

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Using Minitab: A Typical Session Tables vs. Variable Columns Typical Excel Format: Sales Office January February March April 387,980 45,700 456,789 349,050 Central 578,990 600,987 456,789 456,798 Southwest 435,800 542,700 345,988 564,050 Northeast 497,050 827,900 456,789 687,050 Southeast 613,242 61,689 456,789 434,567 Northwest

The best format for analysis of data in Minitab is variable columns.

Format Needed For Minitab: Sales Office Revenue Central 387,980 Central 45,700 Central 456,789 Central 349,050 Southwest 578,990 Southwest 600,987 Southwest 456,789 Southwest 456,798 Northeast 435,800 Northeast 542,700 Northeast 345,988 Northeast 564,050 Southeast 497,050 Southeast 827,900 Southeast 456,789 Southeast 687,050 Northwest 613,242 Northwest 61,689 Northwest 456,789 Northwest 434,567

Month January February March April January February March April January February March April January February March April January February March April

The format of data typically used in Excel is table format. The best format for analysis of data in Minitab is variable columns. There are multiple ways to manipulate data. The major point is that Minitab likes to have the data in columns.

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Using Minitab: A Typical Session Tips For Importing Data Into Minitab–Let’s practice File name: sales_data.xls Sales 1999 Sales Office

January

February

March

April

Central

$387,980.00

$45,700.00

$456,789.00

$349,050.00

Southwest

$578,990.00

$600,987.00

$456,789.00

$456,798.00

Northwest

$435,800.00

$542,700.00

$345,988.00

$564,050.00

Southeast

$497,050.00

$827,900.00

$456,789.00

$687,050.00

Northwest

$613,242.00

$61,689.00

$456,789.00

$434,567.00

$2,513,062.00

$2,078,976.00

$2,173,144.00

$2,318,658.00

Total

What is wrong with the format of this data in terms of its suitability for use in Minitab?

Above is a set of data that has been captured and entered into an Excel spreadsheet.

Note: For additional practice, see the Green Belt Training Support Central Site.

To make the data suitable for use in Minitab: 1. Reformat the data in Excel (hide columns, change dollar format to numeric) before copying and pasting the data into Minitab. Arrange the data in 3 columns as seen on the previous page. 2. Import the data directly into Minitab using Options and Preview in the Open Worksheet dialog box to customize the data structure. Minitab also has several menu options that allow you to reorganize and restructure the data once you have imported it into Minitab. These options are available in the Manip and Calc menus. You may want to first manipulate in Excel prior to exporting the data! © GE Capital, Inc., 2000 DMAIC GB I TX PG

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Using Minitab: A Typical Session

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Step 2: Select menu command

Most of the commands you use in your Green Belt project are in the Stat and Graph menus.

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Using Minitab: A Typical Session

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Step 3: Enter parameters in dialog box

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Using Minitab: A Typical Session

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Step 4: View results in session or graph window

Note: Sometimes there is only a session window. Therefore, check both the session window & the graph (if one exists).

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Using Minitab: A Typical Session Step 5: Copy output to another application Copying graphs: 1. Make sure the graph window is active in Minitab 2. Click right mouse button and select “Copy Graph” 3. Open the application into which you want to copy the graph or table, e.g., Microsoft Word 4. Paste graph using Paste from the toolbar or Ctrl-V

Copying session window output: 1. Highlight the text lines you want to copy 2. Use the right mouse button to copy the text 3. Open the application into which you want to copy the text 4. Paste the text using Paste from the toolbar or Ctrl-V

Note: You can also copy graphs from the window > manage graphs.

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Using Minitab: A Typical Session

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Steps 6 and 7: Print and Save

When you save a project, you can save the worksheet or session window individually, or save an entire project.

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Recruitment Cycle Time Case Study

We will use the following case study to practice basic graphical analysis in Minitab. You are working on a project to reduce cycle time for filling temporary positions in the Information Technology department within the company. Currently, you work with one agency who finds temporary contractors to fill positions on request by the IT department. The performance standard for cycle time to fill these positions is 20 (working) days maximum. This is measured from the time the agency receives the request to the time the position is filled. You have completed the Define and Measure phases. In the Measure phase, you collected cycle time data for a sample of positions filled within the last 6 months. The data is contained in file fill_time.mtw. The column labels are as follows: C1: yrs exp–years experience of the person who filled the position C2: agent–specifies the agent who processed the request and found the resource C3: site–specifies the company site from which the request originated (there are three sites in the area who request temporary resources) C4: type of resource–specifies the type of resource requested (DBA, Programmer, Systems Analyst) C5: cycle time–time to fill position (working) days

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Graphical Analysis Of Data

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Key Questions: How is my data distributed (variation)? What relationships exist between the Y variable and X variables?

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Review–Variation All repetitive activities have variation (fluctuation) Variation is a primary source of customer dissatisfaction In order for our customers to “feel the quality” at GE, we must reduce variation

A fundamental principle of process improvement is the measurement, reduction, and control of variation. Variation is present in all processes, whether they are personal processes (getting to work, fixing dinner) or business processes (approval cycle time, order to delivery). The output of a process will vary as it is repeatedly performed. Although our customers may accept some variation, when variation is too extreme, our customers will be dissatisfied.

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Using Data To Understand Variation Plot The Data Using Variation Tools Study Variation Over Time

Study Variation For A Period Of Time Histogram

Frequency

Measurement

Run Chart

Time

Measurement

For Continuous Data

For Discrete Data

For Continuous Data

For Discrete Data

– Histogram

– Bar Chart

– Run Chart

– Control Charts

– Box Plot

– Pie Chart

– Control Chart

– Run Chart

– Histogram

Variation is a fact of life. There will always be fluctuations in our processes. Graphically displaying measures provides a basic description of the variation and its sources. Following any data collection effort, the first step toward understanding variation is to plot the data.

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Review–Continuous vs. Discrete Data Reminder: Data Type Is Critical! Data type dictates how much variation we will see: Continuous data–the most information about variation in the process Discrete data–less information about variation in the process

Application Cycle Time Upper Specification Limit = 30 Days

Continuous Y = days to process

Discrete Y = late/on-time No. Rec’d

No. Late

30

2

Less variation information

USL

Actual Times 28 21 21 30 12 17

23 16 25 29 11 9

13 24 26 30 27 30

34 11 27 20 23 29

24 49 27 10 24 29

29 21 29 30 28 28

The most variation information

Continuous data holds several advantages over discrete data: – It gives us more information about our process. – Smaller sample sizes are required when we use continuous data.

If you were the customer: – Which type of data would you want? – Which type of data shows what you see?

Consider this: If you were the process owner which would you prefer? – Simply how many applications were processed within the customer specification? OR –The exact time it took to process each application? © GE Capital, Inc., 2000

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5 M’s & 1 P Sources Of Variation

P R O C E S S

Machines Methods Materials Measurements Mother Nature People

Machines–The various appliances used in the transformation from inputs into outputs. For example, a PC can turn various sources of information into an organized manual that then relates to a training service. Methods–The procedures, formal or otherwise, that transform inputs into outputs. For example, there is a standard procedure for billing collections in the GE Capital businesses. Materials–The components, tangible or otherwise, that are transformed from inputs into outputs. For example, paper stock and ink quality will affect a product brochure’s quality. Measurements–The tools that monitor a process’sperformance. For example, a doctor’s blood pressure reading of a patient would determine subsequent activity related to treatment. Mother Nature–The environmental elements within a process that influence a customer need or requirement.

In a training session, failure to regulate the thermostat can result in a non-conducive learning environment. People–The staffing that influences customer needs and requirements. While often dominant in the service industry, this is an area still too often blamed for failure to meet or exceed customer requirements. Sometimes in a service environment, the following categories are used: —

— —

— —

Policies–Higher level decision rules or management practices. Procedures–The way in which tasks are performed. Plant–The building, equipment, work space, and environmental factors that affect performance. People–The human element. Parts–Systems, documents, and other supplies that are needed to perform the service. © GE Capital, Inc., 2000

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Two Types Of Variation Common Versus Special Causes

Type of Variation Common Cause

Special Cause

Characteristics Characteristics Always Present Expected Predictable Normal Not Always Present Unexpected Unpredictable Not Normal

To distinguish between common and special causes variation, use display tools that study variation over time such as Run Charts and Control Charts.

There are two types of variation:

Common causes

Special causes

The distinction between common and special causes is important to determine the basic strategy for process improvement and control.

Common causes are characteristics of the process and exist as a result of the presence and interaction of different process variables. Common causes affect everyone working in the process, and affect all of the outcomes. Common causes are always present and thus are predictable within bounds. Special causes are those causes that occur due to occasional extraordinary circumstances. Special causes are not always present, do not affect everyone working in the process, do not affect all of the outcomes, and are not predictable.

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Describing Variation For A Period Of Time: Data Distributions

25

Key Questions: What is the shape of the distribution–symmetrical, skewed, twin peaks, flat? What is the central tendency (“center”) of the distribution? What is the variation (“spread”) of the distribution–wide or narrow?

When describing variation, we usually focus on two things: – Center – Spread

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Statistics

Statistics is concerned with making inferences about general populations and about characteristics of general populations We study outcomes of random experiments If a particular outcome is not known in advance, then we do not know the exact value assigned to the variable of that outcome: – – – –

The number of invoices received weekly The cost in dollars of reworking each part The number of surfaces that are rough on a cast part The number of calls received every Monday between the hours of 8-9 a.m.

We call such a value a random variable

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Some Distributions A random variable can be expressed in terms of a distribution Uniform Distribution Single roll of a die

P(X) X

All permissible values P(X) are equally likely

Triangular Distribution Sums of a pair of dice

P(X)

Rapidly descending P(X), no tails X

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Distributions Normal Distribution Process/repair times

P(X)

X

Error fluctuations about an operating point

Exponential Distribution Time between arrivals P(X)

Time between random (unrelated) failures X

Events with no memory from one to the next

Processes may have many differently shaped population distributions. The shapes may be uniform, symmetric, skewed, “ramped,” “camel-backed,” exponential, normal, and non-normal. The shapes may be mixtures of normal and non-normal distributions–or unmixed. Stable distributions can have many different shapes. Why does the process, or product, result in a particular shape (distribution) and not some other shape? The answers to these questions may provide a better understanding of the process and how to improve it. The particular shape is not as important as why this shape and why not some other shape? Why this distribution, why not some other distribution?

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Shape Shape is the distribution pattern exhibited by the data Assess shape using a histogram, or more precisely with a Normal Probability Plot

Center Skewed Distribution

7 6 5 4 3 2 1 0

20

Center

Frequency

Frequency

Roughly Normal Distribution

10

0 12 13 14 15 16 17 18 19 Spread

Bimodal Distribution

6

Center

0 10 20 30 40 50 60 70 80 90 Spread

Center

Frequency

5 4 3 2 1 0 7

9

11 13 15 17 19 21 23

The shape of a data set can be determined by examining a histogram, or, if testing the distribution for normality, using a “Normal Probability Plot.” There are many different shapes a data set may assume. The plots above illustrate three common shapes. The top left is a normal distribution, the middle is a bimodal distribution, and the top right plot is a skewed distribution. Because of its predictive qualities, the normal distribution is of special interest.

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The Normal Curve Is The Data Distribution Normal?

Definition: A probability distribution is where the most frequently occurring value is in the middle and other probabilities tail off symmetrically in both directions. Characteristics: The curve does not reach zero The curve can be divided in half with equal pieces falling either side of the most frequently occurring value The peak of the curve represents the center of the process The area under the curve represents 100% of the product the process is capable of producing The normal curve is a probability distribution that forms the basis for many decisions we will make about our processes. The curve is noted by its “bell-shaped” nature, where most of the values fall in the middle and fewer values fall in either direction. The curve has several important characteristics:

Infinity–The curve theoretically does not reach zero. It goes out to infinity in either direction.

Symmetry–Roughly half of the values will be above the average, and half below.

Centering–The peak of the curve tells us where the process is centered.

Process Totality–The area under the curve represents virtually 100% of whatever we are measuring.

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The Normal Curve (continued) Specific Characteristics 34.13%

34.13%

13.60%

2.14%

13.60%

2.14%

0.13%

0.13% -3s

-2s

-1s

X

+1s

+2s

+3s

68.26% 95.46% 99.73%

68.26% Fall Within +\- 1 Standard Deviation 95.46% Fall Within +\- 2 Standard Deviation 99.73% Fall Within +\- 3 Standard Deviation

The normal curve can be divided into a series of segments. Each segment is mathematically called a standard deviation from the mean. It is also noted by the small s.

Most common statistical terms and analysis tools are based on a normal data distribution. If we use these tools with a data set that is not normal, the accuracy of the tools may be compromised.

As you can see, the curve is first segmented into one standard deviation which represents approximately 34% of whatever you are measuring. Because the curve is symmetrical, going one standard deviation in the other direction represents approximately 68% of whatever it is you are measuring. Going out +/– 2 standard deviations is equal to approximately 95% of whatever you are measuring and +/– 3 standard deviations is equal to 99.73% of whatever you are measuring.

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Normal Probability Plot We use a normal Probability Plot to determine if our data is normal Normal Probability Plot .999 .99

Probability

.95 .80 .50 .20 .05 .01 .001 2

12

22

32

Cycle Time Average: 16.3921 StDev: 5.61675 N: 240

Use this method to determine if distribution is normal

Anderson-Darling Normality Test A-Squared: 0.208 P-Value: 0.864

If p>0.05, then data is normal

What Is A Normality Test?

When Should I Use A Normality Test?

A normality test is a statistical process used to determine if a sample, or any group of data, fits a standard normal distribution. A normality test can be done mathematically or graphically.

There are two occasions when you should use a normality test:

A normality test can be thought of as a “litmus test” for determining if a distribution is a normal distribution.

—

—

The Y axis is the cumulative % of data points which fall below the value on the X axis. Why Is A Normality Test Useful? Many statistical tests (tests of means and tests of variances) assume that the data being tested is normally distributed. A normality test is used to determine if that assumption is valid.

When you are first trying to characterize raw data, normality testing is used in conjunction with graphical tools such as histograms and box plots. When you are analyzing your data, and you need to calculate basic statistics such as Z values or to employ statistical tests that assume normality, such as t-Test and ANOVA.

Interpreting A Normal Probability Plot —

—

When plotted data follows a straight line, the Anderson-Darling p-value will exceed 0.05 and will increase, I have normally distributed data. Rule: p > .05 indicates data is normal. © GE Capital, Inc., 2000

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Normal Probability Plot (continued) Distribution Type: Normal

Bimodal curve Bimodal Distribution 6

6

5

4 3 2 1

Skewed Distribution

Long-Tailed Distribution

20

6 5

4

Frequency

5

Long-Tailed

3 2

Frequency

7

Frequency

10

1

0 13

14

15

16

17

18

19

0 7

Normal Probability Plot for a Normal Distribution 99

11

13

15

17

19

21

23

95

StDev:

90

10

20

30

40

50

60

70

80

90

7

14.6382

StDev:

5.47084

Mean:

15.0790

StDev:

12.6232

13

15

17

19

21

23

99 95 90

80

80

70 60 50 40 30

70 60 50 40 30

20

11

Normal Probability Plot for Long-Tailed Distribution

ML Estimates

Mean:

9

Normal Probability Plot for a Skewed Distribution

Percent

Percent

2

0 0

ML Estimates

ML Estimates

Percent

9

Normal Probability Plot for a Bimodal Distribution

Mean:

3

1

0 12

4

Percent

Frequency

Roughly Normal Distribution

Skewed

20

10

10

5

5 1

1 0

10

20

0

30

10

20

30

How Distribution Looks On Normality Curve: Straight line

Zig-zag

Two lines (Stable Operations)

“S” curve

The Normal Probability Plot is another way besides the histogram to plot data and look for normality. Normal data, when plotted with the data value on the X-axis and specially spaced percentiles of the normal distribution on the Y-axis, will fall on a straight line. 95% confidence limits are shown around the line. In the top diagram on the left, we see that all of the data points roughly form a straight line and fall within the limits. We would conclude that there is no serious departure from normality in this data. In the other diagrams, we see that many of the data points fall outside the limits and do not form a straight line. We would therefore conclude that these data sets significantly depart from the normal distribution. What types of process might result in data that follows a bimodal, skewed, and long-tailed distribution? © GE Capital, Inc., 2000 DMAIC GB I TX PG

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What If Your Data Is Not Normal? If you conclude that Y is non-normally distributed, there are two general approaches:

Approach 1: Variance-based Thinking (VBT) Methodology – possibly multiple processes embedded – segmentation and stratification – span reduction

Approach 2: Non-parametric techniques (beyond the scope of this course)

Expectation: Green Belts Should Be Able To Do Approach 1

If your data is non-normal, you may be able to proceed. It is important that you consult with your MBB before proceeding.

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Minitab–Histogram Recruitment Cycle Time Case Study Fill_time.mtw What does the distribution of cycle time to fill positions look like?

Tool:

Histogram

30

Frequency

Datafile: Question:

Data Type: Continuous. The X axis is cycle time, the Y axis is the number of times cycle time fell within the range of each bar or interval in the histogram. The Y axis is calculated for you. Data A single column of data for each Structure: histogram

20

10

0 0

10

20

30

Cycle Time

To Make A Graph > Histogram Histogram: Variable: Cycle Time Click OK

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Minitab–Normal Probability Plot Recruitment Cycle Time Case Study Datafile:

Normal Probability Plot

Fill_time.mtw .999

Are the cycle time data normally distributed?

Tool:

Normality Test

Data Type:

Continuous Y

.99 .95

Probability

Question:

.80 .50 .20 .05 .01 .001 2

Data Structure:

A single column of data

12

22

32

Cycle Time Average: 16.3921 StDev: 5.61675 N: 240

Anderson-Darling Normality Test A-Squared: 0.208 P-Value: 0.864

To Make A Normal Stat > Basic Probability Plot: Statistics > Normality Test Variable: Cycle Time Test For Normality: Choose Anderson-Darling Click OK

Since p > 0.05, the data is normal. There are a few ways to determine normality. We have standardized on this Anderson-Darling normality test. We will discuss p-values later in the Analyze phase.

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“Center” Or Central Tendency Descriptive Statistics: Represents the nominal value of the process.

Normal Distribution

Mean (X) Median (“middle” data point) Quartile Values (Q1, Q3)

x

Long-tailed Distribution

Skewed Distributions

Q1

Q3

A good guess of central tendency can be made by visually examining a histogram. A more precise estimate of central tendency can be made using descriptive statistics such as the mean, median, or quartile values. The distribution shape dictates which metrics should be used.

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“Center” Or Central Tendency (continued)

38

The Mean, sometimes called the average, is the most likely or expected value. The formula for the mean is:

X=

∑X n

i

1. The sum of all data values 2. Divide by number of data values

The Median is literally the middle of the data set where 50% of the data is greater than the median, and 50% of the data is less than the median. The most commonly used symbol ~ for the median is X. The procedure for calculating the median is :

Order the numbers from smallest to largest If the number of values (N) is odd, the median is the middle value. For example, if the ordered values are 3, 4, 6, 9, 20, the median is 6. If the number of values (N) is even, the median is the average of the two middle values. For example, if the ordered values are 1,5,8,9,12,18, the median is 8.5.

For very skewed data, we can describe the central tendency in terms of the quartile values, Q1 or Q3. Q1 is the data point that divides the lowest 25% of the data set from the remaining 75% and is used to describe performance when the data is skewed toward the right. Q3 is the data point that divides the highest 25% of the data set from the remaining 75% and is used to describe performance when the data is skewed toward the left. © GE Capital, Inc., 2000 DMAIC GB I TX PG

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Variation Descriptive Statistics Represents the variation of the process

Normal Distribution

s

Standard Deviation (s) Span Stability Factor (SF) = Q1/Q3

Long-tailed Distribution

p=.01

p=.99

Skewed Distributions

Q1

Q3

Q1

Q3

A question to be answered in describing variation is “What is the spread of the data?” That is, how much variation exists in the data? By examining a histogram, a good guess of variation can be made. A precise measure of variation is accomplished using basic descriptive statistics such as standard deviation, span, or stability factor. Standard Deviation–measures average distance from the mean. Smaller is better. Span–measures unusually low & high distance from the median. Smaller is better. Stability Factor–ratio of first quartile and third quartile, 1.0 is best.

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Variation (continued)

40

Skewed Or Stable Ops Distributions:

Normal Distributions:

The standard deviation is the average distance, or The stability factor (SF) is the ratio of the first quartile and third quartile values. The formula for deviation, that a given point is away from the Stability Factor is: mean. The formula for the standard deviation is: SF = Q1/Q3

Xi-X

As Q1 and Q3 get closer together, their ratio decreases and the variation of the middle 50% decreases.

A- subtract each data value from the mean E- take the square root of the result

Xi

∑ (X − X )

X

2

i

n −1

Q 1 B- square each difference

Q 1

Q 3

Q 3

C- sum the squared differences

D- divide by 1 less than the number of data values

Q 1 Q 3

Long-tailed Distributions:

0

0 More Variation

More Variatio n

Q 1 Q 3

1

Less Variatio n

Less Variation 1

Span is used to indicate the amount of variation in a long-tailed distribution. It is the distance between the two extremes of the data set. For example, in customer delivery span, it is the number of days between the earliest and latest delivery. Because we don’t want span to be determined by only one or two data points, we typically use P95 and P5 (although this changes depending upon sample size). The span is the difference between P95 and P5. The guidelines of what span to use varies with the sample size: Sample Size

Span

P

100-500

90%-10%

P90, P10

501-2000

95%-5%

P95, P5

2001-5000

98%-2%

P98, P2

5001+

99%-1%

P99, P1 © GE Capital, Inc., 2000

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The Computational Equations Population Mean Population Variance Population Standard Deviation

Sample Mean Sample Variance Sample Standard Deviation

N

µ=

∑ Xi i =1

N N

2

σ =

∑ (Xi − µ)

2

i =1

N N

σ=

∑ (Xi − µ)

2

i =1

N

n

∧ µ=X=

∑X i =1

i

n

∑ (X n

∧ σ 2 = s2 =

i =1

∑ (X i =1

− X)

2

n−1

n

∧ σ = s=

i

i

− X)

2

n−1

The difference between population and sample:

population has all the data points, N

sample only has a portion of the total data points, n Basic Statistics > Display Descriptive Statistics:

15.6779 16.0

16.5

17.0

17.5

17.1063

95% Confidence Interval for Sigma 5.1552

6.1698

95% Confidence Interval for Median

Variable: Cycle Time Click Graphs button

95% Confidence Interval for Median

15.7274

17.3441

Select Graphical Summary Click OK twice–once in each dialog box This graphical summary is one of the most widely used charts in Minitab.

Skewness–A measure of asymmetry. A value more than or less than zero indicates skewness in the data. But, a zero does not necessarily indicate symmetry.

Useful Items:

Anderson-Darling normality TEST–We use the pvalue to determine whether our distribution is normal or non-normal. If p > 0.05, the distribution is normal. (we will discuss p-value & hypothesis testing in Analyze, Step 6.)

Kurtosis–A measure of how different a distribution is from the normal distribution. A negative value typically indicates a distribution more peaked than the normal. A positive value typically indicates a distribution flatter than normal.

Mean–Average of the samples.

N–sample size.

StDev–Standard deviation of the samples.

Variance–(Standard Deviation Squared.) A measure of how far the data are spread about the mean.

Confidence Interval for Mu–Tells us the interval in which the true population mean lies (with 95% confidence.)

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Variation Over Time Run Chart A graphical tool to monitor the “stability of Project Y Allows observation of time order properties such as trend Should be used before any detailed data analysis

Example of a Run Chart Median

Is the process stable over time?

An important basic tool for understanding variation is the Run Chart. Run Charts are simple time-ordered plots of data. On these plots one can perform tests for certain patterns in the data. Presence of these patterns indicate special causes. It is important to note that the data should be in time order for run charts to be valid.

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Run Charts–Special Cause Patterns If p < 0.05, then there is significant statistical evidence to show that one of the trends below exists.

Mixture

Cluster

Oscillating

Trend

Minitab Run Chart

Oscillating Pattern

The Minitab Run Chart tests for two kinds of Runs: (A) Consecutive points on the same side of the median. (Thus a new run starts when the median is crossed). (B) Consecutive points in the same direction up or down. (Thus, a new run starts when the direction is changed).

Oscillation represents more than expected number of runs of type (B).

Mixture Pattern A mixture represents more than expected number of runs of type A (above).

Trend Pattern A trend represents less than expected number of runs of type (B). At this point in time, our biggest concern is whether the process is stable or not. We use the abovementioned checks to indicate stability. Minitab will do this for us.

Cluster Pattern A cluster represents fewer than expected number of runs of type (A). © GE Capital, Inc., 2000 DMAIC GB I TX PG

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Minitab–Run Chart Recruitment Cycle Time Case Study Fill_time.mtw

Question:

Does cycle time show any patterned variation over time?

Tool:

Run Chart

Data Type:

Continuous Y

Run Chart for Cycle Time 32

Cycle Time

Datafile:

22

12

2 40

140

240

Observation

Data Structure: A single column of data is all that is necessary. It is assumed that the data is entered in the order in which it is collected (time order). To Make A Run Chart:

Number of runs about median: Expected number of runs: Longest run about median: Approx P-Value for Clustering: Approx P-Value for Mixtures:

124.000 121.000 9.000 0.651 0.349

Number of runs up or dow n: Expected number of runs: Longest run up or dow n: Approx P-Value for Trends: Approx P-Value for Oscillation:

151.000 159.667 4.000 0.091 0.909

Stat > Quality Tools > Run Chart Single Column: cycle time Subgroup size: 1

The 4 p-values circled above indicate stability. Since p>0.05, there are no issues with Mixtures, Clusters, Oscillations or Trends. Therefore, our process appears stable (no special causes).

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Two Types Of Variation Investigating Common vs. Special Causes For new process data, use a Run Chart to look for special causes Investigate special cause points for positive quick-fixes Common cause variation requires systematic improvement effort

For new process data, a Run Chart can be used to detect special cause situations. For processes that are already in statistical control, Control Charts are the preferred method. Control Charts are discussed in the Control phase of DMAIC training. But, here in the Measure and Analyze phase we suggest using the Run Chart to test for stability.

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Two Types Of Variation (continued) Reacting To Common vs. Special Causes How you interpret variation . . .

Common

True variation type...

Causes

Special Causes

Common Causes

Special Causes

Focus on systematic process change

Mistake 1 Tampering (increases variation)

Mistake 2 Under-reacting (missed prevention)

Investigate special causes for possible quick-fixes

Why is it important to know the source of variation and treat it according to the appropriate strategy? Because not reacting appropriately to the type of variation present in a process can seriously impact customer satisfaction and the amount of variation and defects, and it can increase costs.

Treating special causes as common causes is essentially underreacting to individual data points. The problem with making this type of mistake is missing an opportunity to prevent defects and reduce process variation. An example of this type of mistake would be failing to correct the steering on a car heading for a ditch, and ending up in the ditch.

When interpreting variation, you can make two types of mistakes:

Appropriately reacting to the source of variation in a process provides the correct economic balance between over-reacting and under-reacting to variation from a process.

Treating common causes as special causes

Treating special causes as common causes

Treating common causes as special causes is essentially overreacting to individual data points and is often referred to as “tampering.” The problem with making this type of mistake is that it typically leads to increased variation, costs, and defects. It’s like a novice driver who over-reacts to “slop” in the steering of a car. The result is more variation in the path of the car.

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Graphical Analysis Tools Looking For Patterns In Data

Continuous Y Boxplot

Discrete Y Pareto Chart

Scatterplot

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Box Plots What differences do you see between the output from the different shifts?

Measure

60

30

10 Shift 1

Shift 2

Shift 3

Shift 4

Shift 5

Shift 6

Box plots can be used to identify differences in variation between subgroups that exist in your data. Look for 2 major items here: Center–are the medians similar? Spread–do the boxes and the “Whiskers”have similar heights?

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Minitab–Box Plots Recruitment Cycle Time Case Study Datafile:

Fill_time.mtw

Question:

Is there a difference in variation in cycle time between agents? 30

Box Plot

Data Type: Continuous Y, Discrete X To Make:

Cycle Time

Tool:

Graph > Box plot A Boxplot Graph variables: Y Cycle time Click OK

X Agent

20

10

0 1

2

3

4

Agent

Additional Questions: Is there a difference in variation in cycle time between sites? Between types of resource?

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Scatter Diagrams–Analyzing Relationships Use Scatter Diagrams To Study The Relationship Between Two Variables.

Cycle Time (Days) (Y)

40 35 30 25 20 15 10 5 1K

2K

3K

4K

5K

6K

7K

8K

9K

10K

Size Of Loan (X)

A Scatter Diagram is an important graphical tool for exploring the relationship between two continuous variables. Here, it appears that size of Loan and Cycle Time have a relationship (Larger Loans take longer to process– positive relationship).

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Warning! Correlation Does Not Imply Causation

58

Correlation Between Number Of Storks And Human Population 100

200

300

80

80

70

70

60

60

Population (In Thousands)

50 100

50 200

300

Number Of Storks Source: Box, Hunter, Hunter. Statistics For Experimenters. New York, NY: John Wiley & Sons. 1978

This is a plot of the population of Oldenburg at the end of each year against the number of storks observed in that year, 1930-1936. Even strong correlations do not imply causation. (For example, there will likely be a positive correlation–but not causation–between the occurrence of vaporlocks in automobiles and the use of public swimming pools.)

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Common Construction Mistakes Examples Problem

Variable

Axis

Variable

Bank Errors

Size Of Loan

# Of Errors In Closing Cost Estimate

Loan Delays

Length Of Time To Approve Loan

# Of Changes

Computers Are Too Slow

Computer’s Response Time

Computer’s System Load

Delays Unloading Airline Baggage

# Of People On Plane

Time To Unload Baggage

Axis

One of the most common mistakes that occurs with Scatter Diagrams is mixing up the X and Y variables. The X variable is the potential cause and is plotted on the horizontal axis. The Y variable is the effect and is plotted on the vertical axis.

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Interpretation Of A Scatter Diagram

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Look For: Common patterns in the data Range of the predictor variable (X) Irregularities in the data pattern

Common Patterns In The Data See whether the potential cause variable and the effect variable are related to one another. Range Of The Predictor Variable (X’s) The range is the difference between the largest and smallest values. Check that the range of the potential cause variable is wide enough to show possible relationships with the effect variable. Irregularities In The Data Pattern Check whether the data pattern indicates possible problems in the data.

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Interpreting A Scatter Diagram Look For Patterns 1

3

Strong Positive Correlation

Strong Negative Correlation

2

4

Positive Correlation

For all charts:

5

No Correlation

6

Negative Correlation

Other Pattern

Y = Participant satisfaction (scale: 1 – worst to 100 – best) X = Trainer experience (# of hours)

Interpretation Of Patterns: Positive Relationship: X Increases/Y Increases Graphs 1 and 2–as X increases, Y increases Graph 1–Strong, positive relationship between X and Y – Not much scatter – Points form a line with a positive slope Graph 2–Weaker, positive relationship between X and Y – Scatter is wider – Points still form a line with a positive slope As trainer experience increases, participant satisfaction also increases. Negative Relationship: X Increases/Y Decreases Graphs 2 and 3–as X increases, Y decreases Graph 3–strong negative relationship between X and Y – Not much scatter – Points form a line with a negative slope Graph 4–weaker negative relationship between X and Y – Scatter is wider

As trainer experience increases, participant satisfaction decreases No Relationship: For any value of X, there are many values of Y Graph 5–there is no relationship between X and Y No one line best describes the data There is no relationship between trainer experience and participant satisfaction Non-Linear Relationship–The relationship between X and Y is complex and cannot be summarized with a straight line. Graph 6–Inverted u As trainer experience increases, participant satisfaction also increases until a critical threshold is reached, at which point participant satisfaction decreases. This is not a linear relationship.

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Minitab–Scatter Plot Recruitment Cycle Time Case Study Fill_time.mtw

Question:

Is there an association between cycle time and years experience?

Tool:

Plot

Data Type:

Continuous Y, Continuous X

To Make A Graph > Plot Scatter Plot: Y Cycle time X Years Experience

30

Cycle Time

Datafile:

20

10

0 0

5

10

15

20

25

Yrs Exp

Click OK

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Pairs Exercise–Analyze Patterns

63

With A Partner: Review scatter diagrams on following pages as assigned Determine the type of relationship you observe (e.g., negative, positive, strong, weak, etc.) Describe an example from your business of this type of relationship

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Common Scatter Diagram Patterns (continued)

Plot

+/- Other

Strong, Weak, Other

64

Example

Effect

1

Potential Cause

Effect

2

Potential Cause

Effect

3

Potential Cause

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Common Scatter Diagram Patterns (continued)

Plot

+/- Other

Strong, Weak, Other

65

Example

Effect

4

Potential Cause

Effect

5

Potential Cause

Effect

6

Potential Cause

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Common Scatter Diagram Patterns (continued)

Plot

+/- Other

Strong, Weak, Other

66

Example

Effect

7

Potential Cause

Effect

8

Potential Cause

Effect

9

Potential Cause

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Common Scatter Diagram Patterns (continued) Plot

+/- Other

Strong, Weak, Other

67

Example

Effect

10

Potential Cause

Effect

11

Potential Cause

Effect

12

Potential Cause

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Pareto Charts Is There A Defect That Occurs Frequently?

Frequency

C

A

E

D

B

Category of Defect

We were introduced to Pareto charts in the CTQ tools module.

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Minitab–Pareto Chart Recruitment Cycle Time Case Study Question:

Which agent has the most cycle time defects?

Tool:

Pareto Chart

Data Structure:

A single column where the defect categories are recorded OR

Pareto Chart for Agent Y

180 160 140 120

A tally table in two columns. One column contains the Type of Defect, the second column contains the frequency of the defect. To Make A Pareto Chart:

Additional Questions:

Stat>Quality Tools>Pareto Chart Chart Defects Data In: Agent By Variable: Cycle _Time_Defect Choose: One Chart Per Page, Independent Ordering of Bars Click: OK

100 80 100 80 60 40 20 0

60 40 20 0

Defect Count Percent Cum %

4

1

2

3

35 56.5 56.5

12 19.4 75.8

8 12.9 88.7

7 11.3 100.0

Percent

Fill_time.mtw

Count

Datafile:

Which site has the most cycle time defects? Which type of resource has the most cycle time defects?

To find out which site has the most defects: Follow steps above except, place “Site” in “Chart Defects Data In” Box. Alternate Method (Splitting A Worksheet) MANIP > SPLIT WORKSHEET By variable: Cycle_Time_Defect Click: OK

Alternate method (subsetting a worksheet) MANIP > SUBSET WORKSHEET Name: No Transactions Include or Exclude: CLICK ON “Specify which rows to include” Specify which rows to include: CLICK ON “Rows that Match”

Now you have 2 worksheets-one with “N” transactions and one with “Y” transactions

CLICK ON “Condition” Button Condition: Double Click on C6 then = “N” (‘cycle_time_defect’) = “N”

Activate the correct worksheet and then follow the steps in the slide above

Click “OK” twice Now you have a worksheet with “N” transactions

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Measure Collection And Collect Data Define 3–Plan ReviewData Objectives

1

What does it mean to Establish A Data Collection Plan, Validate the Measurement System, and Collect Data? A project data collection plan is a written strategy for collecting the data you will use in your project. A validated measurement system is one that has been shown to provide reliable data that represents the process output. Why is it important to Establish A Data Collection Plan, Validate the Measurement System, and Collect Data? A project data collection plan and a validated measurement system are important because they define a clear strategy for collecting reliable data efficiently.The data collection plan helps ensure that resources are used effectively to collect only data that is critical to the success of the project. A validated measurement system is important because it ensures that the collected data accurately represents the true nature of your process. Data collection is costly; therefore, you need to make sure that both the data collection plan and the measurement system are sound. What are the project tasks for completing Measure 3? 3.1 Develop a plan to collect data 3.2 Validate the measurement system 3.3 Collect data per plan

MEASURE STEP OVERVIEW

Measure 1: Select CTQ Characteristic

Measure 2: Define Performance Standards

Measure 3: Establish Data Collection, Validate MSA

3.1 Develop a plan to collect data 3.2 Validate the measurement system 3.3 Collect data per plan

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Measure 3–Plan data collection, validate measurement system, and collect data

Data Collection Plan Worksheet Define Review Objectives

2

Data collection purpose:

What to measure (output measure and segmentation factors)

Measure (Name)

Measure Type (Y, X)

Data Type (Discrete)/ (Continuous)

Operational Definition

Range Of Values

How to measure: Sampling Plan (Scheme, Frequency, Size)

Measurement Procedure Refer to more detailed documentation, if necessary.

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Measurement System Analysis (MSA) Worksheet Define Review Objectives Type of Gage R&R Conducted (Check One): Gage R&R (Continuous Data) Gage R&R Results 1) Two-Way ANOVA

3

Date Conducted:

Significant?

Part p-value Oper p-value Oper & Part p-value

Y Y Y

N N N

Pass? 2) 3) 4) 5)

% Tolerance % Contribution % Study # Distinct Categories

[ 90% ] 2) % Reproducibility [ >90% ] 3) % Accuracy [ >90% ] _______________________________________________________________ 1) Gage R&R Pass? Y N, If NO: Plan for improvement: _______________________________________________________________ _______________________________________________________________ © GE Capital, Inc., 1999 DMAIC GB J TX PG

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Define Review Objectives

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Plan For Data Collection Define Review Objectives

1

Establish Data Collection Goals

Clarify purpose of data collection Identify what data to collect

2

Develop Operational Definitions And Procedures

Write and pilot operational definitions Develop and pilot data collection forms and procedures Establish a sampling plan

1

3

Ensure Data Consistency And Stability

Test and validate measurement systems

4

Collect Data And Monitor Consistency

Train data collectors Pilot process and make adjustments Collect data Monitor data accuracy and consistency

Data Collection Is The First Step To Understanding The Variation The Customer Feels Data collection occurs multiple times throughout DMAIC. The data collection plan described here can be used as the guide for data collection regardless of where you are in DMAIC or what type of data you are collecting. Using this model will help ensure that you collect useful, accurate data that is needed to answer your process questions.

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Step 1: Establish Collection Goals Define Review Data Objectives

2

In order to establish your data collection goals you must: State the purpose of the data collection Identify what data is required Asking these questions may help you clarify your goals: What do I need to know about my process? What data do I need? What is the plan for analysis once the data is collected? What data is already available?

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Preparing For TheObjectives Analyze Phase Define Review

3

Segmentation: – An analysis technique that involves temporarily dividing a large group of data into smaller logical categories to look for areas of very good vs. very poor performance – Can be used to understand which X’s drive variation of the Project Y

Collect Project Y data to identify patterns and performance trends and establish current baseline defect rate Collect segmentation factor data to be used for later analysis

Segmentation Helps Us Understand Variation In Project Y Think ahead about how you plan to analyze the data. Collect additional information corresponding to the Project Y that may be helpful in subsequent analysis. – Include possible external factors that may be useful for segmenting the total Y data set.

For example, in deal businesses where the Project Y is the cycle time of closing the deal, a potential segmentation factor is client size (large, medium, or small). .

– Consider how to collect continuous data instead of discrete data. Thinking about segmentation factors now allows you to gather these conditions along with data on your Project Y so they don’t have to be reconstructed after the measurement is completed. Segmentation factors include external variables outside our control that may explain patterns in the Project Y measures. © GE Capital, Inc., 1999 DMAIC GB K TX PG

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Common Segmentation Factors Define Review Objectives

4

Segmenting by external factors will help us identify the drivers of variation in the process Possible categories: Customer Product Market Time Geography Size of account Degree of dissatisfaction

What Data Is Needed?

2. Y = On-time delivery of services

Project Y data, collected over X time period

Objective:

Examples: 1.

Y = Application cycle time

Objective: Understand cycle time performance of credit approvals process. Identify potential sources of poor or irregular performances. Data Required: Physical cycle time data (collect several business cycles) for individual credit applications.

Measure on-time delivery performance for customer service center Identify possible sources of poor or irregular performance. Data Required: Deviations from target date/time for individual orders (minutes/hours, early or late) Data for segmenting factors [e.g., customer, market, geography, time (day, month, hour), request type]

Data on possible segmentation factors external to the process (e.g., customer information, time/date applications received with product type, processing center). © GE Capital, Inc., 1999 DMAIC GB K TX PG

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Common Segmentation Factors Define Review Objectives

5

Other Categories Factor

Example

What type

Complaints, defects, problems

When

Year, month, week, day

Where

Country, region, city, work site

Who

Business, department, individual, customer type, market segment

Tip: Begin with factors “outside” the process box–often these are factors that were not considered when the process was first designed

In service-related processes, “When” elements to pay special attention to include: relationship to deadline (e.g., end of quarter), time/number in queue, or timing versus systems changes. Note: Your team will need to segment the data in several different ways in order to uncover where the most significant differences occur.

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How To Collect Data For Segmentation Define Review Objectives

6

Identify the factors for segmentation before you start collecting data Make sure the segmentation factors can be measured reliably Record the segmentation factors for each Y data point collected Segmentation factors are typically easy to collect, so collect more segmentation factors rather than fewer

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Step 1: Breakout (5 Minutes) Define Review Activity Objectives Objective

Instructions

Time

7

Determine Segmentation Method

For your Project Y: – Brainstorm a list of segmentation factors – Remember to also segment on “unlikely” parameters

5 Minutes

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Step 2: Develop Definitions and Procedures Define ReviewOperation Objectives

8

Clearly specify variables to be collected: Operational definitions for all metrics Specific descriptions of how to take the measurement Specify the details of the data collection process: How to collect the data How to record the data The period of time for data collection The sampling plan to be followed

To help ensure consistency, clearly define each metric and the process for collecting it. Attention to these details will help ensure that the data you collect will give you an accurate picture of the variation in your process.

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Operational Definitions Define Review Objectives

9

Defining The Measure Definition

An operational definition is a clear, concise description of a measurement and the process by which it is to be collected To remove ambiguity

Purpose

– Everyone has a consistent understanding

To provide a clear way to measure the characteristic – Identifies what to measure – Identifies how to measure it – Makes sure that no matter who does the measuring, the results are consistent

Always Pilot Your Operational Definitions

Operational definitions guide what properties will be measured and how they will be measured. There is no single right way to write an operational definition. There is only what people agree to for a specific purpose. The critical factor is that any two people using the operational definition will be measuring the same thing.

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Operational Definitions–Scale Define Review Objectives Of Scrutiny

10

Choosing The Level Of Measurement Measure one scale or level smaller than what your customer measures For Example: If your customer measures cycle time in days, your scale of scrutiny would be hours If your customer measures cycle time in hours, your scale of scrutiny would be in minutes Scale of scrutiny may expose larger true variation

The scale of scrutiny is how finely you measure your process. Measuring one level smaller than your customer allows you to more fully understand and capture the variation in the process.

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Sampling Define Review Objectives

1

Sampling is the process of: Collecting only a portion of the data that is available or could be available, and drawing conclusions about the total population (statistical inference) Population x

x

x x x x x x x x x x x x x

N = 5,000 What is the average resolution time?

Sample x x x

x x x

x

n = 100 From the sample, we infer that the average resolution time ( ) is 1.2 days

Sampling is the process of collecting a portion or subset of the total data that may be available. All of the data available is often referred to as a population (N). The purpose of sampling is to draw conclusions about the population using the sample (n). This is know as statistical inference. In the example above, the population is all of the written inquiries received at a processing center last month (5,000). The manager of the process wants to know the average resolution time for the inquiries received last month. Measuring the resolution time for each inquiry is too expensive; therefore, a decision is made to take a sample. A random sample of 100 inquiries is made and the average resolution is estimated.

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When To Review Sample Objectives Define

2

When to sample Collecting all the data is impractical or too costly Data collection can be a destructive process When measuring a high-volume process When not to sample A subset of data may not accurately depict the process, leading to a wrong conclusion (every unit is unique – e.g., structured deals)

Statistically Sound Conclusions Can Often Be Drawn From A Subset Of The Total Available Data

One of the first questions to ask is ‘Do I need to sample?” The major reason sampling is done is for efficiency reasons-it is often too costly or time consuming to measure all of the data. Sampling provides a good alternative to collect data in an effective and efficient manner. If the circumstances surrounding the data collection plan do not justify sampling, then sampling should not be done. This is often the case in low volume processes (e.g., deal processes).

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Goal Of AReview Useful Sample Define Objectives

3

Representative Samples Representative sample: All parts of the target population are represented (i.e., selected for measurement) equally The customer’s view is captured How to guarantee a representative sample: Design a sampling strategy Understand special characteristics of the population before sampling

Regardless of the situation, a sample must be “representative” of the population. For practical purposes a sample is representative if it accurately represents the target population. Consideration that may hinder collection of a representative sample include: The cost and ease of obtaining samples Time constraints Unknown characteristics of the population Samples that are not representative of a target population are called biased samples. Often, the biases are not recognized until the collected data has been analyzed. © GE Capital, Inc., 1999 DMAIC GB L TX PG

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Sample For Continuous DefineSize Review ObjectivesData

4

How Do I Determine Sample Size? Sample size (n) depends on three things Level of confidence required for the result, “How confident I am that the result represents the true population” – Level of confidence increases as sample size increases

Precision or accuracy (∆) required in the result, “The error bars or uncertainty in my result” – Precision increases as sample size increases

Standard deviation of the population (σ), “How much variation is in the total data population” – An estimate of standard deviation is needed to start

As standard deviation increases, a larger sample size is needed to obtain reliable results 2  1.96 × σ  n=  ∆  

In this equation, “1.96” represents a 95% confidence level

Consider the following example: We want to estimate average call length in handling customer inquiries, and we want our estimate to be accurate to within + 1 minute. Based on a small random sample of 30 inquiries we know that the variation in call length, as measured by a statistic called the standard deviation, is 5 minutes. We want to have 95% confidence that the estimate will be in the range of specified accuracy – i.e., + 1 minute.

Therefore, from the statistical theory we can answer according to the formula:  1.96 × σ  n=  ∆  

2

Where n = sample size, u = standard deviation and ∆ = degree of precision required. In our example, the required sample size is: n = [(1.96x5)/1] 2 = 96.04 or 96 samples

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Common Segmentation Factors Define Review Objectives

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Other Categories Factor

Example

What type

Complaints, defects, problems

When

Year, month, week, day

Where

Country, region, city, work site

Who

Business, department, individual, customer type, market segment

Tip: Begin with factors “outside” the process box–often these are factors that were not considered when the process was first designed

In service-related processes, “When” elements to pay special attention to include: relationship to deadline (e.g., end of quarter), time/number in queue, or timing versus systems changes. Note: Your team will need to segment the data in several different ways in order to uncover where the most significant differences occur.

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Calculating A Sample Size Define Review Objectives

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Continuous Data To Derive Sample Size Formula

CI –X Given Solve for n

σ – X ± Zα/2 * n – ∆ X ± σ ∆ = Zα /2 n Z α /2 *σ n =

∆

n =

Standard error

2

(∆ ) Zα /2 *σ

n = sample size ∆ = precision of the estimate. How much error is ok? The smaller ∆, larger the sample size. May be a business decision. CI = Confidence Interval Zα/2 = Z score we usually set at 1.96 for 96% confidence. σ = estimated standard deviation

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How To Estimate Deviation When It Is Unknown Define Review Standard Objectives

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3 Ways To Estimate σ Use an existing Xbar or R chart σˆ = R /d2 where d2 is control chart factor

(

)

σˆ = UCL − X /3 Collect a small pre-sample & calculate s (n = 30) Ask subject matter experts to take an educated guess at the plausible range of data

σˆ = (Highest known value - Lowest known value )/6

Control Chart Factor d2

n

d2

2

1.128

3

1.693

4

2.059

5

2.326

6

2.534

σˆ = R /d 2

Range or moving range chart should be in statistical control (stable) to use this estimate of σ

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Sample For Continuous DefineSize Review ObjectivesData (continued)

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What Is The Performance For Delivery Time? Population Y = Delivery Time (Days)

 1.96 × σ  n=  ∆  

2

Calculate sample size (n) based on: Precision (∆) 95% confidence Level (1.96) Standard deviation (σ)

Sample n Values

∆ ⌧-∆

∆ ⌧

⌧+∆

Calculate average (⌧)

Conclusion: I know with 95% confidence that the population mean is ⌧ + ∆

Whenever samples are taken to estimate a population there will be differences between the “true” population values and the sample values. Through statistical theory we can determine the amount of variation we can expect in our estimates. This is known as a confidence interval. Confidence intervals are stated in terms of an interval and a confidence level. For example, when estimating average inquiry resolution time from samples, we may obtain a 95% confidence interval for the average 1.2 - 2.3 days. This means that if repeated samples were taken from the same population, 95 times out of 100 we would expect the sample average to be between 1.2 and 2.3 days.

Confidence intervals are important when precise estimates of populations are required, and the degree of precision in the estimate needs to be known. For those statistically inclined, an important statistical theory supporting confidence intervals is the “central limits theorem”. The central limit theorem states that regardless the shape of the population, sample averages will always be “normally” distributed and inversely proportioned to the square root of the sample size.

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Finite Population Define Review Correction Objectives

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If You Have A Finite Population 1. Calculate sample size (n) 2. If n/N > .05 OR If n > N…

Where n = sample size; N = population size

3. Calculate n finite nfinite = n/(1+n/N)

Operational definitions guide what properties will be measured and how they will be measured. There is no single right way to write an operational definition. There is only what people agree to for a specific purpose. The critical factor is that any two people using the operational definition will be measuring the same thing.

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Sample For Discrete Data DefineSize Review Objectives

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How Do I Determine Sample Size? Sample size (n) depends on three things: Level of confidence required for the result, “How confident I am that the result represents the true population” – Level of confidence increases as sample size increases

Precision or accuracy (∆) required in the result, “The error bars or uncertainty in my result” – Precision increases as sample size increases

Estimated proportion defective of the population (P) – An estimate at P is needed to start – Sample size is maximized at P = 0.5 2

 1.96  n=  P(1 − P )  ∆ 

In this equation, “1.96” represents a 95% confidence interval

You need to know the approximate proportion defective for the population to be sampled to calculate the sample size. For example: P

∆

n

.05

.02

456

.50

.02

2400

.95

.02

456

This calculation procedure is based on the binomial model and should only be used when nP > 5. As for continuous measurements, if the sample size (n) is more than 5% of the population size (N), the finite population correction should be used n (finite) = n/(1 + n/N) and n (finite) should be used as the sample size.

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Sample For Discrete Data (continued) DefineSize Review Objectives

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What Is The Defect Rate (P) Of A Process? Population 2

Y = Proportion Defective

 1.96  n=  P(1 − P )  ∆ 

Calculate sample size (n) based on: Precision (∆) 95% confidence Level (2) Estimated proportion defective (P)

Sample

n Values

Conclusion: I know with 95% confidence that the population proportion defective is P + ∆ Calculate Proportion Defective (P)

Recalculate n* based on the calculated P. If the new required sample size (n*) is more than the number of samples taken, take (n*-n) samples and recalculate P based on the full sample size. If it is not practical to take more samples, then use the actual n and P to recalculate the actual precision (∆).

Minimum Sample Size 2

 1.96  n=  P(1 − P )  ∆ 

Example We want to estimate the defect rate (P) within + 0.02 (I.e., ∆ = 0.02). We expect P to be approximately 0.05. 2

 1.96  n=  0.05(1 − 0.05 ) = 456  0. 2 

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How To Estimate and ∆ Define Review P Objectives

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Estimate P Take a small pre-sample of data (n = 100) and calculate P Use X from an existing control chart Set P = .5 as a worst case (largest n) Estimate ∆ See estimation of ∆ for continuous data To determine ∆ for a given sample size

∆ = Ζ α/2

Px (1− P ) n

Sample Size & P

n 0

.5

1

P

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Sample Considerations DefineSize Review Objectives

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Beyond The Formulas… The formulas give an approximate sample size Don’t forget these important factors: – Is the population homogeneous? If not, you will need to segment before sampling – What is the opportunity for bias? Plan ahead to make sure your data is representative of the true population

What Is The Impact On The Customer If Your Sample Size Is Not Representative Of The Process?

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Sampling ExerciseObjectives Define Review Objective Instructions

Apply Sample-Size Formulas 1.

2. 3.

4.

5.

Time

14

In your table-team, answer the assigned questions and be prepared to report your answers. Assume confidence level of 95%. Determine the sample size needed if the following is known. P = 0.20, ∆ = 0.0784 Give an estimated proportion defective guessed to be 5%, how many observations should we take to estimate the proportion defective within 2%? We want to estimate the average cycle time within 2 days. A preliminary estimate of the population standard deviation is 8 days. How many observations should we take? We want to estimate average hold time at one of our cost centers within ± 2 seconds. We will assume hold time standard deviation is 10 seconds. How many calls do we need to sample?

10 Minutes

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Measurement System Analysis–Objectives

1

Recognize that observed variation of a product/process includes the true variation of the product/process & the variation due to the measurement system Identify & describe possible sources of variation in a measurement process Describe the importance of a validated measurement system Describe the terms precision, accuracy & resolution in relation to MSA Use appropriate tools to validate measurement system, analyze, and interpret results – Gage R&R for continuous data – Attribute R&R for discrete data

One of the objectives of the Measure Phase is to validate your measurement system. A Gage R&R Study will help us do this! The focus of this module is to review the methodology and tools to validate your measurement system. MSA = Measurement System Analysis Gage R&R = Gage Repeatability & Reproducubility

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Possible Sources Of Variation

Inputs

Process Outputs

Inputs

2

Measureme nt Process

Observations Outputs Measuremen ts Data

Observed Process Variation

Actual Process Variation

Long-term Process Variation

Shortterm Process Variation Accuracy Accuracy (Bias) (Bias)

Measurement Process Measurement Process Variation Variation Variation Variation due to due to gage gage

Variation Variation due to due to operator operator

“Other” “Other” sources sources

(Environment (Environment , etc.) , etc.)

Discriminatio Discriminatio nn (Resolution) (Resolution)

Precision Precision (Measureme (Measureme nt Error) nt Error)

To Address Actual Process Variability; The Variation Due To The Measurement System Must First Be Identified And Separated From That Of The Process Measurement System Variation We will be evaluating the variation in our measurement systems. We will include the variation due to the operator and gage (Accuracy, Precision and Discrimination). When collecting data, we are seeing the process through the lens of our measurement system. We never really see the actual process variation-instead, we see the actual process variation and the measurement process variation. Therefore, the total observed variation can be broken down into 2 parts: the actual process variation and the variation (or measurement error) created by the measurement process.

Why is MSA important?

Data is only as good as the process that measures it MSA identifies how much variation is present in the measurement process Understanding measurement variation is necessary for identifying “true” process variation and maximizing true Y improvements Without MSA, you run the risk of making decisions based on an inaccurate picture of your process MSA helps direct efforts aimed at decreasing measurement variation Excessive measurement variation distorts our understanding of what the customer feels

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Measurement Error vs. Process Variation

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Call Taking Y= Time to Respond (Response Time) – Process Variation: Time to answer a question varies for different operators, locations, etc. – Measurement Error: Error in capturing the time measurement due to vague definition of when to stop.

Application Processing Y= Time to Decision – Process Variation: Different types of applications vary in time to complete. Associates vary in their productivity. – Measurement Error: Error in measurement time. Time stamp inconsistencies or application arrival times not recorded accurately.

Deal Approval Y = Time to Complete – Process Variation: Differing cycle times. Clients are treated differently. – Measurement Error: Inconsistencies in start-up or set-up definitions.

Deal Approval Y = Agreeable Terms and Conditions – Process Variation: Deal value variation (net income generated). – Measurement Error: Errors in recording net income. Measurement Error vs Process Variation When conducting a Gage R&R, you will be looking at the Measurement Error and determining if it is at an acceptable level. We want to minimize the measurement error (or measurement process variation). By conducting a Gage R&R, you will know how much of the total variation is due to the measurement process itself. In other words, by knowing the Measurement Error, we can assume that the variation we are observing in the process is mainly due to the process variation and not due to the measurement error. If the measurement error is found to be unacceptable, the measurement process must be fixed prior to collecting and/or analyzing data and trying to

make process improvements. The Minitab results obtained from your Gage R&R will indicate where the largest sources of measurement variation are hiding. Your goal will be to fix or reduce this variation and then to re-run the Gage R&R. You cannot collect and/or use your data until the Gage R&R passes.

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Planning Your MSA

4

Questions to ask: What are you measuring? Who is measuring? What do you use to measure (gage)? How are you measuring? Do you always use the same procedure? Under what conditions are you measuring (6 m’s)? What is the resolution of your measurement system? Does the customer measure the same way? Which analysis will you use (continuous, Attribute and/or Destructive)?

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Performing An MSA

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An MSA can be conducted with Continuous or Discrete Data (we will review each method). When conducting the MSA, the following guidelines are suggested: – Choose 2-3 “operators” who normally perform the measurements. – For continuous data, choose 10 parts/samples (e.g., applications, calls, deals, trucks, etc) to measure. The parts should be as dissimilar as possible (within the normal measurement range). These same, ten parts will be used throughout the entire MSA study. – For discrete data, choose 30-40 parts/samples (higher is better). – The parts must be labeled with a number. The part numbers will remain constant throughout the MSA. – Each operator will measure the parts 2-3 times. A blank data collection form should be used for each trial. – The Gage should be “calibrated” as per the calibration procedure prior to conducting the MSA.

Choosing Parts for your Study: The “Parts” are NOT randomly chosen. They should be chosen specifically for the study. For example, you need to choose parts that vary from one another (in size, weight, length of time, etc.) because one output in the MSA tells you if your measurement system can distinguish between parts. Measuring the Parts: The operators should measure each of the 10 parts and record them on a data collection form. On their second round of measurement, they should have a new blank form. Never allow the operator to see previous measurements or measurements from other operators. Analyzing the Results: After all the data is collected, you will run the MSA in Minitab (for Continuous data) or in Excel (for Discrete data). The remaining pages in this section explain the MSA output. © GE Capital, Inc., 2000 DMAIC GB M TX PG

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Measurement System Analysis

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Five Components Of An MSA: Accuracy–the differences between observed average measurement and a standard Repeatability–variation when one person repeatedly measures the same unit with the same measuring equipment Reproducibility–variation when two or more people measure the same unit with the same measuring equipment Stability–variation obtained when the same person measures the same unit with the same equipment over an extended period of time Linearity–the consistency of the accuracy across the entire range of the measurement system

Think in terms of shooting at a target. Accuracy: How well do you hit the target? Do you hit where you are aiming? Repeatability: Can you keep hitting the target in the same place? Reproducibility: Can another person with the same gun hit the target in the same place? Stability: If you come back to shoot at other times are you still able to shoot as accurately (consistency over time)? Linearity: Are you as accurate at 50 meters as you are at 250 meters? © GE Capital, Inc., 2000 DMAIC GB M TX PG

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Process Flow For MSA (Measurement System Analysis)

7

Conduct MSA

Take Preventive And Corrective Actions

OK? No Yes Continue Process Improvement

For Attribute R&R: 90% matches for each Repeatability, Reproducibility, and Accuracy analysis.

Examples of Corrective Actions:

Review data and decisions

Institute stopgap measures

Note: Attribute = Discrete

Examples of Preventive Actions:

Correct mechanical or definitional errors

Institute or upgrade training

Examples of Process Improvement:

Measure gage over time to address stability

Study linearity of gage

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Attribute Data AR&R’s

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With Discrete Data, we will look at these things: – Repeatability: Do repeated measures match within an operator? – Reproducibility: Do repeated measures match between operators? – Accuracy: Do the measures match the standard value?

An MSA helps us determine if our measurement system must be improved, and if so, gives guidance as to how

Although it has been emphasized that it is best to find a Y that is associated with continuous data, this is not always possible. In some cases, the response will be discrete. The measurement system must still be validated. Attribute = Discrete AR&R = Attribute Repeatability and Reproducibility is the method we’ll use to analyze Discrete Data.

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AR&R Guidelines For Evaluation

9

Repeatability: 90% of repeated measures within an operator match Reproducibility: 90% of the repeated measures across operators match Accuracy: 90% of the individual measures match the standard

Guidelines for determining how to design an AR&R study: 1. For accuracy: The sample size is the total number of measurements. (40 parts x 3 repeated measures x 3 operators = 360 measures.)

The examples that follow balance all three characteristics of an AR&R study.

2. For repeatability: The more repeated measures on the same unit, the better the sensitivity. Increasing the number of units has a minimal effect on sensitivity. (Rather than measure 40 parts 3 times, measure 10 parts 12 times.) 3. For reproducibility: The more operators, the better the sensitivity. More units have a minimal effect on sensitivity. (Rather than measure 40 parts with 3 operators, measure 10 parts with 12 operators.)

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How To Determine Sample Size In The AR&R

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How many samples should I take for an AR&R Study? Typically, 30-40 samples should give you a good indication of your measurement system Ten samples may be enough if running 30-40 samples would be too costly or time consuming. Use your “Business Sense” and learn from the study. Always ensure you choose samples that represent typical measures in your process.

For example, if your process requires a Customer Service Representative to code customer complaints as “A-K” categories, you would need to ensure your samples represented each of those codes. You also should choose samples that clearly fit that category and also ones that may fall within a “gray” area. (if such samples exist.) Therefore, the AR&R study will show whether your current measurement system is adequate.

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AR&R Data Sheet 'True' Operator 1 Sample Answer Trial1 Trial2 N N 1 N N N 2 N N N 3 N D D 4 D D D 5 D N N 6 N N D 7 D N N 8 N N N 9 N N N 10 N D D 11 D N N 12 D D D 13 D N N 14 N D D 15 D D D 16 N N N 17 N N N 18 N N N 19 N N N 20 N D D 21 D N N 22 N N N 23 N N N 24 N N N 25 N D D 26 D N N 27 N N N 28 N N N 29 N N D 30 D D D 31 D N N 32 N D N 33 N N N 34 N N N 35 N D D 36 D N N 37 N N N 38 N N N 39 N N N 40 N

11

Trial3 N N N D D N N N N N D N D N D D N N N N D N N N N D N N N N D N N N N D N N N N

Operator 2 Trial1 Trial2 N N N N N N D D D D N N D D D N N N N N D D D D D D N N D D N N N N N N D D N N D D D D D D N N N N D D N N N N N N D D D D N N D D N N N N D D N N N N N N D D

This data sheet uses 3 operators, 3 trials, and 40 units to measure repeatability, reproducibility and accuracy.

Repeatability of the measurement system is assessed by determining the proportion of times each operator matches on (e.g., three) repeated measures of one unit. For this example, there are 120 opportunities for a repeatability match.

Reproducibility of the measurement system is assessed by determining the proportion of times all operators match on (e.g., nine) repeated measures of one unit. For this example, there are 40 opportunities for a reproducibility match.

Accuracy of the measurement system is assessed by determining the number of times each individual measure matches a standard. For this example, there are 360 opportunities for an accuracy match.

Trial3 N N N D D N D D N N D D D N D N N N D N D D D N N D N N N D D N N N N D N N N D

Operator 3 Trial1 Trial2 N N N N D N D D D N N N D D N N N N D N D D D D D D N N D D N N N N N N N N D D D D N N N N D D N N D D N N N N N N D D D D N N N N N N N D D D D N N N N N N N

Trial3 N N N D D N D N N D D D D N D N N N N N N N N D N D N N N D D N N N N D N D N N

An extra column is added to define the true state of the standard according to a subject matter expert. In this example, N = Non-defective and D = Defective.

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AR&R Example: Repeatability Sample 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Operator 1 Tr1 Tr2 TR3 N N N N N N N N N D D D D D D N N N N D N N N N N N N N N N D D D N N N D D D N N N D D D D D D N N N N N N N N N N N N D D D N N N N N N N N N N N N D D D N N N N N N N N N N D N D D D N N N D N N N N N N N N D D D N N N N N N N N N N N N Operator 1

Match? Y Y Y Y Y Y N Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y N Y Y N Y Y Y Y Y Y Y 0.925

Operator 2 Tr1 Tr2 Tr3 N N N N N N N N N D D D D D D N N N D D D D N D N N N N N N D D D D D D D D D N N N D D D N N N N N N N N N D D D N N N D D D D D D D D D N N N N N N D D D N N N N N N N N N D D D D D D N N N D D N N N N N N N D D D N N N N N N N N N D D D Operator 2

Repeatability of the measurement system is assessed by determining the number of times each operator matches on (e.g., three) repeated measures of one unit.

In this example: – A Y in the “Match?” column indicates a match, and an N indicates a non-match. On Unit 2, operator 2, for example, all three measures matched, while on Unit 3, Operator 3, only trials 2 and 3 matched. – There are 40 samples *3 operators which yield 120 opportunities for a defect. Subtract (number of nonmatches/120) from 1 and multiply by 100% to get the percent match for repeatability. 13/120 = .1083 did not match. – The percent matched = 100 (1- .1083) = 89.17% – Since 89.17% matched is very close to 90% matched, gage repeatability technically fails but is practically acceptable.

12

Match? Y Y Y Y Y Y Y N Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y N Y Y Y Y Y Y Y 0.950

Operator 3 Tr1 Tr2 Tr3 N N N N N N D N N D D D D N D N N N D D D N N N N N N D N D D D D D D D D D D N N N D D D N N N N N N N N N N N N D D N D D N N N N N N N D D D N N N D D D N N N N N N N N N D D D D D D N N N N N N N N N N D N D D D D N N N N D N N N N N N Operator 3

Match? Y Y N Y N Y Y Y Y N Y Y Y Y Y Y Y Y Y N N Y Y Y Y Y Y Y Y Y Y Y Y Y N Y N N Y Y 0.800

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AR&R Example: Reproducibility Sample 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Operator 1 Tr1 Tr2 TR3 N N N N N N N N N D D D D D D N N N N D N N N N N N N N N N D D D N N N D D D N N N D D D D D D N N N N N N N N N N N N D D D N N N N N N N N N N N N D D D N N N N N N N N N N D N D D D N N N D N N N N N N N N D D D N N N N N N N N N N N N Operator 1

Operator 2 Tr1 Tr2 Tr3 N N N N N N N N N D D D D D D N N N D D D D N D N N N N N N D D D D D D D D D N N N D D D N N N N N N N N N D D D N N N D D D D D D D D D N N N N N N D D D N N N N N N N N N D D D D D D N N N D D N N N N N N N D D D N N N N N N N N N D D D Operator 2

Operator 3 Tr1 Tr2 Tr3 N N N N N N D N N D D D D N D N N N D D D N N N N N N D N D D D D D D D D D D N N N D D D N N N N N N N N N N N N D D N D D N N N N N N N D D D N N N D D D N N N N N N N N N D D D D D D N N N N N N N N N N D N D D D D N N N N D N N N N N N Operator 3

Reproducibility (plus repeatability) of the measurement system is assessed by determining the number of times operators match on the same unit.

In this example: – A Y in the “Match?” column indicates a match, and an N indicates a non-match. On Unit 1, for example, all three operators matched, while on Unit 3, only Operators 1 and 2 matched. – There are 40 samples or 40 opportunities for a defect in reproducibility. 19/40 = .475 did not match. – The percent matched = 100 (1-.475) = 52.50% matched. – Since 52.50% matched is lower than 90% matched, gage reproducibility is not acceptable.

13

Match? Y Y N Y N Y N N Y N Y N Y Y Y N Y Y N N N N N N Y Y Y Y Y N Y Y N Y N Y N N Y N 0.525

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AR&R Example: Accuracy Sample 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 # of N

Std Value N N N D D N D N N N D D D N D N N N N N D N N N N D N N N D D N N N N D N N N N

Operator 1 Tr1 Tr2 N N N N N N D D D D N N N D N N N N N N D D N N D D N N D D D D N N N N N N N N D D N N N N N N N N D D N N N N N N N D D D N N D N N N N N D D N N N N N N N N 5 2

Tr3 N N N D D N N N N N D N D N D D N N N N D N N N N D N N N N D N N N N D N N N N 4

14

Operator 2 Tr1 Tr2 N N N N N N D D D D N N D D D N N N N N D D D D D D N N D D N N N N N N D D N N D D D D D D N N N N D D N N N N N N D D D D N N D D N N N N D D N N N N N N D D 6 5

Tr3 N N N D D N D D N N D D D N D N N N D N D D D N N D N N N D D N N N N D N N N D 5

Accuracy of the measurement system is assessed by determining the number of non-matches to the standard for each individual measure

In this example, – The “Non-Match?” column contains a count of nonmatches to the standard value (std value) for the unit (row). For example, all operators matched the standard for unit 2, so the number of non-matches is 0. For unit 3, operator 3 failed to match the standard on trial 1, so the number of non-matches is 1. – There are the 40 units *9 repeated measures, or 360 individual measurements. 40/360 = .1111 did not match. – The percent matched = 100 (1-.1111) = 88.89% matched. – Since 88.89% matched is very close to 90% matched, gage accuracy technically fails but is practically acceptable.

Operator 3 Tr1 Tr2 N N N N D N D D D N N N D D N N N N D N D D D D D D N N D D N N N N N N N N D D D D N N N N D D N N D D N N N N N N D D D D N N N N N N N D D D D N N N N N N N 5 4

Tr3 N N N D D N D N N D D D D N D N N N N N N N N D N D N N N D D N N N N D N D N N 4

Not Match? 0 0 1 0 1 0 2 2 0 2 0 3 0 0 0 3 0 0 3 2 1 3 3 3 0 0 0 0 0 2 0 0 3 0 1 0 1 1 0 3 40

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AR&R Analysis Example: Accuracy (continued)

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To summarize the AR&R MSA Repeatability: 13/120 non-matched = 100 (1-.1083) = 89.17% (Fail–But Close!) Reproducibility: 19/40 non-matched = 100 (1-.475) = 52.50% matched (Fail) Accuracy: 40/360 non-matched = 100 (1-.1111) = 88.89% matched (Fail–But Close!)

Note: For Repeatability, 89.17% (and Accuracy 88.89%) we considered both of these as “Passing” due to the closeness to 90%. Use your judgment. If an improvement can be made, feel free to improve the measurement system. The 90% rate is an approximation not a “hard” limit.

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Measurement System Analysis (MSA) Worksheet

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Type of Gage R&R Conducted (Check One): Gage R&R (Continuous Data) Gage R&R Results

Date Conducted: 1/2/01

1)

Two-Way ANOVA Part p-value Oper p-value Oper & Part p-value

Significant? Y N Y N Y N Pass?

2) 3) 4) 5)

% Tolerance % Contribution % Study # Distinct Categories

[ 90% ] 89.17% OK 2) % Reproducibility [ >90% ] 52.5% Need to improve. See plan below 3) % Accuracy [ >90% ] 88.89% OK Gage R&R Pass? Y √ N, If NO: Plan for improvement: Will work on Reproducibility problem by conducting a team meeting with the 3 operators and discussing the differences in their measurements. Suspect that additional training is needed for less experienced operators because the data showed less experienced operators answering differently. Will also investigate if there is anything unique with each of the samples where reproducibility was an issue.

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Causes Of Measurement System Variation

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If you fail the Gage R&R, here are some factors that could cause measurement process variation (measurement error). Repeatability Operational definitions Maintain stability Reproducibility Operational definitions Consistent use of gage Training Varying work environment AUDIT-follow-up on training Human/physical characteristics Performance measures Unclear requirements If the Gage R&R fails, you need to improve the measurement system before moving on. Use these factors above as places to begin looking for areas of variation in your measurement system. By improving some of these factors, your measurement system variation should be reduced (or brought to an acceptable level).

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Causes Of Measurement System Variation (continued)

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Accuracy Error in master Instrument used improperly by appraiser Operational definition Standard not understood

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Other Considerations

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Temporal Effects Gage R&R depends upon our ability to measure things multiple times If the item is an event, it may not happen the same way twice. For this reason, Gage R&R may be impossible. If the event is recorded, it may be possible to conduct a Gage R&R study If the event cannot be recorded, but multiple judges can observe at once, reproducibility can be estimated, but repeatability cannot

Video cameras or audio voice recordings can allow a Gage R&R to be conducted. Use today’s technology to help you in validating your measurement system.

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Other Considerations

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Temporal Effects Example 1 Many Olympic sports are judged based on a numerical score sheet filled out by a judge. The difference among different judge’s readings of one live event is a measure of reproducibility. For this same case, repeatability can be estimated only if the competition is taped. A random sample of 10 performances shown to five judges, two times each, would allow estimates of both repeatability and reproducibility.

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Other Considerations

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Temporal Effects Example 2 Call centers field service calls from around the world at centralized locations. Call duration and call quality are both recorded and tracked very closely. Call quality is calculated based on a scoring sheet filled out by a quality monitor. Calls are scored on a continuous scale from 1-100 and can be assumed to be continuous for the purposes of a Gage R&R calculation.

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Other Considerations

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Temporal Effects Example 2 (continued) In one monitoring scenario, monitors listen in live and score the calls. For a “live listen” it is impossible to calculate repeatability, but if two monitors listen at the same time, it is possible to calculate reproducibility. In another monitoring scenario, calls are recorded at random and scored at a later date. For this recorded scenario, both repeatability and reproducibility may be calculated.

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Continuous Data MSA, First Step

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Test-Retest Study

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Test–Retest Study

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Best Practice Hint: Do Test-Retest before Gage R&R–a quick look at the situation. Why: Determine the precision of the system, instrument, device, or gage–where Precision = Measurement Error = Repeatability How: Repeatedly measure the same item Same conditions, operator, device, and location on item–same, same, same Completely mount and dismount item for each measurement–exercise gage through full range of normal use Data: Twenty (20) or more measurements is an adequate sample size. If measurements are difficult or expensive, then 10-15 may be OK. More is better. Calculate the sample mean ( Χ) and standard deviation (s) of the repeated measurements.

Test–Retest studies are sometimes called Calibration Tests. This study is done prior to a Gage R&R. A Test–Retest Study will indicate if you have either a precision or accuracy problem. A Test–Retest Study is typically run using a certified or working “Standard.” The same item is measured repeatedly.

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Test–Retest Study Guidelines

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Device precision should be less than 1/10 of the tolerance: s < 1/10 x tolerance* If s exceeds 1/10 x tolerance*, then the measurement system is unacceptable because it lacks precision. Action is required to find and remove the sources of this error, including the replacement of the device. Device accuracy may be estimated if you know the true value of the test unit: Inaccuracy = Bias = X - True Value

Precision is a term used to describe the amount of measurement error (repeatability error) in a measurement system. Precision is also used to describe the term ∆ (delta) in confidence intervals. There it indicates ½ width of a confidence interval. If your gage lacks precision or accuracy, you may need to remove or replace the measurement device. Perhaps a better or updated device can be used. *For a one-sided specification you can: (1) Use the mean minus the tolerance. Note: the new formula would be: (½) S ≤ 1/10 (USL – X) or (½) S ≤ 1/10 ( X-LSL). (2) use the natural boundary (for example, use 0 for a cycle time measurement) as the other spec. (Tolerance = USL-0).

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Process Flow For MSA (Measurement System Analysis)

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Conduct MSA

Take Preventive And Corrective Actions

OK? No Yes Continue Process Improvement

For continuous data we’ll look at these major items: %Tolerance, % Contribution, % Study and # Distinct Categories. MSA is a set of methods for estimating the current amount of variation in the Measurement System. Examples of Corrective Actions:

Review data and decisions

Institute stopgap measures

Examples of Preventive Actions:

Correct mechanical or definitional errors

Institute or upgrade training

Examples of Process Improvement:

Measure gage over time to address stability

Study linearity of gage

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Precision & Accuracy

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Target Analogy ==

Xbar

True Value = Bull's Eye

I. Precise, not accurate Xbar

== True Value

II. Accurate, not precise Xbar

== True Value

III. Precise and accurate

Precision: What kind of repeatability does the whole system have? What is the scatter? (standard deviation)

Accuracy: Does the average reading agree with the actual size of the part? (mean)

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Measurement System

Inputs

Process

Product Variation

Example

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Observations Inputs Measurement Outputs Measurements Process Data

Outputs

Measurement Variation

(Actual variation)

Total Variation (Observed variation)

#1

Example

σ 2Actual (Part) + σ 2Meas. System = σ 2Observed (Total)

#2 Measurement System Variability - Investigated through “R&R Study”

The measurement system will also contribute some variation to the overall total observed variation.

σ2

= variance

Here are two examples of the effect of measurement variation. This variation comes from both the gage and the operator. In a Gage R&R Study, we will determine how large the measurement variation contributes to the overall variation we’re observing in our process. The key will be to minimize the measurement variation so that we are mainly seeing process variation.

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Types Of Variation Estimated By The Gage R&R

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Equipment Variation (EV) (Repeatability) (Sources of variation from within the process) Within Gage–Within Operator–Within Part/Process–Etc. The variation introduced into the measurement process from within one or more elements of the measurement process–such as: within operator variation–within gage variation–within part variation–within method variation.

Appraiser Variation (AV) (Reproducibility) (Source of variation from across the process) Across Gages–Across Operators– Across Parts/Process–Etc. The variation introduced into the measurement process by effects going across the measurement process–such as different appraisers–different part configurations–different checking methods. Equipment variation–variation within a sample group. Appraiser variation–variation between sample groups.

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Relationship Between EV, AV And R&R

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R&R is the Reproducibility (AV) and Repeatability (EV) of the Measurement System. It represents the total variation in the Measurement System.

R&R

EV

AV

σ 2Equipment + σ 2Appraiser = σ 2Total (R&R) EV = Equipment Variation AV = Appraiser Variation The variation due to the equipment and appraiser do not directly add up to determine the total (R&R) variation. There is an overlap between EV and AV. You can use the Pythagorean theorem (right angles) to add to the influence of each EV and AV to calculate the total variation.

Repeatability: variation when one person repeatedly measures the same unit with the same measuring equipment. Reproducibility: variation when two or more people measure the same unit with the same measuring equipment.

σ 2= variance

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Relating R&R To Specification Window

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How much of the tolerance is used up by the Measurement System variation?

99%

R&R (5.15σ)

Lower Spec. Limit

Upper Spec. Limit

Specification Window (tolerance)

About 50% Of The Tolerance In This Example Is Used Up By The Measurement System Variation This Leaves Only 50% For The Process Variation We’re interested in how this variation compares to the tolerance with which we are working. If the measurement system takes up lots of variation, we don’t have any room for process variation. Minitab calls this variation % Tolerance. This is one or our 4 key metrics in the Gage R&R Study.

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Gage R&R For Continuous Data: Example

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GB Case Study: On Time Delivery of Shipments to Customers Background: The dispatchers for “Capital Logistics” keep a record of the time when truck drivers radio in to report delivery of the shipment was made to the customer (this is a requirement from the customers). Since there are 3 dispatchers recording the delivery time and 10 truck drivers calling in, the Green Belt needs to validate these delivery times for repeatability, reproducibility & accuracy.

First, we will walk through the process to conduct a Gage R&R Study in Minitab, analyze the results and draw conclusions. We will use Capital Logistics’ study of the delivery of shipments to customers. Then, you will do an activity to conduct a Gage R&R Study in Minitab with a new set of data from the same Capital Logistics’ study.

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Gage Reproducibility & Repeatability (GR&R) Study: Steps

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1. Set up a Minitab Worksheet 2. Perform study–collect & enter Data. (use file: “Gage R&R-Continuous Data.mtw) 3. Perform calculations & prepare Charts. – Perform Gage R&R Study–ANOVA method (ANOVA = Analysis of Variance)

4. Analyze–interpret & draw conclusions. 5. Investigate variation in measurement system, take action, make recommendations–keep, improve, or replace the measurement system. If measurement system is changed, repeat above steps to validate accuracy, repeatability & reproducibility of new measurement.

We have standardized on using the “ANOVA” method in Minitab. ANOVA simply stands for Analysis Of Variance. Minitab will partition the total variation and allocate this variation to gage variation or process variation. In the Gage R&R Study, we analyze the gage variation and want to understand how much gage variation is present. If we have too much measurement variation, we’ll need to fix our measurement system prior to collecting any data. We want to ensure the variation we are observing is mainly process variation.

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Case Study Setup

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Does my measurement system provide me a clear view of my process... To help answer this question the GB established the following analysis: 1. The GB developed a master matrix which listed the times each truck was supposed to arrive at the customer. The GB gave a copy of the matrix to each of the three dispatchers. 2. The GB had each of the truck drivers radio a message from a radio truck, identifying himself as one of the 10 units listed in the matrix.. 3. So that the GB could get repeatability & reproducibility data, the GB had the message recorded and then sent to the dispatchers throughout a 3 day period. The GB was able to program the phone system to deliver the messages precisely at the same time both days. The dispatchers were able to hear the call-in simultaneously via speakerphone. 4. Therefore, both days, the dispatchers, all in the same room at the same time, would receive the radio message and record the difference in minutes, from the target time listed on the matrix. At the end of the day, the GB would collect the data collection sheets from each dispatcher and give them a blank form for the following day. This procedure was then repeated the second day. 5. The GB then consolidated the data into a single Minitab file for analysis. (Gage R&R–continuous data.mtw).

…or does it cloud what I see?

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Gage R&R For Continuous Data: Example

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Step 1: Set up Minitab data sheet. GB asked 3 dispatchers to record the truck driver call-in time for the 10 different truck drivers. Data sheet for recording the data was set up in Minitab to keep track of the 10 trucks (Part/Truck), 3 dispatchers (Oper), 2 runs (Trial) and the “Y” of Difference from Target (Meas). Open the File: Gage R&R–Continuous Data.mtw

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Gage R&R For Continuous Data: Example (continued)

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Step 2: Perform Study–Collect & Enter Data. Truckers called in to report delivery and dispatchers recorded the difference from target time. The data was collected and recorded on a data sheet and was input into Minitab (see Data column). Minitab File: Gage R&R – Continuous Data.mtw

Use Minitab file: Gage R&R–Continuous Data.mtw

Columns 1-3 in the Minitab worksheet represent the data collected by the dispatchers as each truck driver called on their delivery times. 1. Part/Truck–indicates which of the 10 trucks 2. Oper–indicates which one of the 3 dispatchers 3. Meas–indicates the difference, in minutes, from the target time 4. Trial–indicates the trial number when the operator took the measurement.

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Gage R&R For Continuous Data: Example (continued)

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Step 3: Perform Calculations & Prepare Charts Perform Gage R&R Study–ANOVA method

Now let’s perform the Gage R&R study on this dispatching process example. ANOVA is the best method–it breaks down the overall variation into three categories:

part-to-part repeatability reproducibility

and….it breaks down reproducibility further into its components:

operator operator by part The standard value for a 2-sided specification is 5.15. This is the number of standard deviations needed to capture 99% of your process measurements. If you only have a 1-sided spec, you would use 2.575 (half of 5.15).

In Minitab: Click on STAT > Quality Tools > Gage R&R Study In the Gage R&R Study dialog box: 1. Select Columns for part, operator & measurement. 2. Select the ANOVA method 3. Select Options: Enter Tolerance width (note: Tolerance was set to 20 minutes here). The customer wanted the delivery within +/- 10 minutes of the target time. 4. Click “OK”, twice.

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Gage R&R For Continuous Data: Example (continued)

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Minitab Output will generate the following items which we will use to determine if our measurement system is acceptable: 1. 2. 3. 4. 5. 6.

Graphical Summary Two-Way ANOVA Table with Interaction (p-values) % Comparisons Table (% Contribution) % Comparisons Table (% Tolerance) % Comparisons Table (% Study) Discrimination Index

We will cover each of these 6 outputs in this section.

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The Central Question In A Gage R&R Study There are 2 ways to answer the question “Is my measurement variation too big?”

(1) FUTURE STATUS: Will my measurement variation be too large when I reach the 6-Sigma goal (i.e., with small process spread, good capability)?

R&R R&R %Tolerance %Tolerance

39

(2) PRESENT STATUS: Is my measurement variation too large right now, compared to a realistic estimate of current process spread (which may be narrow next year)?

R&R R&R %Contribution %Contribution

Number Numberof of Distinct Distinct Categories Categories

R&R R&R% %Study Study Variation Variation

(Ratio (Ratioof ofStdDev’s StdDev’s---AIAG) AIAG)

(Discrimination (Discrimination Index) Index)

30% 30%

8% 8%

44

30% 30%

10% 10%

2% 2%

10 10

15% 15%

Green

Yellow

Red

(Ratio (Ratioof ofVariances) Variances)

CAUTION: The magnitude of these %’s are exaggerations

If the Gage R&R (as a percent of tolerance) is less than 10%, the MS is green, or acceptable; if Gage R&R is 10-30% , the MS is yellow, or marginal; if Gage R&R is greater than 30%, the MS is red, or unacceptable. This estimate may be appropriate for evaluating how well the measurement system can perform with respect to specifications. We can use it to look into the future and ask “Will my measurement system variation be too large when I reach the 6 Sigma goal (with small process spread, good capability)?”

If Gage R&R (as a percent contribution) is less than 2%, the MS is green, or acceptable; if the Gage R&R is 2-8%, the MS is yellow, or marginal; if Gage R&R is greater than 8%, the MS is red, or unacceptable.

If the discrimination index (number of distinct categories) is greater than 10, the measurement system (MS) is green, or acceptable; if the discrimination index is 4-10, the MS is yellow, or marginal; if the discrimination index is less than 4, the MS is red, or unacceptable. The discrimination index is just a transformation of %R&R contribution (for ease of interpretation.) It addresses the same issues and contains the same information.

If Gage R&R (as a percent study) is less than 15%, the MS is green, or acceptable; if Gage R&R is 15-30%, the MS is yellow, or marginal; if Gage R&R is greater than 30%, the MS is red, or unacceptable.

Note: the limits shown above can be derived from one another. Some rounding was done for ease of interpretation.

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Rules Of Thumb–Acceptable Ranges

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Step 4: Analyzing Gage R&R Results A. R&R% of Tolerance 1. R&R less than 10%–Measurement System “acceptable” 2. R&R 10% to 30%–May be acceptable–make decision based on classification of Characteristic, Application, Customer Input, etc. 3. R&R over 30%–Not acceptable. Find problem, re-visit the Fishbone Diagram, remove Root Causes. Is there a better gage on the market, is it worth the additional cost?

RULES OF THUMB: 1. Less than 10% = Good 2. 10% to 30% = Fair–improvements possible; look to find opportunities in process and training. 3. Over 30% = Problem–measurement system not acceptable; fix problem with training, improved instruments, correct measuring process, and/or improved operational definitions for data collection. The gage is not adequate for Product/Process Acceptance decisions.

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Rules Of Thumb (continued)

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B. % Contribution (or Gage R&R StdDev): GR&R Variance should be “small” compared to Part-to-Part Variance– applies in cases where Tolerance Width is not meaningful, and %Tolerance is unavailable–such as one sided specs. 1. % Contribution < 2%–Measurement System “acceptable” 2. % Contribution 2%-8%–Measurement System “marginal” 3. % Contribution > 8%–Measurement System “unacceptable”

Questions to ask for validating the measurement system:

Are we capturing the correct data? Does the data reflect what is happening in the process?

How big is the measurement error?

Can we detect process improvement if and when it happens?

What are the sources of measurement error?

Are the measurements being made with measurement units which are small enough to properly reflect the variation present?

Is the Measurement System stable over time

Is the Measurement System “capable” for this study?

How much uncertainty should be attached to a measurement when interpreting it?

How do we improve the measurement system?

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Rules Of Thumb (continued)

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C. Number of Distinct Categories A “Signal-to-Noise” Ratio = (StdDevparts/process/StdDevGR&R) x 1.41 and rounded Guidelines: < 2 =>no value for process control, parts all “look” the same = 2 =>can see two groups–high/low, good/bad = 3 =>can see three groups–high/mid/low ≥ 4 =>acceptable measurement system (higher is better)

D. R&R % Study 1. % Study less than 15%–measurement system acceptable. 2. % Study 15% to 30%–may be acceptable (marginal) 3. % Study over 30%–not acceptable

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Minitab Gage R&R–Session Window Analysis

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Here are the Results: % Comparison Table–Found in our Minitab Session Window Source Total Gage R&R Repeatability Reproducibility Oper Oper*Part/Truck Part-To-Part Total Variation

%Contribution

%Study Var

%Tolerance

10.67 Fails! 3.10 7.56 2.19 5.37 89.33 100.00

32.66 Fails! 17.62 27.50 14.81 23.17 94.52 100.00

171.53 Fails! 92.54 144.43 77.76 121.70 496.41 525.21

Number of distinct categories = 4 pass!

We fail the Gage R&R!

% Tolerance is 171.53% which fails, based on our criteria.This shows us the % of the Tolerance which is being taken up by the gage. In this case, 171.53% of our tolerance is taken up by the variation of the gage. Note: You must put in the tolerance in Minitab in order to get this data. If you do not enter a tolerance, these figures will not appear. If you do not have a tolerance, then % Contribution would be more important in your analysis

% Study, probably the least important, (because % contribution tell us roughly the same thing) also fails based on our criteria. This gives us a measure of gage variation compared to 99% of a normal distribution.

Number of distinct categories passes! This tells us the number of divisions the measurement system can accurately measure across the seen process variation.

% Contribution is 10.67% which fails our criteria. % Contribution is based on overall measure of gage variation (regardless of the specification).

For a more detailed explanation of output, refer to the end of this section.

.

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Minitab Gage R&R–Graphical Analysis

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Now Let’s Review the Graphical Summary: Gage name: Date of study : Reported by : Tolerance: Misc:

Gage R&R (ANOVA) for Meas

1

2

Oper*Part/Truck Interaction 3

3.0SL=87.96 X=80.75 -3.0SL=73.54

0

Average

1

Sample Mean

Xbar Chart by Oper 110 100 90 80 70 60 50 40 30

1 2 3

Part/Truck

1

2

3

4

R Chart by Oper

2

Sample Range

15

1

2

3

3.0SL=12.52 10 5

R=3.833 -3.0SL=0.00E+00

0

400

Percent

8

9

10

2

300

3

By Part/Truck %Total Var %Study Var %Toler

200 100 0 Reprod

7

5 1

Components of Variation 500

Repeat

6

110 100 90 80 70 60 50 40

Oper

Gage R&R

5

4

By Oper

0

3

Oper

110 100 90 80 70 60 50 40

Part-to-Part

110 100 90 80 70 60 50 40

Part/Truck

6 1

2

3

4

5

6

7

8

9

10

Chart 4:

Chart 5:

The chart shows the 10 parts and the average measurement of those parts broken-out by operator. Ideally, all 3 lines should be on top of each other. We can see that there is some measurement variation in parts 4, 8 and 10. We should investigate why.

This chart shows the average reading for all parts by operator. The red circle is the average. This could show us if one operator is measuring higher/lower (on average) than the others.

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Next Steps For The Green Belt

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Sit down with your BB and/or Mentor to ensure proper analysis After an initial look at the Gage R&R Results for this example, the Green Belt will investigate the following: – – – – –

Look at the feasibility of changing the gage to a digital clock Talk with the operators to find out why they are measuring differently Can a spreadsheet be developed to calculate time automatically? Can we implement a driver call-in procedure to reduce variation? Why was it harder to measure parts 4, 8 and 10?

Continue on to see the GB’s Next Steps…

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Causes Of Measurement System Variation

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If you fail the Gage R&R, here are some factors that could cause measurement process variation (measurement error). Repeatability

Operational definitions Calibrating too often Granularity of the measure (e.g., nearest hour, minute, second) Maintain stability

Reproducibility

Operational definitions Consistent use of gage Training Varying work environment AUDIT–follow-up on training Human/physical characteristics Performance measures Unclear requirements

If the Gage R&R fails, you need to improve the measurement system before moving on. Use these factors above as places to begin looking for areas of variation in your measurement system. By improving some of these factors, your measurement system variation should be reduced, (or brought to an acceptable level).

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Causes Of Measurement System Variation (continued)

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Accuracy

Error in master Instrument not calibrated Worn components/trend or drift in master Instrument used improperly by appraiser Calibrating too often Operational definition Range of the master

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Causes Of Measurement System Variation

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Linearity Instrument calibrated incorrectly Error in master Worn instrument

Stability

Error in master Worn instrument Instrument measuring wrong characteristic Instrument not calibrated properly Instrument used improperly by appraiser

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Gage R&R Action Plan

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Step 5: Investigate sources of variation in the measurement system and make recommendations–keep, improve or replace the measurement system. After completing the analysis of the measurement system, the Green Belt investigated the sources of variation. By observing the process, the GB found: The % Tolerance is the largest issue (171.53%). With the current gage and measurement process in place, the gage is not acceptable. To address this issue the GB has done the following: – Changed the Gage – Implemented a standardized call-in procedure – Implemented a new spreadsheet

Explanation of Bullets:

The Dispatchers are using a clock on the wall that is not digital. Therefore, the GB implemented a new procedure to use the computer clock. All computers were synchronized and a procedure was implemented to have the system automatically synchronize clocks each day with the Atomic Clock.

The GB also found that the Truck Drivers were inconsistent in calling in their arrival times. After going into the field and interviewing some truck drivers, the GB found that a new call-in process needed to be implemented. Part of the problem was not with the gage but with “when” the truck driver called in the delivery time. In many cases, the truck driver was within the 10 minute window but had forgotten to call in the arrival. A standardized process was implemented to address this issue.

The GB also noticed that all the data was positive, (indicating that the deliveries were always late). Upon investigation, the GB found that the dispatchers did not know that they should enter both positive and negative numbers. A new spreadsheet was created to fix this issue

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Gage R&R Action Plan

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Step 5 (continued) The % Contribution also failed (10.67%). From the Minitab data, the GB found Reproducibility to be the larger issue and the interaction between certain trucks and certain operators was the issue. To address these issues, the GB has done the following: – The data indicates that the measuring of the arrival time for trucks 4 & 10 seem to vary from operator to operator. By going back and reviewing the data and talking to the operators, the following was found: There was a typo on the recording of time from Operator 1 on truck 4. He accidentally typed in the wrong number. To address this problem, a new spreadsheet was developed and now the Dispatcher is asked to verify his data prior to saving it in the spreadsheet. For Truck 10, the Operators had a very difficult time hearing the recording because the Truck Driver was using a cell phone with a poor connection. The GB changed the procedure so that each Dispatcher was now required to repeat-back the time given by the truck driver. The Truck Driver then confirms that the correct time is being recorded.

– The data also indicated that Operator 2 seems to measure slightly lower than Operators 1 & 3. The GB found that Operator 2 was sitting on an angle and when he read the clock his time was distorted. By converting to the computer clock, this issue should be resolved.

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Gage R&R For Continuous Data–Activity (15 minutes)

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Desired Outcome: Determine if the improved measurement system utilized by the Capital Logistics dispatchers is “acceptable” or not What

How

Preparation

Choose a facilitator, scribe

Conduct MSA

Complete 5 steps for a Gage R&R study and record results

Who

Timing

Team

10 mins.

Team

5 mins.

Use File: Gage R&R–Continuous Data.mtw and use columns C6-C9 Report Out

Complete Report Summary Present findings to class (see next page for report summary) Are there any additional items the GB should consider to improve the MSA even further?

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Measurement System Analysis (MSA) Worksheet

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Type of Gage R&R Conducted (Check One): Gage R&R (Continuous Data) Gage R&R Results

Date Conducted:

1)

Two-Way ANOVA Part p-value Oper p-value Oper & Part p-value

Significant? Y N Y N Y N Pass?

2) 3) 4) 5)

% Tolerance % Contribution % Study # Distinct Categories

[≤ 30%] [≤ 8%] [≤ 30%] [≥ 4]

Graphical Output

4)

Effective Resolution [ >50% ] Stability [R Chart] Consistency Between Xbar consistency Between Oper Systematic Shift [Oper/Part Inter. Plot]

Attribute Gage R&R

1) 2) 3)

Y Y Y Y

N N N N

OK? Y Y Y

N N N

Y

N

1) Repeatability [>90%] 2) % Reproducibility [>90%] 3) % Accuracy [>90%] Gage R&R Pass? Y N, IF NO: Plan for improvement:________________________________________ __________________________________________________________ © GE Capital, Inc., 2000 DMAIC GB M TX PG

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Analyzing The Gage R&R Results

53

Rules of Thumb 1. R&R (% Tolerance) Less than 10%–Measurement System is acceptable 10% to 30%–maybe acceptable–make decision based on classification of characteristic, hardware application, customer input, etc. Over 30%–Measurement System is not acceptable. Find problem, re-visit the fishbone diagram, remove root causes. Validate Measurement System again

2. % Contribution (or Gage R&R StdDev) : GR&R Variance should be “small” compared to Part-to-Part Variance–applies in cases where Tolerance Width is not meaningful, and % Tolerance is unavailable–Such as one-sided specs. 1.% Contribution < 2%-Measurement System “acceptable” 2.% Contribution 2%-8%-Measurement System “marginal” 3.% Contribution > 8%-Measurement System “unacceptable”

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Analyzing The Gage R&R Results (continued)

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3. Number of Distinct Categories = a “Signal-To-Noise” Ratio = (StdDevparts/StdDevGR&R) X 1.41 and rounded Guidelines: < 2–no value for process control, parts all “look” the same = 2–can see two groups–high/low, good/bad = 3–can see three groups–high/mid/low > 4–acceptable measurement system (higher is better)

4. R&R % Study 1. % Study less than 15%–measurement system acceptable 2. % Study 15% to 30%–may be acceptable (marginal) 3. % Study over 30%–not acceptable

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Summary–Measurement System Analysis

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Variation in the measurement system will contribute to the observed variation in a process The resolution is the ability of the gage to see the variation in the process – The gage should be accurate: mean close to the true mean of the process, and precise: small variation.

Minimize the measurement process variation Use MSA (Gage R&R for Continuous Data or Attribute R&R for Discrete Data) to identify the amount of measurement system variation and process variation Understand how measurement error impacts your customer Measurement error is always a bigger deal than you think! Make Sure Your MSA Is Examining The Actual Measurement System Itself

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Measure Step 3–Green Belt Project Activity (30 minutes)

56

Desired Outcome: Outline of a Data Collection Plan and MSA for your GB project What Your Individual GB Project

How 1. Data Collection plan*

Timing 15 mins.

Review and finalize your Data Collection Plan for your GB project Have you answered: What data will you need to collect? How will you collect it? From where? Who will collect the data? (can refer to the data collection worksheet) 2 . MSA*

15 mins.

Develop an MSA for your project Y data List factors that might cause measurement system variation and how you would reduce the impact of those factors

*Refer to the Self-Paced Workbook pp 43-49.

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Gage R&R Details–Optional Information

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Pages 58-69 contain Optional/Additional information that will not be covered in the 3-Day Workshop

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Full Gage R&R Details–Optional Information

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Graphical Output •ANOVA •ANOVAsimply simplystands standsfor for““Analysis AnalysisofofVariance” Variance” •It•Itisisaatool used to analyze tool used to analyzethe thetotal totalvariability variabilityamong amongdifferent differentsources. sources. •It•Itpartitions the total variation into “buckets”, and then allocates partitions the total variation into “buckets”, and then allocateseach eachbucket buckettotoeach eachsource source (part, (part,operator, operator,oper*part oper*partinteraction). interaction). Gage name: Date of study : Reported by : Tolerance: Misc:

Gage R&R (ANOVA) for Meas

1

2

Oper*Part/Truck Interaction 3

3.0SL=87.96 X=80.75 -3.0SL=73.54

0

Average

1

Sample Mean

Xbar Chart by Oper 110 100 90 80 70 60 50 40 30

1 2 3

Part/Truck

1

2

3

4

R Chart by Oper

2

Sample Range

15

1

2

3

3.0SL=12.52 10 5

R=3.833 -3.0SL=0.00E+00

0

Oper

500

Percent

300 200 100 0 Reprod

7

8

9

10

5 1

2

3

By Part/Truck %Total Var %Study Var %Toler

400

Repeat

6

110 100 90 80 70 60 50 40

Components of Variation

Gage R&R

5

4

By Oper

0

3

Oper

110 100 90 80 70 60 50 40

Part-to-Part

110 100 90 80 70 60 50 40

Part/Truck

6 1

2

3

4

5

6

7

8

9

10

What do the graphs tell you about the measurement system? Is it acceptable?

5 Scatter of individual measures should be equal by operator.

1 > 50% of points should be outside control limits.

6 Scatter of individual measures should be equal by part (truck.)

2 Range of measures by operator should be in control (this is showing repeatability.) 3 “D” should be largest, then A, B & C approximately equal. 4 Parallel lines will show no problems with certain parts (trucks.)

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Minitab Gage R&R ANOVA Graphical Output Average of 2 measurements taken by operator 1.

Gage name: Date of study : Reported by : Tolerance: Misc:

Gage R&R (ANOVA) for Meas

1

Oper*Part/Truck Interaction

2

3

3.0SL=87.96 X=80.75 -3.0SL=73.54

0

Oper 1

Oper 2

Oper 3

Average

Sample Mean

Xbar Chart by Oper 110 100 90 80 70 60 50 40 30

59

1 2 3

Part/Truck

1

2

3

4

R Chart by Oper Sample Range

15

1

3

3.0SL=12.52 10 5

R=3.833

0

-3.0SL=0.00E+00

Oper

500

Percent

300 200 100 0 Reprod

Part-to-Part

Xbar chart by Operator:

7

8

9

10

1

2

Plots the average for each part measured by each operator (average of 2-3 #’s). In our example, it is the average of 2 measurements.

We want the parts to be “out of control” If they are not out of control, we can’t tell one part from another! Remember , we’ve chosen parts that are different from each other. Usually, we want 50% of our points to be outside the control limits.

3

By Part/Truck %Total Var %Study Var %Toler

400

Repeat

6

110 100 90 80 70 60 50 40

Components of Variation

Gage R&R

5

By Oper

2

0

Range of 2 measurements taken by operator 1.

Oper

110 100 90 80 70 60 50 40

110 100 90 80 70 60 50 40

Part/Truck

1

2

3

4

5

6

7

8

9

10

We want the R chart to be “in control”. If it is not, then this may be an indication that repeatability is poor. Our data in our session window will confirm if we have a Repeatability issue. At this point, make a mental note. Look for any points outside the Upper Control Limit (verify the measurement is not a typo!) In this case, the R Chart looks OK. The chart is in control indicating that Repeatability is probably not an issue.

In this example, the Xbar chart looks OK (more than 50% of the points are outside the control limits.) R Chart by Operator:

Plots the range of each average point in the Xbar chart. This is the difference between the highest and lowest measurement for all 10 parts for each operator. © GE Capital, Inc., 2000

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Minitab Gage R&R ANOVA Graphical Output Gage name: Date of study : Reported by : Tolerance: Misc:

Gage R&R (ANOVA) for Meas

1

2

Oper*Part/Truck Interaction 3

3.0SL=87.96 X=80.75 -3.0SL=73.54

0

Average

Sample Mean

Xbar Chart by Oper 110 100 90 80 70 60 50 40 30

60

1 2 3

Part/Truck

1

2

3

4

R Chart by Oper Sample Range

15

1

2

3

10 5

R=3.833 -3.0SL=0.00E+00

0 0

Oper

%Total Var %Study Var %Toler

Percent

400 300 200 100 0

A

B

C

7

8

9

10

1

2

3

By Part/Truck

500

Reprod

6

110 100 90 80 70 60 50 40

Components of Variation

Repeat

5

By Oper 3.0SL=12.52

Gage R&R

Oper

110 100 90 80 70 60 50 40

Part-to-Part

110 100 90 80 70 60 50 40

Part/Truck

1

2

3

4

5

6

7

8

9

10

D

Graphical Display MSA Indicators by Components of Variation:

This is a graphical display of the components of variation. You can view the actual data in the session window.

% Total Var ==> same as saying % Contribution

% Toler ==> % Tolerance

Remember, we want the variation in the parts (Part-toPart) to be the major piece of variation and we want the variation from the gage itself to be small. Therefore, we want “A-C” to be small and “D” to be largest. In this case, the total variation of the parts is contributing 89.33% and the variation in the gage is contributing 10.67% (can be found in the session window). We’ll learn more later on % Contribution and % Tolerance. © GE Capital, Inc., 2000 DMAIC GB M TX PG

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Minitab Gage R&R ANOVA Graphical Output Gage name: Date of study : Reported by : Tolerance: Misc:

Gage R&R (ANOVA) for Meas

1

2

Oper*Part/Truck Interaction 3

3.0SL=87.96 X=80.75 -3.0SL=73.54

0

Average

Sample Mean

Xbar Chart by Oper 110 100 90 80 70 60 50 40 30

1 2 3

Part/Truck

Sample Range

1

1

2

3

4

2

3

10 5

R=3.833

0

-3.0SL=0.00E+00 0

Oper

500

Percent

7

8

9

10

1

2

300

3

By Part/Truck %Total Var %Study Var %Toler

400

200 100 0 Reprod

6

110 100 90 80 70 60 50 40

Components of Variation

Repeat

5

By Oper 3.0SL=12.52

Gage R&R

Oper

110 100 90 80 70 60 50 40

R Chart by Oper 15

61

Part-to-Part

Operator by Part Interaction: Shows interaction between the operator and the part We want the lines to be on top of each other. Crossed lines could indicate the potential for interaction. Confirm suspected interactions with the p-value in ANOVA Table. We want all operators measuring the parts the very similarly (ie, getting the same measurement). Use this chart to help you look at particular parts which operators may be measuring differently. By reviewing this chart, we notice that the operators are measuring Part 4 & Part 10 differently. We would want to investigate why. This chart would also show us if one operator measures higher or lower than the others. It may indicate a Reproducibility issue. It appears that Operator 2 is measuring slightly lower than Operators 1 & 3. The Minitab Session Window can also tell us more.

110 100 90 80 70 60 50 40

Part/Truck

1

2

3

4

5

6

7

8

9

10

By Operator: Main effect plot for Operator We want a flat horizontal line. This would indicate that it is unlikely the operator is having an effect...confirm with the p-value from ANOVA. This chart shows the measurements, by operator. Some dots may be on top of each other. Visually, you can see each operator’s measurements. By Part: Main effect plot for Part. We want to see lots of changes in slope. This would indicate that it is likely that the parts are having an effect. Confirm with the p-value from Anova. (Remember, we set up our study this way. We wanted differences in the parts.) More importantly, look for parts that have varying measurements. For instance, part 10 shows more variation in measurement than some of the other parts. © GE Capital, Inc., 2000

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Minitab Gage R&R ANOVA Table

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ANOVA TABLE Two-Way ANOVA Table With Interaction Source

Sources of Variability

DF

Part/Truck 9 Oper 2 Oper*Part/Truck 18 Repeatability 30 Total 59

SS

MS

F

P

20587.1 480.0 036.7 387.5 22491.2

2287.45 240.00 7.59 12.92

39.7178 4.1672 4.4588

0.00000 0.03256 0.00016

P< 0.05 indicates statistically significant! Are any of these “p-values” less than 0.05? If so, their sources of variation can be considered statistically significant (i.e, Active, Influential).

For this gage... parts, operators and the interaction between parts & operators are statistically significant sources of variation!

There are 4 major outputs other than the graphical summary. We will discuss each separately. Explanation of output for ANOVA Table: Part/Truck: p=0.00000; I would expect the parts to be significant because we chose truck travel routes that were really different from each other (short runs and long runs).

Oper*Part/Truck: p=0.00016; This is the interaction between the operator and the parts (eg, when operators measure/record certain travel times). Since this is statistically significant, it is indicating that there may be some issues when some operators measure/record certain runs. We will look further into the Minitab output to find out which run and which operators.

Oper: p=0.03256; This is telling us that the Operators are statistically significant. I need to look further to find out if it’s a repeatability or a reproducibility issue (Minitab does this for us in both the Comparisons Table and in the charts. We’ll show you later!)

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Minitab Gage R&R % Tolerance

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% Comparisons Table P/T P/TRatio Ratio

(Precision-to-Tolerance (Precision-to-ToleranceRatio) Ratio)

“R&R “R&Ras asaa% %of of Tolerance” Tolerance”

Source

%Contribution

Total Gage R&R Repeatability Reproducibility Oper Oper*Part/Truck Part-To-Part Total Variation

%Study Var

10.67 3.10 7.56 2.19 5.37 89.33 100.00

%Tolerance

32.66 17.62 27.50 14.81 23.17 94.52 100.00

171.53 92.54 144.43 77.76 121.70 496.41 525.21

% Tolerance Acceptable Ranges Not Acceptable

30%

Questionable

10%

Acceptable If you wanted to calculate %Tolerance by hand:

% T o le r a n c e =

5 .1 5 • σ

R & R ( M e a s . S y s t .)

T o le r a n c e

This shows us the % of the Tolerance which is being taken up by the gage. For instance, in this case, 171.53% of our tolerance is taken up by the variation of the gage. Refer to the next page for a visual explanation of % Tolerance. Note: You must put in the tolerance in Minitab in order to get this data. If you do not enter a tolerance, these figures will not appear. If you do not have a tolerance, then % Contribution would be more important in your analysis.

∗1 0 0 %

If % Tolerance is unacceptable now, then once you reach a Six Sigma Process, the measurement variation will be too large compared to the process variation. In this case, the gage fails % Tolerance.

% Tolerance = A good indicator for Future Status

For this Gage: %Tolerance GRR = 171.53%

This Gage Fails the Criteria for %Tolerance for the Total Gage RR Piece.

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Minitab Gage R&R % Tolerance Graphically

64

%Tolerance: Graphically LSL

USL

%Tolerance = 10%

%Tolerance = 30%

%Tolerance = 70%

Graphically, this shows the amount of the engineering tolerance used up just from the measurement system.

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Minitab Gage R&R % Contribution % Comparisons Table

Variation due to the gage

%R&R %R&RContribution Contribution(Total (Total Variation) Variation)

“R&R “R&Ras asaa%%of ofTotal TotalProcess Process Variation” Variation”

Variation due to the parts

%Contribution

%Study Var

%Tolerance

Total Gage R&R Repeatability Reproducibility Oper Oper*Part/Truck Part-To-Part Total Variation

10.67 3.10 7.56 2.19 5.37 89.33 100.00

32.66 17.62 27.50 14.81 23.17 94.52 100.00

171.53 92.54 144.43 77.76 121.70 496.41 525.21

=

100%

Further Explanation:

% Contribution Acceptable Ranges

Questionable

+

Source

Source

Not Acceptable

65

8.0%

%Contribution

Total Gage R&R Repeatability Reproducibility

10.67 3.10 7.56

Oper Oper*Part/Truck Part-To-Part Total Variation

2.19 5.37 89.33 100.00

2.0%

3.10 + 7.56 = 10.67

Now, we know that Reproducibility is our bigger issue (contributing more than Repeatability).

2.19 + 5.37 = 7.56

Acceptable

Now, we know that of the Reproducibility, the Oper to Part/Truck interaction is our bigger issue than the Reproducibility of Operators. Check with the Oper*Part/Truck Interaction Graph to find out which parts may be the issue.

% Contribution = a good indicator for Present Status

The measurement system (gage) is contributing to 10.67% of the total variation and the parts are contributing 89.33%.

This Gage Fails the Criteria for % Contribution, but it is close to passing.

% R&R Contribution

=

    

σ

Note: If you don’t have a tolerance, then, % Contribution becomes a very critical measurement for Gage R&R. It gives you a good indication of the measurement variation, now, compared to a realistic estimate of current process spread.

If you wanted to calculate %R&R Contribution by hand:

2 R & R ( M e a s . S y s t .) 2 T o t a l

σ

    

×

1 0 0 %

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Minitab Gage R&R Discrimination Index

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Discrimination Index Number of Distinct Categories = 4

Discrimination DiscriminationIndex Index

For this gage: the Discrimination Index = 4 • This says that the gage has reached the minimum acceptable level. Discrimination Index: Discrimination Index: •Provides the number of divisions that the Measurement System can accurately •Provides the number of divisions that the Measurement System can accurately measure measureacross acrossthe theprocess processvariation. variation.

“Number “Numberof ofDistinct Distinct Categories” Categories”

•Indicates •Indicateshow how well wellaagage gagecan candetect detectpart-to-part part-to-partvariation variation---- process processshifts shiftsand and improvement. improvement.

Discrimination DiscriminationIndex IndexAcceptable AcceptableValues Values •Less than 2, inadequate •Equal to 2, equal to a go/nogo gauge. •Minimum acceptable value = 4. •Optimal = 10 or more.

If you wanted to calculate Discrimination Index by hand: Std Dev (Parts) Std Dev (GRR)

x 1.41

D is c rim =

  σ2 2 •  2 T o ta l  σ R &R  ( M e a s .S y s t . )

   −1  

Discrimination Index will tell us how many categories or “buckets” the measurement device is able to see or discriminate. If you’ve chosen parts that are different (eg, in size, length, width, etc), the Discrimination Index will indicate how many distinct categories are present. In our example, Minitab is able to see 4 distinct categories. Note: If you’ve designed and ran your study with similar parts (on purpose), this reading would be meaningless to you.

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Minitab Gage R&R Key Indices

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33Key KeyIndices Indicesfor forMeasurement MeasurementSystem SystemCapability Capability 11

22

33

P/T P/TRatio Ratio

%R&R %R&RContribution Contribution

Discrimination DiscriminationIndex Index

“R&R “R&Ras asaa% %of of Tolerance” Tolerance”

“R&R “R&Ras asaa% %of ofTotal Total Measure Variation” Measure Variation”

“Number “Numberof ofDistinct Distinct Categories” Categories”

%Tolerance GRR = 171.53%

% R&R Contribution = 10.67%

Discrimination Index = 4

(Precision-to-Tolerance (Precision-to-ToleranceRatio) Ratio)

The next question to be answered: What do I do now that the % Tolerance & % Contribution has failed? Well, this is what we have learned so far about the breakdown of % Tolerance and % Contribution:

For % Tolerance and % Contribution, we know the bigger issue is reproducibility. And, with Reproducibility, the bigger issue is the interaction between parts and operators. By looking at the graphical summary, it appears that trucks 4 and 10 may be the issue. Investigate why there is a difference. Is there something unique about those truck routes? Is it harder to measure the time for Trucks 4 & 10 due to time length? Should there be an Operational Definition or Procedure on how to measure? Was there a problem with calculating the time from target?

We also know that Operators and the Operator*Part/Truck Interaction is significant (from p-value). This is an indication that the operators are measuring differently. It also tells me there is some variation when certain operators measure certain trucks. Again, the graphs indicate which trucks and which operators.

I would investigate those areas mentioned above. Depending on your findings, you may need to implement a new training program with your operators on how to measure/record the time. You also may need to do something like having the computer measure the time when we measure parts similar to Parts 4 & 10. Once you’ve done those items, go back and re-run the Gage R&R using your implemented changes.

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Gage R&R Acceptable Ranges

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Acceptable Acceptable Ranges–ANOVA Ranges–ANOVA METHOD METHOD This tells us how much variation the gage itself is contributing to the variation.

%Tolerance

%Contribution Not Acceptable Questionable Acceptable

This tells us the ratio of each component of variation (the standard deviation for each component divided by the total standard deviation).

This tells us how much of the tolerance is being taken up by the variation the gage.

% Discrimination Index

8.0%

30%

4

30%

2.0%

10%

10

15%

• Provides the number of divisions that the Measurement System can accurately measure across the process variation. • Indicates how well a gage can detect part-to-part variation--process shifts and improvement.

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Measurement System Analysis (MSA) Worksheet Type of Gage R&R Conducted (Check One): Gage R&R (Continuous Data) Gage R&R Results 1) Two-Way ANOVA Part p-value Oper p-value Oper & Part p-value 2) 3) 4) 5)

% Tolerance % Contribution % Study # Distinct Categories

Graphical Output

0.00016

10.67% 32.66% 4

Date Conducted: 1/2/02

Significant? Y N Y N Y N Pass?

0.00000 0.03256

171.53%

69

[≤ 30%] [≤ 8%] [≤ 30%] [≥ 4 ]

Y Y Y Y

N N N N OK?

1) Effective Resolution [ >50% ] Y N 2) Stability [R Chart] Y N 3) Consistency Between Xbar consistency Y N Between Oper 4) Systematic Shift [Oper/Part Inter. Plot] Y N _______________________________________________________________ Gage R&R Pass? Y N, If NO: Plan for improvement:

Look at the gage and possibly change to a digital clock. Review/Implement a driver call-in procedure. Suspect there is variation between drivers. Review/develop a new spreadsheet for calculating the time. Talk with operators to determine why Oper 2 measures differently than Operators 1 & 3. Talk with customers about the right specification, if possible. Train all operators and truck drives on new procedures. Re-run Gage R&R to verify improvements.

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Analyze Module Objectives

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Learn and apply the tools and concepts in the Analyze phase

You will learn the concepts and tools for the Analyze phase during this classroom session. After the classroom session, you can use the Six Sigma training CD to review how the Analyze phase is applied.

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Analyze Phase Flowchart

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ANALYZE PHASE OVERVIEW

Analyze 4: Establish Process Capability

Analyze 5: Define Performance Objectives

Analyze 6: Identify Variation Sources

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The12-Step Process Step Define

Description

Focus Tools

Deliverables

A

Identify Project CTQ’s

Project CTQ’s

B

Develop Team Charter

Approved Charter

C

Define Process Map

High Level Process Map

Measure 1 2 3

Select CTQ Characteristics Define Performance Standards Measurement System Analysis

Analyze 4 Establish Process Capabilities 5 Define Performance Objectives 6 Identify Variation Sources

Improve 7 Screen Potential Causes 8 Discover Variable Relationships 9 Establish Operating Tolerances Control 10 Define & Validate Measurement System on X’s in Actual Application 11 Determine Process Capability 12 Implement Process Control

Y Y Y

Customer, QFD, FMEA Project Y Customer, Blueprints Performance Standard for Project Y Continuous Gage R&R, Data Collection Plan & MSA test/Retest, Attribute Data for Project Y R&R

Y

Capability Indices

Y

Team, Benchmarking

X

Process Analysis, Graphical Analysis, Hypothesis Tests

X X

DOE-Screening Factorial Designs

Y, X Simulation

Process Capability for Project Y Improvement Goal for Project Y Prioritized List of all X’s

List of Vital Few X’s Proposed Solution Piloted Solution

Y, X Continuous Gage R&R, MSA Test/Retest, Attribute R&R Y, X Capability Indices Process Capability Y, X X

Control Charts, Mistake Sustained Solution, Proofing, FMEA Documentation

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Analyze Phase Overview What is the Analyze phase? The Analyze phase is when your team: Calculates baseline process capability for the process Defines the improvement goal for the project Analyzes historical data to identify the sources of variation

Why is the Analyze phase important? This phase is important because it clearly defines how well the process is currently performing and identifies how much the process will be improved. Steps involved in the Analyze phase Analyze 4: Establish process capability Analyze 5: Define performance objectives Analyze 6: Identify variation sources

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Statistical Thinking

D M Practical Problem

A Statistical Problem

Statistical Solution

Characterize the Root cause analysis process – Critical X’s – Stability Measure the – Shape influence of the – Center critical X’s on – Variation Data Integrity the mean and variability – MSA Capability – Test – Brainstorm – ZBench ST & LT potential X’s – Model – Sampling plan – Estimate

Problem statement – Project Y – Magnitude – Impact

I C Practical Solution

Verify critical X’s and ƒ(x) Change process Control the gains – Risk analysis – Control plans

Collect data The Practical-To-Statistical-To-Practical Transformation Process

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Analyze 4–Establish Process Capability

1

What does it mean to Establish Process Capability? Process capability refers to the ability of a process to produce a defect-free product or service. In this step, you will determine how consistently your product or process meets the performance standard for your project Y calculating the sigma level. The sigma level is calculated through statistical analysis of the collected data. Why is it important to Establish Process Capability? You can’t set a measurable goal without a clear understanding of where you are. It is important to establish process capability in order to baseline your current process performance. This will be the starting point from which you will set your improvement goals. What are the project tasks for completing Analyze 4? 4.1 Graphically analyze data for project Y (continuous data only) 4.2 Calculate baseline sigma for project Y

ANALYZE STEP OVERVIEW

Analyze 4: Establish Process Capability

Analyze 5: Define Performance Objectives

Analyze 6: Identify Variation Sources

4.1 Graphically analyze data for project Y (continuous data only) 4.2 Calculate baseline sigma for project Y

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Step 4.1: Graphically Analyze Data For Project Y

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Review: Describing Variation

3

Prior to Calculating Capability, we need to know: Key question #1–Stability–Variation over time (Run Chart) How stable is the data? Key Question #2–Shape, Spread–Variation for a period of time: Data Distributions (Graphical Analysis) What is the shape of the distribution–symmetrical, lopsided, twin peaks, long-tailed? (determination of normality) What is the central tendency (“center” or “average”) of the distribution? What is the variation (“spread”) of the distribution–wide or narrow?

These attributes of your data will help determine which statistical calculations are better descriptors of your data set.

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Graphically Analyze Data

4

We can use the following example: Data set: Holdtime.MPJ 1. First, look at Stability: STAT > Quality Tools > Run Chart

Approx p-value for clustering = 0.1139 Approx p-value for mixtures = 0.8861 Approx p-value for trends = 0.2883 Approx p-value for oscillator = 0.7117

p ≥ 0.05 indicates stability. Therefore, data is stable.

2. Secondly, look at Shape: STAT > Basic Statistics > Normality Test Anderson-Darling p-value = 0.885 p-value ≥ 0.05 indicates data is normal. Therefore, data is normal. 3. Third, look at Centering and Spread: STAT > Basic Statistics > Display Descriptive Statistics Again, p-value = 0.885. Data is normal. Mean = 8.5 and S = 0.10

p ≥ 0.05 indicates normal data. Therefore, will use mean and standard deviation to describe data.

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Steps 4.2: Calculate Baseline Sigma

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What Is Process Capability?

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A Measurement Scale Which Compares the Output of a Process to the Performance Standard

Process capability allows us to compare how “capable” the process is of meeting customer CTQ’s by looking at the probability that the process will produce a defect.

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Common Metric For Comparison Process Purchase Order Generation Accounts Receivable Customer Service Supplier Delivery

7

Performance 98% accuracy 33 days average aging 82% rated 4 or 5 on responsiveness 95% on-time delivery

Which process is performing best?

It’s difficult to compare processes with very different kinds of measure. By expressing process capability as a “sigma” value we can compare different types of processes.

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Data Analysis Roundup

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Process Capability Tools and Terminology e.g Light off

e.g Cycle Time, Length, Weight…

e.g Light On

Discrete DiscreteData Data Defects per Opportunity Defects per Million Opportunities Six Sigma Product Report

Continuous Continuous Data Data Six Sigma Process Report: ZLong term ZShort term = ZBench = reported yield

ZShift

In this step you will learn how to calculate discrete and continuous data. A note on terms to describe capability. All the following are synonyms: ZLT = ZBenchLT = Sigma CapabilityLT (or, you may see capability written as σLT or SigmaLT. This is no longer standard usage to denote capability). ZST = ZBenchST = Sigma CapabilityST = ZBench (σ or SigmaST is no longer recommended).

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Process Capability Continuous Data

9

Verify we have a normal distribution Calculate ZLSL and/or ZUSL Determine probability of a defective Determine ZBench

We will look at how to do each of these steps in detail!

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Calculating Z–Continuous Data

10

You can calculate a Z-value for any given value of x. Z is the number of standard deviations which will fit between the mean and the value of x. This is known as a Z-score.

Z=

X− µ σ

z

µ 1σ 2σ 3σ 4σ

The Z-score is a way to transform any normal distribution to the standard normal distribution. The standard normal distribution has a mean of 0 and a standard deviation of 1. This transformation allows us to compare two entirely different processes on a common scale-that of standard deviation units. You must have a normal distribution: A stable process prior to using this method. If not, you’ll need to use the Discrete, DPMO method.

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Calculating Capability

11

X = 8.5 s = 0.1 xx Probability Probability ofofaadefect defect less lessthan than LSL LSL

ZUSL

ZLSL

Standard Deviations -4 Units of Measure 8.1

Probability Probability ofofaadefect defect greater greater than thanUSL USL

USL USL

LSL LSL

-3

-2

-1

0

1

8.2

8.3

8.4

8.5

2

8.6 8.7

3

4

8.8

8.9

ZUSL = USL - X = 8.7 - 8.5 = 0.2 = 2 s

0.1

0.1

ZLSL = X - LSL = 8.5 - 8.2 = 0.3 = 3 s

0.1

0.1

ZUSL = Look up Z = 2.0 => 0.0228 LSL = Look up Z = 3 => 0.00135 Area Total = 0.0228 + 0.00135 = .02415 Yield = 1-.02415 = 0.97585 = 97.6% Go to Memory Jogger (or Abridged Sigma Table) and look up a Yield of 97.6% ZST = 3.4

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Reading The Z Table

12

Yield

Probability Of A Defective Example = .028066

Specification Limit

Z-score

To the right of the Z-score you will note the tail area

0.20 .420740315 1.71 0.25 .401293634 1.76 .382088486 1.81 1.86 1.91 1.96 2.01 2.06 2.11 2.16 2.21 2.26 2.31 2.36

Z = 1.91 1.35 1.40 1.45 1.50

.088507862 .080756531 .073529141 .066807100

2.41 2.46 2.51 2.56 2.61 2.66 2.71 2.76 2.81 2.86 2.91 2.96 3.01

.043632958 .039203955 .035147973 .031442864 .028066724 .024998022 .022215724 .019699396 .017429293 .015386434 .013552660 .011910681 .010444106 .009137469 .007976235 .006946800 .006036485 .005233515 .004527002 .003906912 .003364033 .002889938 .002476947 .002118083 .001807032 .001538097 .001306156

Units of Measure 3.22 3.27 3.32 3.37 3.42 3.47 3.52 3.57 3.62 3.67 3.72 3.77 3.82 3.87 3.92 3.97 4.02 4.07 4.12 4.17 4.22 4.27 4.32 4.37 4.42 4.47 4.52

.000640954 .000537758 .000450127 .000375899 .000313179 .000260317 .000215873 .000178601 .000147419 .000121399 .000099739 .000081753 .000066855 .000054545 .000044399 .000036057 .000029215 .000023617 .000019047

4.73 4.78 4.83 4.88 4.93 4.98 5.03 5.08 5.13 5.18 5.23 5.28 5.33 5.38 5.43 5.48 5.53 5.58 5.63

.000001153 .000000903 .000000705 .000000550 .000000428 .000000332 .000000258 .000000199 .000000154 .000000118 .000000091 .000000070 .000000053 .000000041 .000000031 .000000024 .000000018 .000000014 .000000010

Table Of Area Under The Normal Curve

Yield = Probability of a non-defective From the Z Table, we can get the probability of a defective. 1-Probability of defective = Yield. This is what we’ll need to eventually calculate Process Capability.

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z (Values of Z from 0.00 to 4.99)

Single–Tail Z Table

Z

0.00

0.01

13

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90

5.00e-001 4.60e-001 4.21e-001 3.82e-001 3.45e-001 3.09e-001 2.74e-001 2.42e-001 2.12e-001 1.84e-001

4.96e-001 4.56e-001 4.17e-001 3.78e-001 3.41e-001 3.05e-001 2.71e-001 2.39e-001 2.09e-001 1.81e-001

4.92e-001 4.52e-001 4.13e-001 3.74e-001 3.37e-001 3.02e-001 2.68e-001 2.36e-001 2.06e-001 1.79e-001

4.88e-001 4.48e-001 4.09e-001 3.71e-001 3.34e-001 2.98e-001 2.64e-001 2.33e-001 2.03e-001 1.76e-001

4.84e-001 4.44e-001 4.05e-001 3.67e-001 3.30e-001 2.95e-001 2.61e-001 2.30e-001 2.00e-001 1.74e-001

4.80e-001 4.40e-001 4.01e-001 3.63e-001 3.26e-001 2.91e-001 2.58e-001 2.27e-001 1.98e-001 1.71e-001

4.76e-001 4.36e-001 3.97e-001 3.59e-001 3.23e-001 2.88e-001 2.55e-001 2.24e-001 1.95e-001 1.69e-001

4.72e-001 4.33e-001 3.94e-001 3.56e-001 3.19e-001 2.84e-001 2.51e-001 2.21e-001 1.92e-001 1.66e-001

4.68e-001 4.29e-001 3.90e-001 3.52e-001 3.16e-001 2.81e-001 2.48e-001 2.18e-001 1.89e-001 1.64e-001

4.64e-001 4.25e-001 3.86e-001 3.48e-001 3.12e-001 2.78e-001 2.45e-001 2.15e-001 1.87e-001 1.61e-001

1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90

1.59e-001 1.36e-001 1.15e-001 9.68e-002 8.08e-002 6.68e-002 5.48e-002 4.46e-002 3.59e-002 2.87e-002

1.56e-001 1.33e-001 1.13e-001 9.51e-002 7.93e-002 6.55e-002 5.37e-002 4.36e-002 3.51e-002 2.81e-002

1.54e-001 1.31e-001 1.11e-001 9.34e-002 7.78e-002 6.43e-002 5.26e-002 4.27e-002 3.44e-002 2.74e-002

1.52e-001 1.29e-001 1.09e-001 9.18e-002 7.64e-002 6.30e-002 5.16e-002 4.18e-002 3.36e-002 2.68e-002

1.49e-001 1.27e-001 1.07e-001 9.01e-002 7.49e-002 6.18e-002 5.05e-002 4.09e-002 3.29e-002 2.62e-002

1.47e-001 1.25e-001 1.06e-001 8.85e-002 7.35e-002 6.06e-002 4.95e-002 4.01e-002 3.22e-002 2.56e-002

1.45e-001 1.23e-001 1.04e-001 8.69e-002 7.21e-002 5.94e-002 4.85e-002 3.92e-002 3.14e-002 2.50e-002

1.42e-001 1.21e-001 1.02e-001 8.53e-002 7.08e-002 5.82e-002 4.75e-002 3.84e-002 3.07e-002 2.44e-002

1.40e-001 1.19e-001 1.00e-001 8.38e-002 6.94e-002 5.71e-002 4.65e-002 3.75e-002 3.01e-002 2.39e-002

1.38e-001 1.17e-001 9.85e-002 8.23e-002 6.81e-002 5.59e-002 4.55e-002 3.67e-002 2.94e-002 2.33e-002

2.00 2.10 2.20 2.30 2.40 2.50 2.60 2.70 2.80 2.90

2.28e-002 1.79e-002 1.39e-002 1.07e-002 8.20e-003 6.21e-003 4.66e-003 3.47e-003 2.56e-003 1.87e-003

2.22e-002 1.74e-002 1.36e-002 1.04e-002 7.98e-003 6.04e-003 4.53e-003 3.36e-003 2.48e-003 1.81e-003

2.17e-002 1.70e-002 1.32e-002 1.02e-002 7.76e-003 5.87e-003 4.40e-003 3.26e-003 2.40e-003 1.75e-003

2.12e-002 1.66e-002 1.29e-002 9.90e-003 7.55e-003 5.70e-003 4.27e-003 3.17e-003 2.33e-003 1.69e-003

2.07e-002 1.62e-002 1.25e-002 9.64e-003 7.34e-003 5.54e-003 4.15e-003 3.07e-003 2.26e-003 1.64e-003

2.02e-002 1.58e-002 1.22e-002 9.39e-003 7.14e-003 5.39e-003 4.02e-003 2.98e-003 2.19e-003 1.59e-003

1.97e-002 1.54e-002 1.19e-002 9.14e-003 6.95e-003 5.23e-003 3.91e-003 2.89e-003 2.12e-003 1.54e-003

1.92e-002 1.50e-002 1.16e-002 8.89e-003 6.76e-003 5.08e-003 3.79e-003 2.80e-003 2.05e-003 1.49e-003

1.88e-002 1.46e-002 1.13e-002 8.66e-003 6.57e-003 4.94e-003 3.68e-003 2.72e-003 1.99e-003 1.44e-003

1.83e-002 1.43e-002 1.10e-002 8.42e-003 6.39e-003 4.80e-003 3.57e-003 2.64e-003 1.93e-003 1.39e-003

3.00 3.10 3.20 3.30 3.40 3.50 3.60 3.70 3.80 3.90

1.35e-003 9.68e-004 6.87e-004 4.83e-004 3.37e-004 2.33e-004 1.59e-004 1.08e-004 7.23e-005 4.81e-005

1.31e-003 9.35e-004 6.64e-004 4.66e-004 3.25e-004 2.24e-004 1.53e-004 1.04e-004 6.95e-005 4.61e-005

1.26e-003 9.04e-004 6.41e-004 4.50e-004 3.13e-004 2.16e-004 1.47e-004 9.96e-005 6.67e-005 4.43e-005

1.22e-003 8.74e-004 6.19e-004 4.34e-004 3.02e-004 2.08e-004 1.42e-004 9.57e-005 6.41e-005 4.25e-005

1.18e-003 8.45e-004 5.98e-004 4.19e-004 2.91e-004 2.00e-004 1.36e-004 9.20e-005 6.15e-005 4.07e-005

1.14e-003 8.16e-004 5.77e-004 4.04e-004 2.80e-004 1.93e-004 1.31e-004 8.84e-005 5.91e-005 3.91e-005

1.11e-003 7.89e-004 5.57e-004 3.90e-004 2.70e-004 1.85e-004 1.26e-004 8.50e-005 5.67e-005 3.75e-005

1.07e-003 7.62e-004 5.38e-004 3.76e-004 2.60e-004 1.78e-004 1.21e-004 8.16e-005 5.44e-005 3.59e-005

1.04e-003 7.36e-004 5.19e-004 3.62e-004 2.51e-004 1.72e-004 1.17e-004 7.84e-005 5.22e-005 3.45e-005

1.00e-003 7.11e-004 5.01e-004 3.49e-004 2.42e-004 1.65e-004 1.12e-004 7.53e-005 5.01e-005 3.30e-005

4.00 4.10 4.20 4.30 4.40 4.50 4.60 4.70 4.80 4.90

3.17e-005 2.07e-005 1.33e-005 8.54e-006 5.41e-006 3.40e-006 2.11e-006 1.30e-006 7.93e-007 4.79e-007

3.04e-005 1.98e-005 1.28e-005 8.16e-006 5.17e-006 3.24e-006 2.01e-006 1.24e-006 7.55e-007 4.55e-007

2.91e-005 1.89e-005 1.22e-005 7.80e-006 4.94e-006 3.09e-006 1.92e-006 1.18e-006 7.18e-007 4.33e-007

2.79e-005 1.81e-005 1.17e-005 7.46e-006 4.71e-006 2.95e-006 1.83e-006 1.12e-006 6.83e-007 4.11e-007

2.67e-005 1.74e-005 1.12e-005 7.12e-006 4.50e-006 2.81e-006 1.74e-006 1.07e-006 6.49e-007 3.91e-007

2.56e-005 1.66e-005 1.07e-005 6.81e-006 4.29e-006 2.68e-006 1.66e-006 1.02e-006 6.17e-007 3.71e-007

2.45e-005 1.59e-005 1.02e-005 6.50e-006 4.10e-006 2.56e-006 1.58e-006 9.68e-007 5.87e-007 3.52e-007

2.35e-005 1.52e-005 9.77e-006 6.21e-006 3.91e-006 2.44e-006 1.51e-006 9.21e-007 5.58e-007 3.35e-007

2.25e-005 1.46e-005 9.34e-006 5.93e-006 3.73e-006 2.32e-006 1.43e-006 8.76e-007 5.30e-007 3.18e-007

2.16e-005 1.39e-005 8.93e-006 5.67e-006 3.56e-006 2.22e-006 1.37e-006 8.34e-007 5.04e-007 3.02e-007

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z (Values of Z from 5.00 to 9.99)

Single–Tail Z Table Z

0.00

0.01

14

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

5.00 5.10 5.20 5.30 5.40 5.50 5.60 5.70 5.80 5.90

2.87e-007 1.70e-007 9.96e-008 5.79e-008 3.33e-008 1.90e-008 1.07e-008 5.99e-009 3.32e-009 1.82e-009

2.72e-007 1.61e-007 9.44e-008 5.48e-008 3.15e-008 1.79e-008 1.01e-008 5.65e-009 3.12e-009 1.71e-009

2.58e-007 1.53e-007 8.95e-008 5.19e-008 2.98e-008 1.69e-008 9.55e-009 5.33e-009 2.94e-009 1.61e-009

2.45e-007 1.45e-007 8.48e-008 4.91e-008 2.82e-008 1.60e-008 9.01e-009 5.02e-009 2.77e-009 1.51e-009

2.33e-007 1.37e-007 8.03e-008 4.65e-008 2.66e-008 1.51e-008 8.50e-009 4.73e-009 2.61e-009 1.43e-009

2.21e-007 1.30e-007 7.60e-008 4.40e-008 2.52e-008 1.43e-008 8.02e-009 4.46e-009 2.46e-009 1.34e-009

2.10e-007 1.23e-007 7.20e-008 4.16e-008 2.38e-008 1.35e-008 7.57e-009 4.21e-009 2.31e-009 1.26e-009

1.99e-007 1.17e-007 6.82e-008 3.94e-008 2.25e-008 1.27e-008 7.14e-009 3.96e-009 2.18e-009 1.19e-009

1.89e-007 1.11e-007 6.46e-008 3.72e-008 2.13e-008 1.20e-008 6.73e-009 3.74e-009 2.05e-009 1.12e-009

1.79e-007 1.05e-007 6.12e-008 3.52e-008 2.01e-008 1.14e-008 6.35e-009 3.52e-009 1.93e-009 1.05e-009

6.00 6.10 6.20 6.30 6.40 6.50 6.60 6.70 6.80 6.90

9.87e-010 5.30e-010 2.82e-010 1.49e-010 7.77e-011 4.02e-011 2.06e-011 1.04e-011 5.23e-012 2.60e-012

9.28e-010 4.98e-010 2.65e-010 1.40e-010 7.28e-011 3.76e-011 1.92e-011 9.73e-012 4.88e-012 2.42e-012

8.72e-010 4.68e-010 2.49e-010 1.31e-010 6.81e-011 3.52e-011 1.80e-011 9.09e-012 4.55e-012 2.26e-012

8.20e-010 4.39e-010 2.33e-010 1.23e-010 6.38e-011 3.29e-011 1.68e-011 8.48e-012 4.25e-012 2.10e-012

7.71e-010 4.13e-010 2.19e-010 1.15e-010 5.97e-011 3.08e-011 1.57e-011 7.92e-012 3.96e-012 1.96e-012

7.24e-010 3.87e-010 2.05e-010 1.08e-010 5.59e-011 2.88e-011 1.47e-011 7.39e-012 3.69e-012 1.83e-012

6.81e-010 3.64e-010 1.92e-010 1.01e-010 5.24e-011 2.69e-011 1.37e-011 6.90e-012 3.44e-012 1.70e-012

6.40e-010 3.41e-010 1.81e-010 9.45e-011 4.90e-011 2.52e-011 1.28e-011 6.44e-012 3.21e-012 1.58e-012

6.01e-010 3.21e-010 1.69e-010 8.85e-011 4.59e-011 2.35e-011 1.19e-011 6.01e-012 2.99e-012 1.48e-012

5.65e-010 3.01e-010 1.59e-010 8.29e-011 4.29e-011 2.20e-011 1.12e-011 5.61e-012 2.79e-012 1.37e-012

7.00 7.10 7.20 7.30 7.40 7.50 7.60 7.70 7.80 7.90

1.28e-012 6.24e-013 3.01e-013 1.44e-013 6.81e-014 3.19e-014 1.48e-014 6.80e-015 3.10e-015 1.39e-015

1.19e-012 5.80e-013 2.80e-013 1.34e-013 6.31e-014 2.96e-014 1.37e-014 6.29e-015 2.86e-015 1.29e-015

1.11e-012 5.40e-013 2.60e-013 1.24e-013 5.86e-014 2.74e-014 1.27e-014 5.82e-015 2.64e-015 1.19e-015

1.03e-012 5.02e-013 2.41e-013 1.15e-013 5.43e-014 2.54e-014 1.17e-014 5.38e-015 2.44e-015 1.10e-015

9.61e-013 4.67e-013 2.24e-013 1.07e-013 5.03e-014 2.35e-014 1.09e-014 4.97e-015 2.25e-015 1.01e-015

8.95e-013 4.34e-013 2.08e-013 9.91e-014 4.67e-014 2.18e-014 1.00e-014 4.59e-015 2.08e-015 9.33e-016

8.33e-013 4.03e-013 1.94e-013 9.20e-014 4.33e-014 2.02e-014 9.30e-015 4.25e-015 1.92e-015 8.60e-016

7.75e-013 3.75e-013 1.80e-013 8.53e-014 4.01e-014 1.87e-014 8.60e-015 3.92e-015 1.77e-015 7.93e-016

7.21e-013 3.49e-013 1.67e-013 7.91e-014 3.72e-014 1.73e-014 7.95e-015 3.63e-015 1.64e-015 7.32e-016

6.71e-013 3.24e-013 1.55e-013 7.34e-014 3.44e-014 1.60e-014 7.36e-015 3.35e-015 1.51e-015 6.75e-016

8.00 8.10 8.20 8.30 8.40 8.50 8.60 8.70 8.80 8.90

6.22e-016 2.75e-016 1.20e-016 5.21e-017 2.23e-017 9.48e-018 3.99e-018 1.66e-018 6.84e-019 2.79e-019

5.74e-016 2.53e-016 1.11e-016 4.79e-017 2.05e-017 8.70e-018 3.65e-018 1.52e-018 6.26e-019 2.55e-019

5.29e-016 2.33e-016 1.02e-016 4.40e-017 1.88e-017 7.98e-018 3.35e-018 1.39e-018 5.72e-019 2.33e-019

4.87e-016 2.15e-016 9.36e-017 4.04e-017 1.73e-017 7.32e-018 3.07e-018 1.27e-018 5.23e-019 2.13e-019

4.49e-016 1.98e-016 8.61e-017 3.71e-017 1.59e-017 6.71e-018 2.81e-018 1.17e-018 4.79e-019 1.95e-019

4.14e-016 1.82e-016 7.92e-017 3.41e-017 1.46e-017 6.15e-018 2.57e-018 1.07e-018 4.38e-019 1.78e-019

3.81e-016 1.68e-016 7.28e-017 3.14e-017 1.34e-017 5.64e-018 2.36e-018 9.76e-019 4.00e-019 1.62e-019

3.51e-016 1.54e-016 6.70e-017 2.88e-017 1.23e-017 5.17e-018 2.16e-018 8.93e-019 3.66e-019 1.48e-019

3.24e-016 1.42e-016 6.16e-017 2.65e-017 1.13e-017 4.74e-018 1.98e-018 8.17e-019 3.34e-019 1.35e-019

2.98e-016 1.31e-016 5.66e-017 2.43e-017 1.03e-017 4.35e-018 1.81e-018 7.48e-019 3.06e-019 1.24e-019

9.00 9.10 9.20 9.30 9.40 9.50 9.60 9.70 9.80 9.90

1.13e-019 4.52e-020 1.79e-020 7.02e-021 2.73e-021 1.05e-021 4.00e-022 1.51e-022 5.63e-023 2.08e-023

1.03e-019 4.12e-020 1.63e-020 6.39e-021 2.48e-021 9.53e-022 3.63e-022 1.37e-022 5.10e-023 1.88e-023

9.40e-020 3.76e-020 1.49e-020 5.82e-021 2.26e-021 8.66e-022 3.29e-022 1.24e-022 4.62e-023 1.70e-023

8.58e-020 3.42e-020 1.35e-020 5.29e-021 2.05e-021 7.86e-022 2.99e-022 1.12e-022 4.18e-023 1.54e-023

7.83e-020 3.12e-020 1.23e-020 4.82e-021 1.86e-021 7.14e-022 2.71e-022 1.02e-022 3.79e-023 1.39e-023

7.15e-020 2.85e-020 1.12e-020 4.38e-021 1.69e-021 6.48e-022 2.46e-022 9.22e-023 3.43e-023 1.26e-023

6.52e-020 2.59e-020 1.02e-020 3.99e-021 1.54e-021 5.89e-022 2.23e-022 8.36e-023 3.10e-023 1.14e-023

5.95e-020 2.37e-020 9.31e-021 3.63e-021 1.40e-021 5.35e-022 2.02e-022 7.57e-023 2.81e-023 1.03e-023

5.43e-020 2.16e-020 8.47e-021 3.30e-021 1.27e-021 4.85e-022 1.83e-022 6.86e-023 2.54e-023 9.32e-024

4.95e-020 1.96e-020 7.71e-021 3.00e-021 1.16e-021 4.40e-022 1.66e-022 6.21e-023 2.30e-023 8.43e-024

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Abridged Process Sigma Conversion Table

Long-Term Yield 99.99966% 99.9995% 99.9992% 99.9990% 99.9980% 99.9970% 99.9960% 99.9930% 99.9900% 99.9850% 99.9770% 99.9670% 99.9520% 99.9320% 99.9040% 99.8650% 99.8140% 99.7450% 99.6540% 99.5340% 99.3790% 99.1810% 98.930% 98.610% 98.220% 97.730% 97.130% 96.410% 95.540% 94.520% 93.320% 91.920% 90.320% 88.50% 86.50% 84.20% 81.60% 78.80% 75.80% 72.60% 69.20% 65.60% 61.80% 58.00% 54.00% 50% 46% 43% 39% 35% 31% 28% 25% 22% 19% 16% 14% 12% 10% 8%

ST Process Sigma 6.0 5.9 5.8 5.7 5.6 5.5 5.4 5.3 5.2 5.1 5.0 4.9 4.8 4.7 4.6 4.5 4.4 4.3 4.2 4.1 4.0 3.9 3.8 3.7 3.6 3.5 3.4 3.3 3.2 3.1 3.0 2.9 2.8 2.7 2.6 2.5 2.4 2.3 2.2 2.1 2.0 1.9 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

Defects Per 1,000,000 3.4 5 8 10 20 30 40 70 100 150 230 330 480 680 960 1,350 1,860 2,550 3,460 4,660 6,210 8,190 10,700 13,900 17,800 22,700 28,700 35,900 44,600 54,800 66,800 80,800 96,800 115,000 135,000 158,000 184,000 212,000 242,000 274,000 308,000 344,000 382,000 420,000 460,000 500,000 540,000 570,000 610,000 650,000 690,000 720,000 750,000 780,000 810,000 840,000 860,000 880,000 900,000 920,000

Defects Per 100,000 0.34 0.5 0.8 1 2 3 4 7 10 15 23 33 48 68 96 135 186 255 346 466 621 819 1,070 1,390 1,780 2,270 2,870 3,590 4,460 5,480 6,680 8,080 9,680 11,500 13,500 15,800 18,400 21,200 24,200 27,400 30,800 34,400 38,200 42,000 46,000 50,000 54,000 57,000 61,000 65,000 69,000 72,000 75,000 78,000 81,000 84,000 86,000 88,000 90,000 92,000

Defects Per 10,000 0.034 0.05 0.08 0.1 0.2 0.3 0.4 0.7 1.0 1.5 2.3 3.3 4.8 6.8 9.6 13.5 18.6 25.5 34.6 46.6 62.1 81.9 107 139 178 227 287 359 446 548 668 808 968 1,150 1,350 1,580 1,840 2,120 2,420 2,740 3,080 3,440 3,820 4,200 4,600 5,000 5,400 5,700 6,100 6,500 6,900 7,200 7,500 7,800 8,100 8,400 8,600 8,800 9,000 9,200

15

Defects Per 1,000 0.0034 0.005 0.008 0.01 0.02 0.03 0.04 0.07 0.1 0.15 0.23 0.33 0.48 0.68 0.96 1.35 1.86 2.55 3.46 4.66 6.21 8.19 10.7 13.9 17.8 22.7 28.7 35.9 44.6 54.8 66.8 80.8 96.8 115 135 158 184 212 242 274 308 344 382 420 460 500 540 570 610 650 690 720 750 780 810 840 860 880 900 920

Defects Per 100 0.00034 0.0005 0.0008 0.001 0.002 0.003 0.004 0.007 0.01 0.015 0.023 0.033 0.048 0.068 0.096 0.135 0.186 0.255 0.346 0.466 0.621 0.819 1.07 1.39 1.78 2.27 2.87 3.59 4.46 5.48 6.68 8.08 9.68 11.5 13.5 15.8 18.4 21.2 24.2 27.4 30.8 34.4 38.2 42 46 50 54 57 61 65 69 72 75 78 81 84 86 88 90 92

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Long-Term vs. Short-Term Data

16

Long-Term Data

Y (Continuous)

Short-Term Data

Time

How much variation we observe in a process is influenced by whether we are looking at long-term data or short-term data.

For now, and as a default, treat all data as long-term data. The convention for Six Sigma is to report short-term, as you will see later.

Long-Term:

Why do we report Short-Term Sigma?

Data collected over a long enough period of time and over diverse enough conditions such that it is likely to contain some process shifts and other special causes.

We want to standardize reporting of the best a process can do, given its current capability. Therefore, Short-Term Sigma tells us this.

Short-Term: Data collected over a short enough period of time so that shifts and other special causes are unlikely

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Reporting Sigma Values

17

Short-Term Sigma = Long-Term Sigma + Sigma Shift If “Shift” is unknown, then assume 1.5 Assume that sigma calculated from project data is long-term sigma A rational subgrouping sampling scheme for data collection (in the Measurement Phase) must have been used if you are calculating a shift (other than using 1.5.)

It is possible to calculate short-term, but for most Green Belt projects we do not attempt to do so; instead we use the 1.5 sigma shift rule.

In order to truly calculate short-term sigma, you have to use several rational subgroups. If you did not use a rational sub-grouping sampling scheme for data collection in the Measure phase, it will not be possible to calculate actual short-term sigma. (Therefore, add 1.5 to long-term sigma.)

Special Cause = Between subgroup variation due to assignable causes, non-random influences. Common Cause = Within subgroup variation, inherent in a process, random influences.

To ensure you are sampling* properly, these 3 items must be true: – – –

Representative Data Enough Data (at least 20 subgroups) Measured with something that passes the Gage R&R

*Refer to the workbook for further details on sampling (Tools > Measure phase)

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Principles Of Rational Subgrouping

18

1. Never knowingly subgroup unlike things together 2. Minimize variation within each subgroup –

Group homogeneous units, within a logic, within a reason

3. Maximize variation between subgroups –

The Xbar shows differences between subgroups that are bigger than that shown within subgroups

4. Treat the chart in accordance with the use of the data – – –

Subgroup frequency should reflect the process Use individuals with limited data Use subgroups when logical

Rational subgrouping refers to grouping the data for analysis in a meaningful way to understand variation. Rational subgrouping attempts to select groups of data such that mainly common cause variation is within groups, and mainly special cause variation is between groups.

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Generalizing The Correction

19

Six Sigma Centered Process Capability

.0005 ppm

LSL LSL

.0005 ppm

T T

± 6σ

USL USL USL

Six Sigma Shifted 1.5σ µµ

3.4 ppm

TT LSL

USL

4.5σ

The 1.5 shift is used as a compensatory off-set in the mean to generally account for dynamic non-random variations in process centering. It represents the average amount of change in a typical process over many cycles of that process. If the process is centered, then Six Sigma capability means that 6 standard deviations fit between the mean and the specification limit. If the process center “shifts” by 1.5 sigma , then the average is 4.5 sigma from either the LSL or USL. Six Sigma Short-Term Capability = 4.5 Sigma LongTerm Capability Zero Sigma Short-Term Capability = -1.5 Sigma LongTerm Capability © GE Capital, Inc., 2000 DMAIC GB O TX PG

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The Universal Equation For Z

20

. . . so what are the possibilities?

SL

=USL LSL

Z=

λ=

SL - λ σ

T (Target) µ (Mean)

Z = st (short-term) lt (long-term)

σst σlt

and how do we choose the right one? Z LT =

SL − µ σ LT

The larger the ZShift , the greater the control problem. Typical ZShift = 1.5

Long-term is what is actually going on in the process. SL - m is the distance the specification is from the mean.

ZST =

SL − T σ ST

Short -term is the best the process can do. SL - T is the distance the specification is from the target. ZST is bigger than

ZShift = ZST − Z LT

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Z-Bench

21

Short-Term Long-Term P(d)LSL

LSL

T

USL

SL - µ σ lt

Zst =

USL- µ σ lt

P(d)USL = from Z table

ZLSL=

SL - T σst

Z-Bench-Short-Term

Z-Bench-Long-Term ZUSL=

_ x

Z-Short-Term

Z-Long-Term Zlt =

P(d)USL

µ - LSL

σ lt

P(d)LSL = from Z table

P(d)Total = P(d)USL + P(d)LSL ZB-lt = from Z table

ZUSL=

USL- T σ st

P(d)USL = from Z table

ZLSL=

T - LSL σ st

P(d)LSL = from Z table

P(d)Total = P(d)USL + P(d)LSL ZB-st = from Z table

In Six Sigma, it is common to report out process capability using ZBench. As shown previously, ZBench corresponds to yield, i.e., we look at the chance of being outside the specification limit on either side. ZBench is calculated for both short and long-term. The difference between the two is ZShift.

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Activity–Calculating Process Capability–Continuous Data

22

What is the process capability for a process that has: Mean = 5 Standard Deviation = 2 Upper Spec. Limit = 9

You can use the hand calculation or you can open the spreadsheet: SIGMACAL.xls. Enter: Xbar: 5 S: 2 USL: 9 LSL: (leave blank) Note: This gives you ZST (the 1.5 shift was added to ZLT).

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Graphically Analyze Data–Breakout Activity (20 minutes)

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Desired Outcome: Graphical Analysis of Capital Logistics Project Y Data Minitab File: GB Case Study.mtw What

How

Who

Timing

Run Chart

Use the Run Chart tool in Minitab to investigate the variation in the project Y data over time

All

5 mins.

Shape, Normality, Central Tendency And Spread

Use the Normal Probability Plot in Minitab to analyze the shape of the project Y data

All

10 mins.

All

5 mins.

Use the Descriptive Statistics tool in Minitab to analyze the shape, normality, central tendency and spread of the project Y data Use the Minitab Six Sigma Process Report to calculate Process Sigma

Solutions

You can check your answers using the solution sheets on the following pages

We always analyze the data this way: 1. Look at Stability–Is the process Stable? 2. Look at Shape–Do I have a normal distribution? 3. Look at the Spread–What measure of dispersion should I use? Recall from our Case Study: Time *(minutes early or late) = (Target Arrival Time) – (Actual Arrival Time) Date 1 = Date of Shipment * Spec. for time = ± 60 min.

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Solution–Run Chart

24

Stability Calculations for Case study data.

First Step, Check Stability Stat > Quality Tools > Run Chart

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Solution–Run Chart

25

1. Double click on “C5”

2. Double click on “C1” Each Date is a subgroup 3. Click ”OK”

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Solution–Run Chart

26

Each Date is a column of data points.

Run Chart for time

time

100

0

Median

Each column has it’s mean plotted as a red square

-100 2

7

12

17

Subgroup Number Number of runs about median: Expected number of runs: Longest run about median: Approx P-Value for Clustering: Approx P-Value for Mixtures:

10.0000 9.4706 4.0000 0.6050 0.3950

Number of runs up or dow n: Expected number of runs: Longest run up or dow n: Approx P-Value for Trends: Approx P-Value for Oscillation:

9.0000 11.0000 4.0000 0.1118 Spread 0.8882

If these numbers had a value < .05, then the process is unstable.

This Run Chart indicates that the process is stable over time. By using the Run Chart, I’m looking for stability. How do I analyze this chart?

Look at p-values. P > .05 indicates stability. If the process is unstable, look for the most recent stable period and analyze with Minitab. If there is not a most recent stable time period, investigate & remove special causes.

Note: To manipulate data in Minitab: MANIP > Subset worksheet > include/exclude row #’s

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Solution–Normality Testing

27

In Minitab, you can perform a Normality Test (Stat-Basic Statistics-Normality Test). Use the normality test to validate the shape of your data, when the shape is in question.

Normal Probability Plot

.999 .99

Probability

.95 .80 .50 .20 .05 .01 .001 -100

0

100

time Average: -4.40316 StDev: 43.1714 N: 506

Anderson-Darling Normality Test A-Squared: 0.130 P-Value: 0.983

The data is Normal by this test method if the P-value is > = .05

Second Step: Check Shape (Normality) Stat > Basic Statistics > Normality Test (Variable = Time) The results of the Anderson-Darling Normality Test tell you if the data is normal or not. A p-value of greater than or equal to 0.05 means the data is normal. A p-value of less than 0.05 means that the data is not normal. Step 6 will address p-values in more detail.

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Solution–Normality Testing (continued)

28

Descriptive Statistics Variable: time Anderson-Darling Normality Test A-Squared: P-Value:

-100

-60

-20

20

60

100

95% Confidence Interval for Mu

0.130 0.983

Mean StDev Variance Skewness Kurtosis N

-4.4032 43.1714 1863.77 7.65E-02 -1.2E-01 506

Minimum 1st Quartile Median 3rd Quartile Maximum

-114.021 -35.085 -4.956 23.421 120.046

This data is normal .

95% Confidence Interval for Mu -8.174 -10

-5

0

40.665

95% Confidence Interval for Median

-0.633

95% Confidence Interval for Sigma 46.009

95% Confidence Interval for Median -9.369

0.532

Third Step: Check Spread The graphical summary of descriptive statistics (Stat– Basic Statistics–Descriptive.) Stat > Basic Statistics > Display Descriptive Statistics Variable = Time Click on “Graphs” & choose “Graphical Summary” Test p-value. Minitab will always display a normal curve based on the data’s mean and standard deviation –this may not be a fit to the actual distribution.

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Minitab Six Sigma Process Report

29

MINITAB FILE: GB case study.mtw

1. Double Click C5 time

2. Double click C1 to use Date1 as the Subgroup size 3. Type in Lower and Upper specs 4. Click OK

Now let’s look at how to calculate process capability for continuous data in Minitab, using the Six Sigma Process Report. The subgroup size can be entered in two different ways:

Size of each subgroup –10 (subgroup size must be constant)

ID column–oper 50 (subgroup size may be constant or not)

Warning: If you choose to use a subgroup size of 1, the short-term values calculated in the Six Sigma Process Report will be invalid since there is not variation within the groups.

The Six Sigma Process Report is used to calculate the long-term and short-term z-values of your process. In order to be accurate in the calculation of the z-values, it is important that we enter all of the information available. If a target is available, then enter the target value for the calculation of the z-values. If the upper and lower specification limits are entered and the target is left blank, Minitab approximates the target value as the midpoint of the specific range. If only one specification limit is entered and the target is left blank, then Minitab approximates the target as the mean of the data. Hence, when the target is available, always input the given value to avoid approximations made by Minitab.

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Minitab Six Sigma Process Report

30

Report 1: Executive Summary Process Demographics

Process Performance Actual (LT) Potential (ST)

Date: Reported by:

LSL

Project:

USL

Department: Process: Characteristic: Units:

-100

0

100

1,000,000

Actual (LT) Potential (ST)

Upper Spec:

60

Lower Spec:

-60

Nominal: Opportunity:

100,000

10,000

Process Benchmarks

1000

Actual (LT) Potential (ST)

100

Sigma (Z.Bench)

0.97

0.98

10

PPM

166781 164350

1

0

5

10

15

Report 1 contains the essence:

Sigma potential (ST) = ZBench-ST: if you were to use just one number to indicate the capability of your process, it is this one. If a firm XY claims to be a 5σ company, they talk about this value. If you only see ZST, it means ZBench-ST. It is a convention to benchmark other companies using this value. However, it is a good practice to report out both ZBench values, for the short and long-term.

Sigma actual (LT) = ZBench-LT: this value corresponds to the actual performance of your process, and is easier to comprehend with PPM.

PPM actual = DPMO actual: the actual number of defects per million opportunities that the process produces.

PPM potential (not so important): corresponds to ZBench-ST, not commonly used.

Upper graph: show short (dotted) and long-term (full line) distributions. By definition, the short-term distribution is shown to be on target. In this case, the long-term distribution is slightly below the target.

Lower graph: shows cumulative PPM’s.

Note: When reporting ZST, determine if you will be using the shift calculated from your data or the standard 1.5 shift. If using the 1.5 shift, you will need to manually add the 1.5 to ZLT to get ZST. Minitab cannot accommodate a predetermined shift. (When in doubt, use the 1.5 shift and/or consult your BB/MBB).

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Minitab Six Sigma Process Report

31

Report 2: Process Capability for time Xbar and S Chart

Capability Indices

40 30 20 10 0 -10 -20 -30 -40 -50

1. Between Subgroup Variation

X=-4.403 -3.0SL=-30.29

0

Subgroup

2. Within Subgroup Variation

3. Because variation is not out of control, there is no LT Variation

ST

3.0SL=21.49

5

10

15

80 70 60 50 40 30 20 10

3.0SL=61.28

S=42.70 -3.0SL=24.12

Mean

0.0000

-4.4032

StDev

43.1471

43.1714

Z.USL

1.3906

1.4918

Z.LSL

1.3906

1.2878

Z.Bench

0.9767

0.9670

Z.Shift

0.0098

0.0098

P.USL

0.082175

0.067876

P.LSL

0.082175

0.098905

P.Total

0.164350

0.166781

Yield

83.5650

83.3219

PPM

164350

166781

Potential (ST) Capability

Actual (LT) Capability

Cp

0.46

Process Tolerance

Process Tolerance

Cpk

0.43

-129.508

4. This makes sense, we only have 1 month’s worth of data

129.508

I

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-133.981

I

I

60

-60

I

-60

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Specifications

Report 2 is more detailed:

The table to the right side contains all the details of the calculation of ZBench for short and long-term.

The graphs to the left side are called control charts. This subject will be covered in the “control” session of your training. In order to use Minitab’s calculated shift (right column in the table), the “S” chart must be in control (minimize variation within subgroup)

In this example, S chart is out-of-control (one point outside control limits). It does not meet the condition mentioned in the 2nd bullet, therefore, report ZLT = 0.9670. To get ZST: ZST = ZLT + ZShift ZST = 0.9670 + 1.5 = 2.467

Refer to the next 2 pages for rules on using this Process Capability Report.

I

LT

125.175

Pp

0.46

I

Ppk

0.43

I

60

Specifications

Data Source: Time Span: Data Trace:

Note: When reporting ZST, determine if you will be using the shift calculated from your data or the standard 1.5 shift. If using the 1.5 shift, you will need to manually add the 1.5 to ZLT to get ZST. Minitab cannot accommodate a predetermined shift. (When in doubt, use the 1.5 shift and/or consult your BB/MBB).

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Rules For Using The Six Sigma Process Report

32

Rules for Process Capability 1. Ensure the process is stable (Run Chart). If not, remove special causes first. 2. Ensure normal distribution (if not, use DPMO method to calculate capability) 3. For continuous data: use Six Sigma Process Report. If subgroup size > 1 and the S-chart is in-control, then both columns in the table are valid. If the S-chart is out-of control, only the LT column is valid. Add 1.5 to the ZBenchLT to get ZST. 4. If the subgroup size = 1, use LT column only in the Process Report

Use the Decision Flow on the next page to help you!

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Process Capability Decision Flow Is your Process Stable (use Run Chart)?

Yes

No

Do you have Continuous Data?

Yes

Is the Distribution Normal?

No

33

Yes

No

Analyze for Special Causes-

Six Sigma>Product Report, DPMO, L1 (Input D, U and O)

Should not calculate process capability until the process is stable.

•Sigma Conversion Table gives ZST

Unstable process data can only be used to describe the capability of the current data set, not the future capability of the process.

Use Six Sigma> Process Report (Input Data, Specification Limits and Target as appropriate)

Do you have Rational Subgroups?

No

Use Z Bench-LT only and add 1.5 Shift to get Z Bench-ST

•Z LT = Z ST - Z Shift (1.5) •Product Report and L1 give Z Bench

Yes

•Z Bench = Z ST •Z LT = Z Bench - Z Shift (1.5)

Is the SChart incontrol?

No Use Z Bench-LT only and add 1.5 Shift to get Z Bench-ST

Yes Note:

Z ST = Z LT + Zshift Z ST = Z Bench-ST Z LT = Z Bench-LT

Z Bench-LT , Z Bench- ST & Z Shift all valid on the Process Report

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The Normal Curve And Capability

34

Poor Design Capability High Probability of Defective

High Probability of Defective Good Design Capability

LSL

USL Low Probability of Defective

Low Probability of Defective

LSL

USL

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Summary–Z-Value

35

Basic statistical summaries, histograms, dotplots, boxplots, and run charts are used to visualize data and better understand a process The Z-score is a non-dimensional quantity that enables us to compare different processes–it represents the process capability The Z-score is the number of standard deviations that will fit between the mean and the respective specification limit of a normal distribution The Z-score corresponds to yield, or the area under the curve inside the specification limits

Note on Capability:

Capability can be described as any of the following: – ZBenchST = ZST = σST = Sigma CapabilityST = SigmaST = ZBench – ZBenchLT = ZLT = σLT = Sigma CapabilityLT = SigmaLT

In the new BOK, σST and σLT are not recommended ways to describe capability. σST = pooled standard deviation and σLT = standard deviation.

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Summary–Continuous Data Process Capability

36

The Minitab Six Sigma Process Report is used to describe capability with continuous data – –

Displays the actual capability relative to the target distribution By rationally subgrouping (subgroup size >1), long-term capability, short-term capability, and shift are calculated.

Rational Subgrouping refers to grouping the data for analysis in a meaningful way to understand variation. Rational Subgrouping attempts to select groups of data such that mainly common cause variation is within groups, and mainly special cause variation is between groups. – –

Special Cause = Between group variation, due to assignable causes, nonrandom influences Common Cause = Within group variation, inherent in a process, random influences

A subgroup that contains only common cause variation, or random variation, represents the short-term capability of the process or entitlement (ZBench)

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Process Capability & Yield–Discrete Data

37

Calculate the distribution of defects, defects per million opportunity (DPMO) Utilize Z tables to convert DPMO to yield or sigma level Understand the difference between classical, Throughput Yield, and Rolled Throughput Yield Calculate submitted, observed, and escaping defect levels

Classical Yield (YC) = Final Yield Throughput Yield (YTP) = First Pass Yield Rolled Throughput Yield (YRT)

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Definitions

38

Unit (U) The number of parts, sub-assemblies, assemblies, or systems inspected or tested –

Squares: 4 units

Opportunity (OP) A characteristic you inspect or test –

Circles: 5 opportunities per unit

Defect (D) Anything that results in customer dissatisfaction. Anything that results in a non-conformance. –

Black circles: 9 defects

Note: Black dots indicate a defect. Clarification Defect–Any single non-conformance (defect=black dot) Defective–A unit with 1 or more defects. (defective=any square with 1 or more black dots).

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Formulas

39

Defects per Unit DPU = D/U 9/4 = 2.25

Total Opportunities TOP = U*OP 4*5 = 20

Defects per Opportunity (Probability of a Defect) DPO = D/TOP 9/20 = .45

Defects per Million Opportunities DPMO = DPO*1,000,000 .45*1,000,000 = 450,000

Once we calculate DPMO, we go to the Abridged Sigma Table (next page) to get ZBenchST or ZBenchLT

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ConvertingDPMO DPMOTo ToZZST Converting ZST = Reported Sigma (Short-Term) Abridged Process Sigma Conversion Table

Long term D PMO 500,000 460,172 420,740 382,089 344,578 308,538 274,253 241,964 211,855 184,060 158,655 135,666 115,070 96,801 80,757 66,807 54,799 44,565 35,930 28,716 22,750 17,864 13,903 10,724 8,198 6,210 4,661 3,467 2,555 1,866 1,350 968 687 483 337 233 159 108 72 48 32 21 13 9 5 3.4

Actual Sigm a (long term ) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5

40

Reported Sigm a (s hort term ) 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6

ZST = 1.6 for 450,000 DPMO

ZZST ST 2 3 4 5 6

DPMO DPMO 308,538 66,807 6,210 233 3.4

To Calculate Process Sigma:

Go to the Memory Jogger–Abridged Sigma Conversion Table (or use the table above)

Look up the DPMO value and report Short Term Sigma value (always round to poorer performance if between values in the table.)

In our example, we calculated 450,000 DPMO. This value is not found in the table, therefore, we go to 460,000 and report 1.6 as the Short Term Sigma Value. We’re always conservative. Therefore, report the lower value for ZST or ZLT. And, you cannot interpolate, so choose the lower sigma value.

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DPMO Calculation

41

Example Errors Detected 28 – Wrong amount 14 – Wrong address 12 – Improper accounting code

Prepare Invoice

500 Preliminary Invoices

Review Invoice

Fix Errors

446 Accurate Invoices

30 Invoices Mailed Late

Mail Invoice 470 Invoices Mailed On-Time

Customer CTQs

Invoice mailed on date specified

Invoice is error free – Correct address – Correct amount

How would the customer measure the process performance? First, determine the unit, defect opportunities per unit, and the number of defects from each perspective. For this example, assume the process of reviewing and correcting invoices is 100% effective. Use the worksheets on the following pages.

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42

Calculating Process Sigma Discrete Data Method

1. Number of Units processed

500 U = __________

2. Number of Defect Opportunities Per Unit

OP = __________ 3

3. Total number of Defects made (include defects made and later fixed)

72 D = __________

4. Solve for Defects Per Opportunity D DPO = U∗OP =

( 72 ) ( 500 ) ( 3

)

= 0.048

5. Convert DPO to DPMO DPMO = DPO ∗ 1,000,000 = 0.048 ∗ 1,000,000 = 48,000 6. Look up Process Sigma in Abridged Process Sigma Conversion Table

The unit in this case is an invoice. Hence, there are 500 units for this example.

ZST = 3.1

Now calculate the DPMO and determine the capability.

Based on the CTQ’s listed for this example, there are 3 defect opportunities per unit–late, wrong amount, and wrong address. Therefore, the total number of defects is 30 late, 28 wrong amount, and 14 wrong address for a total of 72. Even though the errors on the accounting code were detected and corrected, they are not counted for this process. The CTQ’s stated here are for our external customers. They do not care if our accounting codes are correct; therefore, this “error” is not one of their CTQ’s. If we were to examine this from the perspective of our internal customer, the list of CTQ’s would be different. . © GE Capital, Inc., 2000 DMAIC GB O TX PG

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43

Exercise–Calculating Process Sigma Discrete Data

1. Number of Units processed

U = __________ 500

2. Number of Defect Opportunities Per Unit

3 OP = __________

3. Total number of Defects made

30 D = __________

4. Solve for Defects Per Opportunity DPO =

D U∗OP

=

5. Convert DPO to DPMO DPMO = DPO ∗ 1,000,000 = (

( (

) )(

)

=

) ∗ 1,000,000 =

6. Look up Process Sigma in Abridged Process Sigma Conversion Table

ZST =

Let’s verify our answer using Minitab’s Product Report. 1.

First open a blank worksheet and enter 3 column headings and your data: Defects 30

Units 500

Opportunities 3

2.

Six Sigma > Product Report Defects = Defects Units = Units Opportunities = Opportunities

3.

Click “OK”

4.

Verify ZBench = ZST (from your calculations)

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Activity–Calculating Process Capability–Discrete Data

Project: Billing Product Improvement CTQ: Complete Billing Information Defect: Information missing from bill Unit: A bill Opportunities for defect per unit: 3 (items of information that can be missing on each bill) Out of 50 bills, you find 20 defects What is the sigma level of the process?

What is the DPMO value for this process?

Now let’s look at how to calculate process capability for discrete data in Minitab, using the Six Sigma Product Report.

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Six Sigma Product Report

45

MINITAB FILE: GB case study.mtw

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46

Discrete Data Examples 1. Select Defects, Units 2, & Opportunities

2. Select OK.

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47

Six Sigma Product Report Output

Report 7: Product Performance

Characteristic

Defs

Units

Opps

TotOpps

DPU

DPO

PPM

ZShift

DPMO

U

ZBench

ZST

D 1

89

506

1

506

0.176

0.175889

175889

1.500

2.431

0.175889

175889

1.500

2.431

OP

Total

89

506

In addition to the Product Performance table, Minitab provides two graphical charts for discrete data. The product benchmarks allows one to see visually how the ZBench values compare for each characteristic (8A). To verify our answer: D

=

89

= 0.175889

DPO =

DPMO = DPO ∗ 1,000,000 = 175,889

Go to Abridged Process Sigma Conversion Table,

U ∗ OP

(506 )(1)

Z = 2.4 ST

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48

Yield

Four parts are made 1. After first inspection: 1 passed, 3 failed Rework 3 parts

2. After second inspection: 1 passed, 2 failed Rework 2 parts

3. After third inspection: 1 passed, 1 scrapped What is the Yield of this Process?

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Types Of Yield

49

Classical Yield = YC = 3/4 = 75%

Classical yield is the percent of defect-free parts for the whole process divided by the total number of parts inspected. If we say the yield is 3/4 or 75%, we lose valuable data on the true performance of the process. This loss of insight becomes a barrier to process improvement.

First-Time Yield = YFT = 1/4 = 25%

First-time yield is the percent of defect-free parts divided by the total number of parts inspected for the first time. If we say the yield is 1/4 or 25%, we are really talking about the First-Time Yield (FTY). This is the best yield estimate to drive improvement. This is also Throughput Yield (YTP): the percent of units that pass through an operation without any defects.

Classical Yield: YC = ¾ # parts making it through final inspections = 3 Total # Parts = 4 First-Time Yield YFT = ¼ # Parts that are acceptable after first inspection = 1 Total # Parts = 4 Probability of Single Unit Being Defect-Free (SDF) SDF = P(0) = e-DPU = e-2.25 = .1054 = 10.54% DPU = Defects per unit = 9/4 = 2.25

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Extending The Concept

50

A given process has two operations. Each operation has a throughput yield of 99 %. The rolled yield equals: Process Centered

Op 1

Process Centered

x

Op 2

99%

99%

Without Inspection or Test

Without Inspection or Test

=

Output 98% Without Inspection or Test

. . . There is an 98% probability that any given unit of product could pass through both operations defect free.

Rolled Throughput Yield = YRT = 98%

When the defects of the subsequent operations are independent, rolled throughput yield (YRT) = .99 x .99 = .9808

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Rolled Throughput Yield (YRT)

51

Receive parts from Supplier

99.53% Yield (YTP)

Following Receiving Inspection and Line Fall-out...

97.13% Yield (YTP)

From Machining Operations

94.52% Yield (YTP)

At Test Stands on first attempt

YRT = .9953*.9713 *.9452 = 91.38%

Right First Time

G. Reimer 12/21/94 - Charlotte NC

You can establish a yield for each step of your process. If you have multiple processes, each time you go through additional steps, you lose yield at the end of the process. This is called Rolled Throughput Yield. YRT is calculated by multiplying all the yields together. The more complex the process, the worse the YRT becomes. We waste a lot of time scooping up the spilled paint.

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Quantification Of Defects

52

Knowing the observed defect level and the test effectiveness, we can estimate submitted defects and escaping defects. For example:

Inspection E = 0.8 Submitted DPU Level (DPUS )

DPUS = DPUO + DPUE DPUO = DPUS x E DPUE = DPUS x (1-E)

Escaping DPU Level (DPUE )

Observed DPU Level (DPUO )

Let n denote the number of defects going into an inspection operation.

Example

Let E denote the proportion likelihood of detecting a defect.

If we have a process that is submitting 100 defects (DPUS =100) and our inspection process is 80% effective (E=.8) at finding these defects, then we could observe 80 (DPUO) and 20 would escape to the customer (DPUE).

Inspection catches E*n. The number escaping to the customer is (1-E)*n. If you submit parts with a DPUS level, inspection observes (catches) a DPUO level of E*DPUS = Observed DPU.

E = 0.8 DPUS=100

DPUE=20

The customer sees a product with an escaping DPUE = (1-E)*DPUS. Submitted DPUS = Observed DPUO + Escaping DPUE.

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Quantification Of Defects (continued)

53

Given: Observed Defects = DPU of 0.25 and E = .8 Then: Submitted Defects = DPUS = DPUO /E = (0.25/0.8) = DPUS = 0.31 Escaping Defects = DPUE = DPUS - DPUO = (0.31 - 0.25) = DPUE = 0.06

Inspection E = 0.8 Submitted DPUS Level = 0.31 (calc)

Escaping DPUE Level = 0.06 (calc)

Observed DPUO Level = 0.25 (given) The only thing that is real is the DPU observed–that is what we caught at inspection. In this example DPUO = .25. A typical value for E = .9. Your operation will differ slightly; in this example E = .8. Review the calculations below: DPUS*.8 = DPUO DPUS = DPUO /.8 DPUE = DPUS- DPUO

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Exercise (15 minutes)

54

Calculating Submitted, Observed and Escaping Defect Levels Given: The requirement is to ship the product with no more than one defect in 500 units shipped The final test is to be performed using automatic test equipment having an effectiveness of 0.95 Knowing the maximum level of escaping defects, we can estimate the maximum defect/unit level: Observed in the final test. (This sets a minimum throughput yield limit.) Submitted to the final test. (This sets a minimum on the combination of defects created in model assembly and from the escaping defect levels from prior tests.)

Use the worksheet on the following page to help you work through this exercise.

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Exercise (continued)

55

Calculating Submitted, Observed and Escaping Defect Levels

Inspection E = 0.95 Submitted DPUS Level

Escaping DPUE Level

Observed DPUO Level

1. Expressed as a decimal, what is the given acceptable maximum escaping defect level? ___________ 2. What then is the acceptable maximum defect level for: a. Units submitted to final test? ___________ b. Defects observed at final test? __________ 3. What is the observed throughput yield figure? ______

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Answers To Exercise

56

Calculating Submitted, Observed, and Escaping Defect Levels 1. DPUE = 1 = 0.002 500 2.

Maximum acceptable submitted defects = DPUS = defects escaping = DPUE = 0.002 = 0.040 DPUS 0.05 1 - effectiveness 1 -E

2b. Maximum acceptable observed defects = DPUO = DPUS - DPUE = 0.040 - 0.002 = 0.038 DPUO 3. YTP = 1-.038 = .962 = 96.2%

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Summary–Discrete Data Process Capability

57

Define defects, units and opportunities with your team. Be sure the definitions make sense and are consistent with similar processes and customer definitions. Defects will be stated as defects per million opportunities. Discrete data is generally considered long-term data. For discrete data, Minitab Six Sigma product report is used to calculate capability from defects and opportunities Determine DPMO (which is long-term), then determine the corresponding Z–value (ST capability)

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Summary–Z-Shift

58

Often, you must assume a shift value (default 1.5) to estimate short-term capability Our customers experience the long-term capability of the process To minimize shift, we need to reduce special cause variation

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Analyze 5–Define Performance Objectives

1

What does it mean to Define Performance Objectives? A performance objective is a statement of your project Y’s performance level that will satisfy the project CTQ(s). It is the projected reduction in defects you plan to achieve for your process or product. Typically, this is stated in terms of defects per million opportunities (DPMO) reduction and a corresponding target Z-value. In Step 4 you determined the current process performance. In Step 5 you will state what the end results of the Six Sigma project will be by statistically defining the goal of the project. In addition, an estimate of financial benefits is due in Analyze. Why is it important to Define Performance Objectives? It is important to identify your improvement goals in measurable terms in order to define the level of improvement you wish to achieve and provide a focused target toward which you can direct your efforts. What are the project tasks for completing Analyze 5? 5.1 Identify Performance Objectives.

ANALYZE STEP OVERVIEW

Analyze 4: Establish Process Capability

Analyze 5: Define Performance Objectives

Analyze 6: Identify Variation Sources

5.1 Identify Performance Objectives.

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How Do I Define My Performance Objectives?

2

Use benchmarking Use other sources

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Defining Performance Objectives With Benchmarking

3

If I benchmark, performance standards are based upon: Closing the gap with the competition Exceeded projected competitive performance Similar performance in dissimilar businesses Gathering best practices from multiple sources to become best in class Becoming as good or better than a substitute product/service

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Defining Performance Objectives With Other Sources

4

If I don’t benchmark, performance objectives are based upon: For a process with ZST ≤ 3 Sigma Capability, decrease % defects by 10x and for ZST > 3, decrease % defects by 2x If your process is in statistical control (Run Chart), the next improved performance objective comes from a capability investment as in facilities, equipment, digitization, etc. Corporate mandate Compliance/legal VOC data

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Nature Of Benchmarking–Reference Material

5

Benchmarking is the process of continually searching for the best methods, practices and processes, and either adopting or adapting their good features and implementing them to become the “best of the best”.

The remaining pages are for your reference on Benchmarking. There are different types of Benchmarking. These include: Competitive Benchmarking Product Benchmarking Process Benchmarking Best Practices Benchmarking

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What It Is And What It Isn’t Benchmarking Is… A continuous process A process of investigation that provides valuable information A process of learning from others; a pragmatic search for ideas A time-consuming, laborintensive process requiring discipline A viable tool that provides useful information for improving virtually any business process

6

Benchmarking Isn’t… A one-time event A process of investigation that provides simple answers Copying, imitating Quick and easy

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Common Benchmarking Mistakes

7

1. Internal process(es) is unexamined 2. Site visits “feel good,” but don’t elicit data or ideas 3. Questions and goals are vague 4. The effort is too broad or has too many parameters 5. The focus is not on processes 6. The team is not committed to the effort 7. Homework and/or advanced research isn’t assigned 8. The wrong benchmarking partner is selected 9. The effort fails to look outside the industry (outside the box) 10. No follow-up action is taken

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Benchmarking Six-Step Process

8

Identify Process to Benchmark

Select process and define defect and opportunities Measure current process capability and establish goal Understand detailed process that needs improvement

Select Organization to Benchmark

Outline industries/functions which perform your process Formulate list of world class performers Contact the organization and network through to key contact

Prepare for the Visit

Research the organization and ground yourself in their processes Develop a detailed questionnaire to obtain desired information Set up logistics and send preliminary documents to organization

Visit the Organization

Feel comfortable with and confident about your homework Foster the right atmosphere to maximize results Conclude in thanking organization and ensure follow-up if necessary

Debrief & Develop an Action Plan

Review team observations and compile report of visit Compile list of best practices and match to improvement needs Structure action items, identify owners and move into Improve phase

Retain and Communicate

Report out to business management and 6σ leaders Post findings and/or visit report on local server/6σ bulletin board Enter information on GE Intranet benchmarking project database

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Sources Of Information Library Database Internal Reviews Internal Publications Professional Associations Industry Publications Special Industry Reports Functional Trade Publications Seminars Industry Data Firms Industry Experts University Sources

9

Company Watches Newspapers Advertisements Newsletters Original Research Customer Feedback Supplier Feedback Telephone Surveys Inquiry Service Networks Worldwide Web

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Capital Logistics Case Study

10

Project Goal(s) Reduction of deliveries that are too early or too late

Benchmarking Process Identified 20 similar 3rd party Logistics providers from Logistician Magazine Selected 3PL (2) that provide supply chain solutions to the petroleum industry (Non-competitors–Capital Logistics strategically avoids supporting petroleum industry because of risks) Polled logistics managers (telephone polls) to determine delivery practices

Results Identified one viable new delivery method…The Dynamic Routing System – Computer system that selects routes based on individual driver performance for load types and regional deliveries

Invited Petro-hauz to Stamford, CT for product demo with Capital Logistics Engineering and Technology Teams

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Benchmarking Example

11

For the Capital Logistics Case Study – Target is the same = 0 minutes – Best in Class performance is a s = 12 minutes – Theoretical calculation of Sigma based on normal distribution would be Report 7: Product Performance

Characteristic

1

Defs

Units

Opps

TotOpps

DPU

DPO

60

25000

1

25000

0.002

0.002400

PPM

2400

ZShift

ZBench

1.500

4.320

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Summary–Analyze 5

12

A performance objective is determined by using Z–short-term, benchmarking, or defect reduction goals Benchmarking is a process of identifying best practices, measuring our own practices against those best practices, and adapting the appropriate best practices to our own processes Revenue & cost implications are also due for benefit analysis

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Analyze 6–Identify Variation Sources

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What does it mean to Identify Variation Sources? In step 6 you develop a list of statistically significant X’s, chosen based on analysis of historical data. This list is then prioritized to identify those X’s that have the most impact on the project Y. The question in this step is “What are the variables that are preventing us from reaching our goal?” You will identify all possible X’s before selecting the Critical (or Vital Few) X’s in the next step. Why is it important to Identify Variation Sources? The output of a process (Y) is a function of the input sources of variation (X’s). In other words, you can change the output of a process (Y) only by changing the input & process variables (X’s). Therefore, in order to improve products and processes, you must shift your focus from monitoring the outputs of a process (Y’s) to optimizing the inputs to the process and correcting the root causes of defects (X’s). You should use data and process analysis to identify potential X’s, and not make any assumptions. What are the project tasks for completing Analyze 6? 6.1 Identify possible causes of variation 6.2 Narrow list of potential causes

ANALYZE STEP OVERVIEW

Analyze 4: Establish Process Capability

Analyze 5: Define Performance Objectives

Analyze 6: Identify Variation Sources

6.1 Identify possible causes of variation 6.2 Narrow list of potential causes

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Identify The Vital Few

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Transfer Function

Y

Project Y

f

(X)

Relationship that explains Y in terms of X

Process variables

=

Understanding The ƒ Gives Insight Into The Vital Few X’s The Project Y (or dependent variable) is determined by the values of the process variables X (or independent variables). Once we have a clearer understanding of the relationship between the X and Y (f–transfer function), we will be able to pinpoint the key X’s that drive the variation in Y.

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Identify The Vital Few

3

Process

Input Measures (X’s)

Outputs (Y’s)

X

X

X

X

Process Measures (X’s)

Definitions:

Process

Project Y (Dependent Variable)

Provides context for improvement

Product or service produced or delivered by the process

Links outputs (Y’s) to inputs (X’s) and process variables (X’s)

Process X’s (Independent Variable)

Those variables that influence the output and are generally controllable by those who operate the process

Input X’s (Independent Variable)

Materials and information used by the process to create the outputs. Inputs are often outside the control of the process operator.

In Analyze 6 we will be analyzing upstream variables, or input and process variables (X’s), to determine how they affect output variables (Y’s) and to what extent. Remember

Y=f (X1, X2, ..., Xn)

or in words…. The results we get (the Y’s) are a function of the process and input variables (the X’s). In Analyze, we will study the process and the data in order to gain understanding of how it all fits together. © GE Capital, Inc., 2000 DMAIC GB Q TX PG

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Analyze 6.1: Identify Possible Causes of Variation

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Methods To Identify Possible Sources Of Variation

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Methods To Identify Vital X’s

Process Map Analysis

Graphical Analysis

Machines

Methods

Materials

Problem Statement Measurement

Mother Nature

People

As we work our way down into the process seeking the vital few causes, we analyze both the data and the process–gaining knowledge of what impacts the output. How do the various X’s impact the Y’s? With this knowledge, we will pursue a solution that will improve the process. We have already learned about graphical analysis, process map analysis and cause and effect analysis in previous modules. In step 6, we will learn how to apply them in the Analyze phase.

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Review: Graphical Analysis

6

Looking For Patterns In Data Continuous Y Boxplot Scatterplot Histogram

Discrete Y Pareto Chart

We learned about these tools in the Minitab and Graphical Analysis module. These graphical analysis tools are used in the Analyze phase to look for patterns in the project Y data that help to identify potential critical X’s. Let’s do an activity to briefly review these tools.

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Review Activity–Which Graphical Analysis Tool Would You Use?

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For each scenario described below, which tool would you use to investigate? For each scenario, what pattern would you look for to make your conclusions? 1. (a) A Six Sigma project is being conducted in the field to improve the cycle time for warranty repair returns. The warranty return cycle time was measured for a period of 6 weeks for 4 regions. The Green Belt wants to investigate whether there is any difference in average warranty repair cycle time between each of the regions. (b) The Green Belt would also like to know if there is any difference in the variance of the cycle time between each of the regions. 2. Checks Are Us is a payroll processing firm. Timecard errors are routinely monitored and recorded. A Black Belt investigating the errors wishes to determine if there are any differences in the number of errors between five of its major customers. The number of errors contained in a sample of 150 employees was recorded for five weeks. How would you proceed with stratifying the data to make this investigation? 3. Tungsten steel erosion shields are fitted to the low pressure blading in steam turbines. The most important feature of a shield is its resistance to wear. Resistance to wear can be measured by abrasion loss, which is thought to be associated with the hardness of steel. How would you investigate the relationship between hardness (the X) and abrasion loss (the Y)?

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Graphical Analysis–Breakout Activity (15 minutes)

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Desired Outcome: Identify possible causes of variation in the Capital Logistics case study data. File: Green Belt Case Study.mtw What Minitab Analysis

How Use the appropriate graphical analysis tool in Minitab to investigate

Who

Timing

All

15 mins.

– Differences in delivery cycle time between the two different load types (See note below) – Differences in delivery time between drivers – Relationship between delivery cycle time and distance Report Out

Be prepared to share your results with the class

All

Load types: D/H Drop & Hook–A driver unhooks their full trailer, and then hooks into an empty to take back. Unload–The driver opens the trailer and allows the store to unload its freight, and brings back the trailer. To create Boxplots: Stat > Basic Statistics: > Display Descriptive Statistics variable: time click: by variable: load type or driver click Graph > Choose Boxplots To create Scatter Plots: Graph > Plot X: Distance Y: Time

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Process Map Analysis

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Types Of Analysis Moments of truth–What does the customer feel? Nature of work–What is of value to the customer? Flow of work–What makes the customer wait?

The purpose of Process Map Analysis is to:

View our process and its performance from the customer’s perspective

Identify current process problems and opportunities

Create a shared sense of urgency for improving the process clearly identify and document valueadded/nonvalue-added activities and process flow measures and characteristics.

The second, Nature of Work, is concerned with value analysis: understanding whether or not the work in your process is valued by the customer or by your internal culture. The third, Flow of Work, characterizes the work along the dimension of time. The two latter components are focused on the “Profitability” piece of the GE Capital Quality Vision.

There are three key components to the Process Map Analysis step: The first, Moments of Truth, ensures that we are “Completely Satisfying Customer Needs” through a customer-focused process improvement perspective.

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Moments Of Truth

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A Typical Deployment Flow Chart Initial Contact

Service/Produce

Customer

Delivery

Follow-Up

Moments of Truth

Intermediaries Or Front Line Backroom Activity Support Or Suppliers

A moment of truth is defined as anytime a customer draws a critical judgment, positive or negative, about the service, based upon a service experience (or lack thereof). Certainly every time we “touch” the customer is a moment of truth, but it isn’t limited to these cases. From the customer’s view, the process is a set of service encounters. In this case, the customers believe the steps should be simple: apply for the loan and receive the money.

“If you’re a service person and you get it wrong at your point in the customer’s chain of experience, you are very likely erasing from the customer’s mind all the memories of the good treatment he or she may have had up until now. But if you get it right, you have a chance to undo all the wrongs that may have happened before the customer got to you. You really are the moment of truth.”

In the best of cases, the customer is unaware of all the hard work, delays, and hand-offs which go into making their loan a reality. It occurs behind the scenes.

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Nature Of Work–Value Analysis Value-Added Work

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Nonvalue-Added Work

Steps That Are Essential Because They Physically Change The Product/Service, The Customer Is Willing To Pay For Them, And They Are Done Right The First Time.

Steps That Are Considered Non-Essential To Produce And Deliver The Product Or Service To Meet The Customer’s Needs And Requirements. The Customer Is Not Willing To Pay For Them.

Steps That Are Not Essential To The Customer, But That Allow The ValueAdding Tasks To Be Done Better/Faster.

Value-Enabling Work

Your policies address only control issues

There are more managers than workers

People get rewarded for managing problems (e.g., Manager of Reissues, Special Expediting)

Rework is a common characteristic of most processes –

RE’s are things in your process that are done more than one time (Redo, Recall, Reissue).

–

RE’s usually cause you to loop back to an earlier point in your process.

–

RE’s consume time, add to the complexity, and use additional resources.

OPTIONAL: Show the video: “Time the dimension of Quality”

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Types Of Nonvalue–Added Work

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Internal Failure

Delay

External Failure

Preparation/Set-Up

Control/Inspection

Move

What Does The Customer Value?

Internal Failure Steps that are related to correcting in-process errors due to failures in current or prior step in the process. Example:

Rework External Failure Steps which relate to fixing errors in the product that the customer has found and has returned to you. Examples:

Customer Follow-up

Recall Control/Inspection Steps for internal process review often referred to as “the checker-checking-the checker.” Examples:

Approval/review

Inspection

Bureaucracy

Delay Steps where work is waiting to be processed at that step. Examples:

Backlogs

Queues

Storage

Bottlenecks

Preparation/Set-Up Steps that prepare work for a subsequent activity in the process. Examples:

Entering into a computer

Retrieve policies/pricing

Move Steps that entail the physical transport or transmit of outputs between activities in a process. Example:

Fax/mail

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Flow Of Work

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Process Time

+

Delay Time

Cycle Time

To analyze the flow of work, break the process flow down to its lowest component, and analyze the movement of the component through the process. For example, “become an application” and trace its progress through the process. It is similar to a process flowchart, but with the value-added and nonvalue-added steps clearly identified.

Terms Cycle Time The total time from the point in which a customer requests a good or service until the good or service is delivered to the customer. Cycle time includes process time and delay time. Process Time The total time that a unit of work is having something done to it other than time due to delays or waiting. It includes the time taken for value-added steps, internal failure, external failure, control, inspection, preparation/set-up, and more. Delay Time Total time in which a unit of work is waiting to have something done to it.

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Flow Of Work–Process Disconnects

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Gaps Redundancies Implicit or unclear requirements Inefficient hand-offs Conflicting objectives Common problem areas

Process disconnects can often be found where there are delays in the process. These are points in the process where work can be disrupted or delayed, or where defects can be created. They include:

Gaps: responsibility for a given step in the process is unclear, or the process seems to go off track.

Redundancies: duplication of efforts such as when two people or groups approve a document. Redundancies occur when different groups take action that they are unaware is being done somewhere else in the process.

Implicit or unclear requirements: operational definitions do not exist or clear differences exist in perspective or interpretation.

Inefficient hand-offs: no check is in place to assure the process is continuing without delays. For example, Department A sends something to Department B but neither has a way to know if it was properly received. Conflicting objectives: the goals of one group cause problems or errors for another. For example, one group is focused on process speed while another is oriented to error reduction–the result may be that neither group accomplishes its objectives. Common problem areas: occurs when steps are repeated in a variety of places in process. Noting these areas may provide insight into potential solutions.

Your team should encode these “disconnects” and highlight them directly on your process map.

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Flow Of Work–”Be The Unit”

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Unclear requirements 1. Receive application in mail and open envelope 2. Place application in mail slot

Redundancy

5. Retrieve application and review for completeness

Yes

No

10. Review for completeness and make decision

Inefficient hand-off

19. Generate turndown letter

9. Queue application for credit review

3. Move application to Entry Dept.

4. Place application in in-box

Are we extending loan?

11. Make loan decision

Unclear requirements

Is application complete?

Inefficient hand-off

8. Score application

Yes

7. Enter application to computer system

12. Generate loan packet

13. Place in out-box

18. Postman picks up outbound mail

14. Move to mailroom

17. Place in outbound mail basket

15. Wait for postage

16. Post package or letter

No 6. Call to obtain necessary information

Cycle time is the total time taken from the point at which the customer requests a good or service until the good or service is delivered to the customer. It is the sum of the process time, move time, inspect time, delay time, and storage time. Cycle time analysis often provides eye-opening insights. People seldom think of work in this context. When an Improvement Team presents cycle time data, management may become defensive. For example, when one manager at a commercial insurer found out it was taking 100 days, on average, to process the commercial line of a new business, she resisted the analysis. After heated “discussion,” she suggested that the period sampled did not reflect normal conditions. She recommended looking at another period of time to get a “better number.” The team obliged. The next sample averaged 103 days!

Constructing a time line helps identify areas of potential improvement by illustrating the time required for each step in a process. Remember: Time data may not be available for all steps in a process. Some possible sources include:

Time, schedule, and activity logs Files, studies, and reports

If data is not available: Estimate and ten track to determine actual average value

Use minimum of 30 data points to determine an average value when calculating averages, also record the highest and lowest time so consistency is understood. © GE Capital, Inc., 2000

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Linking Value Analysis With Process Flow

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Summarized Analysis Process Step

1 2

Est. Avg. Time (Mins)

1 120 15 120 3 180 7

Value-Added

9

3

4 5 6 7

8 9 10 11 12 13 14 15 16 17 18 19 Total 1 120 5

9

10 15

90 15 120 2 120

99

9

5

8

99

% Total

957

100%

48

5.0%

180

18.8%

8

.8%

690

72.1%

30

3.1%

% Steps

Nonvalue-Added

9

Internal Failure External Failure

9

Delay

9

9

Control/Inspection

9

9

9

9

9

Prep/Set-Up

9

Move Value-Enabling

9 9

Total

Linking value analysis with cycle time analysis creates a compelling business case for change. Displaying this information on process maps emphasizes focus areas for improvement.

1 957

.1% 100%

Conclusion: Example 7 steps (-40% of total steps) provide 100% value and take 48 minutes or 7% of total cycle time. 11 steps (-61% of steps) are non-value-added, and consume 94.9% of cycle time.

Tips/Traps

Don’t get stuck on deciding if a step is value-added or nonvalue-added – Allow the team to discuss it. – Consensus with 2/3s majority vote. Push the team to make the process map a true “as is.” – The ratio for an average “as is” map is 20% valueadded, 80% nonvalue-added. – Think of the process map from the point of view of the product or service. © GE Capital, Inc., 2000

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Review: Cause & Effect Diagrams

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A visual tool used by an improvement team to brainstorm and logically organize possible causes for a specific problem or effect.

Machines

Methods

Materials

Problem Statement

Potential High-Level Causes

Measurement

Mother Nature

People

We learned about this tool in the Measure phase. In the Analyze phase the Cause and Effect diagram is often used to identify X’s.

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Cause & Effect Diagrams–The Five Why’s

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The “Five Why’s” drill deep into the process to identify potential Root Cause(s) Ask “why” five times to identify deeper causes Use process data to answer each “why” question

Example A project team has verified that the X (complicated form) accounts for the difference in cycle times between small and medium loans. They use the Five Why’s to drill deeper in the process.

4. Why is the format confusing? Because the directions are hard to read 5. Why are the directions hard to read? Because the font size is too small

1. Why do complicated forms cause delays in the underwriting steps? Because underwriters receive incomplete applications 2. Why do they receive incomplete applications? Because customers don’t fill out the form accurately or completely 3. Why don’t customers fill out the form accurately or completely? Because the format is confusing © GE Capital, Inc., 2000 DMAIC GB Q TX PG

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Cause And Effect–A Breakout Activity (25 minutes)

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Desired Outcome: Identify possible causes of variation in the Capital Logistics case study data What

How

Who

Timing

Preparation

Select a facilitator, scribe and timekeeper

All

5 mins.

Construct Cause And Effect Diagram

As a result of the QFD constructed in Measure 1 for the Capital Logistics customer service desk, a project team elects a project Y of cycle time to resolve customer problems

All

15 mins.

In the Analyze phase of the project, the team uses a cause and effect diagram to brainstorm potential X’s Construct a cause and effect diagram for the problem statement “Why is it taking too long to resolve customer problems?” Base cause and effect diagram on your general knowledge of customer service desks. What might be potential X’s? Five Why’s

Use the ask “why” approach to identify deeper causes as appropriate

All

Close

Choose a spokesperson to share the results with the class

All

5 mins.

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Prioritization Of X’s–Control/Impact Matrix

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IMPACT High

C O N T R O L

Medium

Low

In Our Control

Out Of Our Control

Always Verify With Data Use your team’s process knowledge and business experience to list possible X’s in a Control/Impact Matrix. Then use process data to verify or disprove placement of the X’s. Prioritization Steps 1. Using the Control/Impact Matrix shown above, examine each X in light of two questions: What is the impact of this X on our process? Is this X in our team’s control or out of our team’s control? 2. With your team, place each X in the appropriate box on the matrix. 3. The validated matrix is a guide to addressing the X’s. Begin with the “High Impact/In Our Control” category. © GE Capital, Inc., 2000 DMAIC GB Q TX PG

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Prioritization Of X’s–Control/Impact Matrix (continued)

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Example Machines

Measurements

Methods

Materials

Mother Nature

People

Why Is There Difference In The Variation In Cycle Time Between Small And Medium Loans?

IMPACT Medium

High

C O N T R O L

In Our Control

Out Of Our Control

Too many defects

Complicated form

Too much review

Duplication of effort

Too long to get credit report

Too long for customer number

Not enough staff

Not well trained

Low

Complexity

Evaluation of risk worthiness

The project team completed the Cause & Effect diagram and the prioritization matrix. The X’s that are identified as “in control/high impact” appear to be the top priority. However, the team should discuss the other X’s to make sure they have reached consensus for those priority X’s.

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Control/Impact Matrix–Breakout Activity (15 minutes)

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Desired Outcome: Practice using a Control/Impact Matrix to prioritize X’s What

How

Who

Timing 2 mins.

Preparation

Choose a facilitator, scribe, timekeeper and/or note taker

All

Construct Cause And Effect Diagram

Review the potential X’s generated for the customer service desk project in the cause and effect diagram activity

All

Prioritize Potential X’s

Use the Control/Impact Matrix on the next page to prioritize the X’s identified by your team

All

10 mins.

Close

Choose a spokesperson to report out on your high impact X’s. Are all of these X’s within the control of the team?

All

3 mins.

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Prioritization Of X’s–Control/impact Matrix

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IMPACT High

C O N T R O L

Medium

Low

In Our Control

Out Of Our Control

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Analyze 6.2 Narrow list of Potential Causes

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The Idea Of Sampling

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Based on the sample, we make decisions about the population.

Population (Universe): A set of characteristics that defines membership in the complete set. Sample: A subset of members that possesses the same characteristics as that of the population. Why should we take a sample? Should the sample be random? Is it possible to have sampling error? How many samples should be taken? What are some everyday examples of sampling? In most cases under study, it is impossible to measure every element of a population. In particular, we want samples that consist of observations that are independent and random. These samples, called random samples, can be used to make decisions about the population. This involves a certain amount of risk. We can minimize this risk, and, more importantly, understand what the risks are if we use statistical tests. If you were interested in finding the average height of all of the people in the United States, what advantages would exist in taking a sample?

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Hypothesis Testing–Introduction

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Refers to the use of statistical analysis to determine if observed differences between two or more data samples are due to random chance or to be true differences in the samples Increase your confidence that probable X’s are statistically significant Used when you need to be confident that a statistical difference exists

An assertion or conjecture about one or more parameters of a population(s).

To determine whether it is true or false, we must examine the entire population, this is impossible!!

Instead, use a random sample to provide evidence that either supports or does not support the hypothesis

The conclusion is then based upon statistical significance

It is important to remember that this conclusion is an inference about the population determined from the sample data

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Hypothesis Testing For Equal Means

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The histograms below show the height of inhabitants of countries A and B. Both samples are of size 100, the scale is the same, and the unit of measurement is inches. Question: Is the population of country B, on average, taller than that of country A?

Country A

Country B 60.0 62.0 64.0 66.0 68.0 70.0 72.0 74.0 76.0 78.0 80.0

[inch]

Issue: how conclusive is the evidence that the sample results indicate a real, more-than-random effect in the underlying population or process? In the Analyze phase we will try to determine which X’s have an effect on the Y. We can compare two sets of data, with X set at different values, thereby determining if that X has an effect. Examples: Does a process perform better using machine/material/fixture/tool A or B? Does the purchased material conform to the desired specifications? Is there a difference in performance between vendor A or B? Is there a difference in your process after you make a change? Is the process on target?

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Concepts Of Hypothesis Testing 1. All processes have variation.

28

2. Samples from one given process may vary.

3. How can we differentiate between sample–based “chance” variation and a true process difference?

To improve processes, we need to identify factors which impact the mean or standard deviation.

This way everyone makes the same decisions.

Once we have identified these factors and made adjustments for improvement, we need to validate actual improvements in our processes. Sometimes we cannot decide graphically or by using calculated statistics (sample mean and standard deviation) if there is a statistically significant difference between processes. In such cases the decision will be subjective. We perform a formal statistical hypothesis test to decide objectively whether there is a difference.

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Kinds Of Differences

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Continuous data: Differences in averages Differences in variation Differences in distribution “shape” of values Discrete data: Differences in proportions

There are a variety of different hypothesis tests. Each one tests for a different kind of “difference.”

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Hypothesis Testing

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Guilty vs. Innocent Example The American justice system can be used to illustrate the concept of hypothesis testing. In America, we assume innocence until proven guilty. This corresponds to the null hypothesis. It requires strong evidence “beyond a reasonable doubt” to convict the defendant. This corresponds to rejecting the null hypothesis and accepting the alternate hypothesis. Ho: person is innocent Ha: person is guilty

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Nature Of Hypothesis

Null Hypothesis (Ho): Usually describes a status quo The one you assume unless otherwise shown The one you reject or fail to reject based upon evidence Signs used in Minitab: = or > or <

31

Alternative Hypothesis (Ha): Usually describes a difference Signs used in Minitab: ≠ or < or >

Note that we are not proving the hypothesis to be true or false. We will reject or fail to reject the null hypothesis based on the evidence from our samples. Failing to reject the null hypothesis implies that the data does not provide sufficient evidence to conclude that a difference exists. On the other hand, rejection of the null hypothesis implies that the sample data provides sufficient evidence to say that a difference exists.

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Activity–Hypothesis Statements (10 minutes)

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Write the null and alternate hypothesis testing statements for each Scenario 1: You have collected delivery time of supplier A and supplier B. You wish to test scenario below: whether or not there is a difference in delivery time from supplier A and B.

Null hypothesis : collected delivery time of supplier A and supplier B. Scenario 1: statement You have You wish to test statement: whether or not there is a difference in delivery time from Alternate hypothesis supplier A and B. Scenario 2: You suspect that there is a difference in cycle time to process purchase orders in site 1 of your company compared to site 2. You are going to perform a hypothesis test to verify your hypothesis. Null hypothesis statement : Null hypothesis statement :

Alternate hypothesis statement: Alternate hypothesis statement:

Scenario 2: You that there is a difference in the cycle time process Scenario 3: You have suspect implemented process improvements to reduce cycle time to to process purchase orders in your havecompany collected cycle time before process purchase orders incompany. site 1 ofYou your compared tothe site 2. You are improvements and after the process improvement was implemented. You are going to perform a going to perform a that hypothesis to verifyhave yourresulted hypothesis. hypothesis test to verify the processtest improvements in a reduction in cycle time.

Null hypothesis statement : Null hypothesis statement : Alternate hypothesis statement:

Alternate hypothesis statement: Scenario 3: You have implemented process improvements to reduce the cycle time to process purchase orders in your company. You have collected cycle time before the process improvements and after the process improvement was implemented. You are going to perform a hypothesis test to verify that the process improvements have resulted in a reduction in cycle time. Null hypothesis statement : Alternate hypothesis statement:

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Hypothesis Testing

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Guilty vs. Innocent Example The only four possible outcomes: 1. An innocent person is set free.

Correct decision

2. An innocent person is jailed.

Type I error = α

– The probability of this type of error occurring we represent as

3. A guilty person is set free.

Type II error = β

– The probability of this type of error occurring we represent as

4. A guilty person is jailed.

Correct decision

Why is it important to minimize the chance of making a Type I error in a six-sigma project?

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Hypothesis Testing–Another View

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Ho: Person is innocent. Ha: Person is guilty.

Truth Truth Ho

Ho

Innocent

Guilty

Innocent, Set Free

Guilty, Set Free Type II β

Innocent, Jailed Type I α

Guilty, Jailed

Set Free Verdict Verdict Ha

Jailed

Ha

This is a visual way of looking at the four possible outcomes of hypothesis testing.

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Hypothesis Testing

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The P-value is calculated by Minitab The probability of getting the observed difference or greater when the Ho is true. If p ≥ 0.05, then there is no statistical evidence of a difference existing. Ranges from 0.0 - 1.0 The alpha (α) level is usually set at 0.05. Alpha is the probability of making a Type I Error (concluding there is a statistical difference between samples when there really is no difference).

P < α: Reject Ho P > α : Accept Ho

The p (probability) value is the statistical measure for the strength of H0, usually reported with a range between 0.0 and 1.0. The higher the p-value, the more evidence we have to support H0, that there is no difference. Think of the null hypothesis as a jury trial: the accused is innocent until proven guilty. In hypothesis testing, the samples are assumed equal until proven not. Since we are usually doing a hypothesis test to prove there is a difference, we are looking for p-values less than 0.05. By convention if p >.05 accept H0 (no difference). If p ≤.05 reject H0 (difference exists).

Accept Ho Not Different

Reject Ho Different 0.00

0.05

1.00

p-value

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Statistical Tests In Minitab

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Some basic statistical tests are shown below with the command for running each test in Minitab. What The Tool Tests Mean of population data is different from an established target. Mean of population 1 is different from mean of population 2. The means of two or more populations is different.

Variance among two or more populations is different.

Statistical Test 1-Sample t-test

Graphical Test Histogram

Stat > Basic Statistics > 1-Sample t

2-Sample t-test

Histogram

Stat > Basic Statistics > 2-Sample t

1-Way ANOVA

Histogram

Stat > ANOVA > One-Way

Homogeneity of Variance

Scatter Plots

Stat > ANOVA > Homogeneity of Variance

Output (Y) changes as the input (X) changes.

Linear Regression

Box Plots

Output counts from two or more subgroups differ.

Data is normally distributed

Chi-Square Test of Independence Stat > Tables > Cross Tabulation OR Chi-Square Test

Frequency

Stat > Regression >Fitted Line Plot

Pareto C AB D E Category

M NO

Normality Test Stat > Basic Statistics

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Select A Statistical Test

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Hypothesis tests to find relationships between project Y and potential X’s

Y Continuous Continuous

X Discrete

Discrete

Simple Linear Regression 2 Sample t-Test (Compare Means of two samples)

Chi-Square Test

ANOVA (Compare means of multiple samples) Homgeneity of Variance (Compare variances)

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Hypothesis Test Summary Normal Data Variance Tests (Continuous Y) X2 - Compares a sample variance to a known population variance. F-test- Compares two sample variances. Homogeneity of Variance Levine’s–Compares two or more sample variances Mean Tests (Continuous Y) T-test One-sample–Tests if sample mean is equal to a known mean or target. T-test Two-sample–Tests if two sample means are equal. ANOVA One-Way–Tests if two or more sample means are equal. ANOVA Two-Way–Tests if means from samples classified by two categories are equal. Correlation–Tests linear relationship between two variables. Regression–Defines the linear relationship between a dependent and independent variable. (Here, “Normality” applies to the residuals of the regression.)

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Non-Normal Data Variance Tests (Continuous Y) Homogeneity of Variance Levine’s–Compares two or more sample variances. Median Tests (Continuous Y) Mood’s Median Test–Another test for two or more medians. More robust to outliers in data. Correlation–Tests linear relationship between two variables. Proportion Tests (Continuous Y) P-Test–Tests if two population proportions are equal. Chi-Square Test–Tests if three or more relative counts are equal.

There are a number of hypothesis tests for both normal and non-normal data. You should consult a Black Belt or Master Black Belt if you are not sure which test to use for you project, or if your project involves non-normal data. The next page shows a summary of the tests that we will look at in detail during this training. We have already looked at the Normality Test in previous modules.

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We Always Look At Our data In This Way 1. 2. 3. 4.

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Check Stability–Run Chart, p-values Check Shape–Anderson-Darling Normality Test Check Spread–Appropriate Hypothesis Test Check Center–Appropriate Hypothesis Test

The remainder of this module will teach you how to choose the correct hypothesis test. Not all material will be covered in class. The instructor will choose the tests to cover, based on time restrictions. Prior to taking the GB certification exam you should review this section and go through the Minitab commands.

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Choosing The Correct Hypothesis Test

Are X’s Discrete?

YES

NO

Is the data normal?

NO

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Mood’s Median HOV

YES

Regression Are Y’s Continuous?

NO

CHI SQUARE (χ2)

YES

Comparing Only 2 Groups?

NO

Multiple Groups ANOVA HOV

YES

Can I Match X’s With X’s?

YES

Paired t Note: In order to use this chart, we are assuming our X’s are discrete. Otherwise, use Regression. Moods Median Test Ho = Median1 = Median 2 = ...Median n Ha = At least one Median is Different Homogeniety of Variance (Hov) – Levene’s Test Ho = σ12 = σ 22 = σ 32 ...σ 2n Ha = At least σ 2 is Different

NO

Are We Comparing To A Standard?

NO

2 Sample t–Test HOV

YES

1 Sample t Paired t-Test Ho = Difference = 0 Ha = Difference ≠ 0 One Sample t-Test Ho = µ = Target Ha = µ ≠ Target Two Sample t-test Ho = µ 1 = µ 2 Ha = µ 1 ≠ µ 2

Chi Square Ho = χ 2 = 0 Ha = χ 2 ≠ 0 Analysis of Variance (ANOVA) Ho = µ 1 = µ 2 = ...µ n Ha = At least one µ is Different © GE Capital, Inc., 2000 DMAIC GB Q TX PG

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Which Hypothesis Testing Tool Would You Use?

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For each scenario described below, which hypothesis testing tool would you use? Assume normal distribution, where appropriate 1. A six-sigma project is being conducted in the field to improve the cycle time for warranty repair returns. The warranty return cycle time was measured for a period of 6 weeks for 4 regions. The Green Belt suspects that there is a difference in average warranty repair cycle time among each of the regions. How would you test whether there is a statistically significant difference in mean cycle time for the different regions? 2. Tungsten steel erosion shields are fitted to the low pressure blading in steam turbines. The most important feature of a shield is its resistance to wear. Resistance to wear can be measured by abrasion loss, which is thought to be associated with the hardness of steel. How would you test whether there is a statistically significant relationship between resistance to wear and abrasion hardness of steel? 3. Your business purchases sheet stock from two different suppliers. It has found an unacceptably large number of defects being caused by thickness beyond tolerance levels. Data for overall mean thickness data was analyzed and found to be on target. Data was collected that would identify a potential difference in the variation of the thickness of the material by supplier. 4. Checks Are Us is a payroll processing firm. Timecard errors are routinely monitored and recorded. A Black Belt investigating the errors wishes to determine if there are any differences in the number of errors among five of its major customers. The number of errors contained in a sample of 150 employees was recorded for five weeks. How would you test if there is a statistically significant difference in the number of errors among the customers?

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Data Analysis

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Stability–Minitab Run Chart

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Let’s look at an example from our GB ANOVA.mpj. Step 1: Check the stability of the processing time for SOUTH Territory. Are there any trends in the data? MINITAB FILE: GB ANOVA.mpj

File Description: Territory (C1): Sales Territory Zone (C2): city within the sales territory Total Time (C3): Processing Time- stacked Territories C4-C8– processing time per territory noted Use Minitab to check the stability of your processing time data by territory. The Run chart is used to look at the stability of data in time order or sequentially ordered. Is the process stable over time for the South Territory?

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Stability–Minitab Chart Stability–Minitab Run Run Chart

44 44

1. Double Click.

2. Type in a “1.”

Process is Stable if all p-Values are > 0.05

It is important to note that the data should be in time order for run charts to be valid. A run is one or more consecutive points in the same direction. A new run begins each time there is a change in direction. Do not count points exactly on the median. Test for Clusters: Ho: No fewer runs observed than expected. Ha: Fewer runs observed than expected. Clusters result from sampling from one process for a period of time and then from another process with a different center for a period so there are fewer runs than expected by sampling error alone. Test for Mixtures: Ho: No more runs observed than expected. Ha: More runs observed than expected. Mixtures result from two or more processes with different centers alternately sampled so there are too many runs than expected by sampling error alone.

Test for Trends: Ho: No fewer runs observed than expected. Ha: More runs observed than expected. Trends result from a gradual increase or decrease in the measure so that there are fewer runs than expected by sampling error alone. Test for Oscillations: Ho: No more runs observed than expected. Ha: More runs observed than expected. Oscillations are similar to mixtures in that they indicate too many runs—more than expected by sampling error alone. Since all p-values are less than 0.05, the process is stable for the south territory. You would also need to check each of the other territories for stability.

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The P-Value Review

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Alpha is the probability of making a Type I error The p-value is the probability of getting the observed difference or greater when Ho is true Unless there is an exception based on engineering judgment, we will set an acceptance level of a Type I error at a = 0.05 Thus, any p-value less than 0.05 means we reject the null hypothesis

p < α: Reject Ho p > α: Accept Ho The alpha is another decision criteria. It will give you the same conclusions as the confidence interval. In general, comparing p-value to alpha is the decision criteria we use most often in this course.

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Data Analysis

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Shape–Minitab Descriptive Statistics

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Step 2: Check the shape of the data. Is the data normally distributed? MINITAB FILE: GB ANOVA.MPJ

Ho: The data is normally distributed Ha: The data is not normally distributed

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Descriptive Statistics–Input and Output

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1. Double Click

3. Click OK

2. Click on Graphs, Select Graphical Summary

Descriptive Statistics Variable: South Anderson-Darling Normality Test A-Squared: P-Value:

0

10

20

30

40

95% Confidence Interval for Mu

Non-normal distribution!

3.095 0.000

Mean StDev Variance Skewness Kurtosis N

11.9348 11.1064 123.351 1.75318 2.69797 46

Minimum 1st Quartile Median 3rd Quartile Maximum

1.0000 4.0000 9.0000 14.2500 45.0000

95% Confidence Interval for Mu 8.6366 7

8

9

10

11

12

13

14

15

16

9.2120

95% Confidence Interval for Median

15.2330

95% Confidence Interval for Sigma 13.9887

95% Confidence Interval for Median 6.9173

12.0000

Data is Normal if P-Value is > 0.05 (Accept Ho)

If the p-value is > 0.05, then we Accept the Ho and the data is normally distributed. In this case, our p-value is 0.000, therefore, we have a non-normal distribution.

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Non-Parametric Tests

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What if I don’t have normal data? Perform Non-parametric Tests Use HOV for spread and Mood’s Median for Center

Normal data allows a great variety of techniques to be used in analyzing it However, responding correctly is critical if the data is not normal (which is not at all uncommon)

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Non-Parametric Tests

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One of the advantages of nonparametric tests is that they assume no knowledge about the underlying distributions. They often use an analysis of the ordered ranks of the data. Nonparametric tests are more powerful for non-normal data than the equivalent t-tests and ANOVA tests The Mood’s Median and Homogeneity of Variance Test (HOV) are nonparametric tests which are very similar to the One-Way ANOVA test

Many times in commercial projects the data are not normally distributed. Cycle time is one example. Cycle time will often be skewed to the right. Another example is ordinal data. This is data that is not continuous but can be placed in ordered categories such as good, better, and best. This often occurs with survey data. In these cases a test that does not depend on assumptions of normality may be very useful

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Spread–Test On Variances

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Many times we want to know if we have succeeded in reducing the variation of a process, or we might want to know if a change in a variable (X) changes the variation in the output (Y). Knowing if the variances of two (or more) samples are different is also a prerequisite to the test on means. Are these Variances Different? Xb Xa

The hypothesis test for comparing variances is the Homogeneity of Variance Test In the Analyze phase we will try to determine which X’s have an effect on the Y. We can compare two sets of data, with X set at different values, thereby determining if that X has an effect. Examples: Does a process perform better using machine/material/ fixture/tool...A or B? Does the purchased material conform to the desired specifications (m & s)? Is there a difference in performance between vendor A or B? Is there a difference in your process after you make a change? Has a variation source been removed?

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Spread–Homogeneity Of Variance

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Step 3: You want to compare the variability of the Sales Regions. You have established that each process is stable but non-normally distributed. Perform the Homogeneity of Variance Test . MINITAB FILE: GB ANOVA.MPJ

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Test On Variances, Example–Input

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2 2 = 2 = 2 = 2 = Ho : σEast σ West σ IFG σ Central σ South Ha : at least one is different α = .05

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Test On Variances, Examples–Output 2 2 = 2 = 2 = 2 = Ho : σEast σ West σ IFG σ South σ Central

Ha : at least one is different

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α = .05

Homogeneity of Variance Test for total time 95% Confidence Intervals for Sigmas

Factor Levels Central

Bartlett's Test Test Statistic: 58.348 East

P-Value

: 0.000

IFG

Levene's Test South

Test Statistic: 10.396 P-Value

: 0.000

West

5

15

25

35

45

55

We have standardized on The Levene’s test because

p < α: Reject Ho

it is more robust to nonnormality of samples.

p > α: Accept Ho If you want to compare the performance of two territories, you should test their variances independently of the other territories. This way the extra noise of the other territories will not interfere with the analysis. You may end up with different conclusions running them independently, versus running them with all the other territories. The confidence intervals that are shown are intervals for the standard deviation, even though we are comparing variances (variance = σ2).

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Center–Non-Normal Data Test

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Mood’s Median Test A Mood’s Median Test is used to test two or more population medians. This test is robust to outliers or errors in data (shows statistical significance). This test will show statistical significance. It will not show practical significance.

Just as with our earlier example, a picture is worth a thousand words. Looking at a graphical depiction of the data can help to verify whether or not findings (even findings with statistical significance) have any practical significance. By way of an analogy, even though you could statistically prove that people are heavier before a haircut than they are afterwards, nobody seeks out a barber shop when they go on a diet. Even though a statistical difference might be able to be proven, the difference is negligible from a practical standpoint. Viewing the data graphically helps to confirm how much practical significance exists in what you’ve found.

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Center–Mood’s Median Test

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Step 4: Check the centers. Are the centers different by region? MINITAB FILE: GB ANOVA.MPJ Stat > Nonparametrics > Mood’s Median Test – Response = Total Time – Factor = Territory

Answer the following questions: 1.Are the medians different? (interpret the p-value) 2.Which medians are different? (interpret the confidence intervals) ~ ~ ~ ~ ~ H :X = X = X = X = X o

1

2

3

4

5

H : At least one is different a

Another type of analysis that may be investigated is whether or not multiple samples of data can be shown to be different from each other by a (statistically) significant amount. The example shown here is questioning whether similar territories are taking different amounts of time to process loan applications as measured in days. One test which can check for this condition in nonnormal data is called a Mood’s Median Test. It should be noted that, unless it can proven otherwise, the two groups are assumed to have the same median. In other words, the null hypothesis for a Mood’s Median Test is that the medians are equal.

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Mood’s Median Test

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Mood’s Median Test

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Mood Median Test Mood median test for total ti Chi-Square = 108.88 DF = 4 P = 0.000 Individual 95.0% CIs Territor

N Median

Central

97

15

3.0

Q3-Q1

East

47

1

10.0

8.8

IFG

2

11

28.0

56.5

South

25

21

9.0

10.3

West

22

91

15.0

17.5

4.7

---------+---------+---------+------(+ (+) ------+---------------------) (-+) (+-) ---------+---------+---------+------20

40

60

Overall median = 9.0 Recall, when two groups are equal, the confidence intervals overlap. Ho: All medians are equal Ha: At least one median is not equal

Notice that Minitab has converted the continuous data into attribute data. For each level of the X, Minitab supplies a count of how many values fall at or below and above the overall median. The Mood’s Median test then performs a simple Chisquare test (which we’ll cover later) on this summary table −

If the number above and below are proportional, Chisquare will be low and p will be high, resulting in the conclusion that the medians are equal.

−

If the number above and below are not proportional, Chisquare will be high and p will be low, resulting in the conclusion that the medians are not equal

The results from manually performing a Chi-square test using this summary table are the same as the Mood’s Median test © GE Capital, Inc., 2000 DMAIC GB Q TX PG

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Hypothesis Testing Procedure

1. Write the null hypothesis

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Ho: There is no difference between Population A and B

µpop1 = µpop2 Team preparation 2. Write the alternate hypothesis

Ha: There is a difference between Samples A and B µpop1 ≠ µpop2

3. Decide on the alpha level

α =.05 (typical for DMAIC projects)

4. Chose hypothesis test

Choose the correct test, given the type of X and Y data.

5. Gather evidence and test/conduct analysis

Collect data, run analysis, get p-value

6. Decide to Reject H0, or not reject H0, and draw conclusion

If p ≥ 0.05 conclude, no difference between populations If p < 0.05 conclude, the populations are different

The first step in hypothesis testing is to write a null hypothesis for the population being investigated. State that there is no difference between populations that you are studying. The next step is to write the alternate hypothesis (which is often what your team REALLY thinks is true), which indicates that a difference does exist between the population. The decision regarding a p-value is usually straightforward. By convention, a p-value of .05 is typical because that is sufficient to give us the confidence we need to go forward whether we reject or do not reject the null hypothesis. The team then collects whatever additional data is necessary. The correct hypothesis test can then be chosen and the analysis is conducted. The team now has the necessary information in order to know whether or not to reject or accept the null hypothesis.

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1-Sample Hypothesis

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1. Ho : µ = constant = T Ha : µ ≠ constant = T

Ho

Ha

T

2. Ho : σ 2 = constant = T Ha : σ 2 ≠ constant = T There are 7 types of hypotheses that we will be covering. We are standardizing the method by always trying to accept, with a degree of confidence, the alternative hypothesis when evidence supports the decision. We are the prosecuting attorney. Set up the hypotheses according to this standard convention.

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1-Sample t-Test

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Ho : µ = constant = T Ha : µ ≠ constant = T

Minitab File: GB case study.mtw Null Hypothesis: There is no difference in June’s delivery time average with that of a target set by May’s delivery time average of 5 minute’s late. Minitab Command: Stat > Basic Statistics > 1–Sample t–test

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1-Sample t-Test

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MINITAB FILE: GB case study.mtw

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1-Sample t-Test

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1. Double click anywhere on the C5 line to select time as a variable

2. Click Test Mean and enter 5.0 as May’s average, the Alternative is that they are not equal 3. Click Graphs to show a pictorial

4. Click on Histogram of data 5. Click OK

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1-Sample t-Test

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Histogram of time (with Ho and 95% t-confidence interval for the mean)

50

Frequency

40 30 20 10 _ X Ho [ ]

0

-100

0

100

time

The session window has our answer. If the p-value is less than .05, we reject the Null Hypothesis and accept its alternate, that there is a statistical difference in averages between this month’s data and May’s data.

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2-Sample Hypothesis

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3. Ho :µ1 = µ2 Ha : µ1≠ µ2 4. Ho : µ1 ≤ µ2 Ha : µ1 > µ2

µ1

µ2

5. Ho : σ1 2 = σ22 Ha : σ1 2 ≠ σ22

σ1

σ2

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2-Sample t-Test

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Ho :µ1 = µ2 Ha : µ1≠ µ2

Minitab File: GB case study.mtw Null Hypothesis: There is no difference in the average delivery time between the two different load types. Minitab Command: Stat > Basic Statistics > 2–Sample t–Test

Let’s test the hypothesis that there is no difference in the average delivery time between the two different load types. D/H–Drop & Hook–A driver unhooks their full trailer, and then hooks into an empty trailer to take back. Unload–The driver opens the trailer and allows the store to unload it’s freight, and brings back the trailer.

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2-Sample t-Test

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MINITAB FILE: GB case study.mtw

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2-Sample t-Test

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1. Double click anywhere on the C5 line to select time as a variable for samples. 2. Click on C3 to chose LoadType as the variable for subscripts.

3. Click Graphs to show a pictorial.

4. Click on Boxplots of data.

5. Click OK.

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2-Sample t-test

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Boxplots of time by LoadType (means are indicated by solid circles)

time

100

0

-100 D/H

Unload

LoadType

The session window has our answer. If the p-value is less than .05, we reject the Null Hypothesis and accept its alternate, that there is a statistical difference in our Drop & Hook and Unload averages.

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Multi Sample Hypothesis

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6. Ho : µ1 = µ2 = . . . = µn Ha : at least one is not equal.

7. Ho : σ12 = σ22 = . . . = σn2 Ha : at least one is not equal.

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Analyze Of Variance (ANOVA)

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Ho : µ1 = µ2 = . . . = µn Ha : at least one is not equal.

Minitab File: GB case study.mtw Null Hypothesis: There is no difference in the average delivery time between Capital Logistics drivers. Minitab Command: Stat > ANOVA > One-Way

Let’s test the hypothesis that there is no difference in the average delivery time between Capital Logistics drivers, Temporary drivers working for us, and our 3 Third party carriers we use in areas that are not supported by Capital Logistics.

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Analysis Of Variance (ANOVA)

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MINITAB FILE: GB case study.mtw

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Analysis Of Variance (ANOVA)

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1. Double click anywhere on the C5 line to select time as a response variable.

2. Double click C2 for Driver as a factor.

3. Click Graphs to show a pictorial. 4. Click on Boxplots of data. 5. Click OK.

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Analysis Of Variance (ANOVA)

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Boxplots of time by Driver (means are indicated by solid circles)

time

100

0

Trans, Inc.

Temp Labor

JJ Truck

DNGY Inc.

Driver

Cap. Log.

-100

1. Note the sample number for each group.

2. These 3 are alike.

3. These 2 are definitely different.

The session window has our answer. If the p-value is less than .05, we reject the Null Hypothesis and accept its alternate, that there is a difference in at least 1 average between the 5 different groups of drivers.

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Homogeneity Of Variance (HOV)

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Ho

:

σ12 = σ 22 = ... = σn2

Ha : at least one is not equal

Minitab File: GB case study.mtw Null Hypothesis: There is no difference in the variation in delivery time between Capital Logistics drivers. Minitab Command: Stat > ANOVA > Homogeneity of Variance

Let’s test the hypothesis that there is no difference in the variation in delivery times between Capital Logistics drivers, Temporary drivers working for us, and our 3 Third party carriers we use in areas that are not supported by Capital Logistics.

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Homogeneity Of Variance (HOV)

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MINITAB FILE: GB case study.mtw

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Homogeneity Of Variance (HOV)

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1. Double click anywhere on the C5 line to select time as a response variable.

2. Double click C2 for Driver as a factor.

3. Click OK.

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Homogeneity Of Variance (HOV)

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1. We have standardized our Levene’s Test because it is more robust for non-normal data.

2. Our p-value is less than 0.05.

The graphical output has our answer. If the p-value is less than .05, we reject the Null Hypothesis and accept its alternate, that there is a difference in standard deviation between at least two of the drivers. Always use the p-value for Levene’s Test.

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Review: Scatter Plots

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R-value

y

r = –1.0

x

x

r = +.7

y

r = –.7

y

x

x

r=0

y

r = +1.0

y

x

r=0

y

x

The correlation coefficient r measures the strength of linear relationships. –1 ≤r ≤1 When a relationship exists, the variables are said to be correlated. Perfect negative relationship: r = –1.0 No linear correlation: r = 0 Perfect positive relationship: r = +1.0 If no correlation is apparent, don’t stop. Use histograms, regression, rational sub-grouping, etc. to try to extract some meaning from the data.

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Simple Linear Regression

80

We have shown/talked about positive and negative correlation of two data sets Regression analysis is a statistical technique used to build the Y = ƒ(x) relationship between two or more variables. The model is often used for prediction. Regression is a hypothesis test. Ha: The “X” is a significant predictor of the response. It may be used to analyze relationships between the “X’s”, or between “Y” and “X” Regression is a powerful tool, but can never replace process knowledge about trends

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Simple Linear Regression

81

Y = b 0 + b 1X 1 Y

X

Ha: The model is a significant predictor of the response. b0 = Predicted value of Y when X1 = 0 b1 = Slope of line change in Y per unit change in X1

Minitab File: GB case study.mtw Null Hypothesis: There is no correlation between our continuous Y metric (time) and a continuous X metric (distance) Minitab Command: Stat > Regression > Fitted Line Plot

Let’s test the hypothesis that there is no correlation between our continuous Y metric–time and a continuous X metric–distance.

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Simple Linear Regression

82

MINITAB FILE: GB case study.mtw

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Simple Linear Regression

83

1. Double click anywhere on the C5 line to select time as a response variable.

2. Double click C6 for Distance as a predictor.

3. We believe there to be a linear relationship. 4. Click OK.

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Simple Linear Regression

84

Regression Plot Y = -29.1923 + 0.174971X R-Sq = 10.5 %

time

100

2. This value means that 10.5% of the variation in Y - time is explained by this X - distance.

0

-100

1. There is a very weak positive relationship between distance and timely delivery

0

100

200

300

400

Distance Distance is a significant factor.

Entire model is significant.

The session window has our answer. If the p-value is less than .05, we reject the Null Hypothesis and accept its alternate, that there is a correlation between delivery time and distance, but that it is a very weak one (as seen by Low R-Sq value). Hypothesis test for the model (p-value given for “Regression”) Ho: Model = O Ha: Model ≠ O

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Chi-Square Test

85

Y Continuous

Discrete

Continuous

X Discrete Chi-Square Test

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Chi-Square Tests

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The Chi-Square Tests Used for: 1 - Goodness-of-Fit Test: To test if an observed set of data fits a model (an expected set of data) 2 - Test of Independence: To test hypothesis of several proportions (contingency table)

It’s for discrete data, any number of categories For all cases,

Ho: no difference in data Ha: difference exists

2 χ The Chi-Square test provides a way to determine if a given set of data has the hypothesized distribution. For example, if we roll a die 600 times., the number 1 occurs 96 times, 2–88 times, 3–104 times, 4–107 times, 5–112 times, and 6–93 times. In theory, each number should occur 100 times. The Chi-Square test enables us to determine if the observed set of data, the output of 600 rolls of a die, fits an expected model. The Chi-Square test will also let you know if any factor has an impact on the output. If there is no difference in the data (Ho), this means no factor(s) have an impact on the output. If a difference exists (Ha), one or more factors have an impact on the output.

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The Nature And Use Of Chi-Square

g

χ = 2

Σ

j=1

Suppose we flip a coin N = 100 times and observe 63 heads and 37 tails. Could this ratio of heads to tails occur by chance or should we conclude that the coin is somehow biased ?

87

fo - fe fe

2

g = number of categories fo = observed frequency fe = expected frequency

Penny

(f0-fe)2 fe

Heads

63/50*

3.38

Tails

37/50*

*=Observed Expected (f0) (fe)

3.38

χ 2 = 6.76

The Goodness-of-Fit test examines the difference between what is expected and what is observed. If this difference is large, you should be suspicious that something is influencing the output (one of the factors). The c 2 value represents a test statistic used for comparison to a critical value. In this example, you would expect an unbiased coin to have equal occurrences of heads and tails (50/50). We know that we won’t always have this ratio of heads to tails because of random chance. If there is a large difference between what is expected and what is observed, the chi-square value will be large (see formula). If the observed value is close to the expected value, the chi-square value will be small. How large does chi-square have to be to say the coin is biased?

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The Goodness Of Fit Test

88

To determine whether a sample comes from a population with a known distribution, calculate chi-square as shown on the previous page. H0 = good fit (observed distribution is consistent with random outcomes from the expected model) Ha = sampled population does not have the expected distribution If the observed frequencies are close to the expected frequencies, chisquare is small. So a low chi-square leads to rejecting Ha. If chi-square is greater than a critical value, the null hypothesis is rejected. The critical values of chi-square for various confidence levels are given in the table “Chi-Square Distribution.” Each of the expected frequencies must be at least 5 for this test to be valid.

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Degrees Of Freedom

89

The chi-square distribution has “degrees of freedom” as a parameter. For a goodness-of-fit test, the number of degrees of freedom is k1, where k is the number of possible outcomes. Thus for the penny example, df = 2 - 1 = 1

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The Statistical Test

90

For the penny example: Critical value ( α = 0.05, dof = 1) = 3.841 χ2Calculated > χ2Table => There is a difference (I’m seeing something unusual). Since the statistic from the data, 6.76, is greater than the table critical value, the alternative hypothesis is accepted: we are confident that we saw unusual behavior with that penny.

Use the tables on the next two pages to determine the chisquare critical value.

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The Chi-Square Distribution

91

df=(# columns-1) x (# Rows-1) df

.250

.100

.050

.025

.010

.005

.001

1 2 3 4 5

1.323 2.773 4.108 5.385 6.626

2.706 4.605 6.251 7.779 9.236

3.841 5.991 7.815 9.488 11.070

5.024 7.378 9.348 11.143 12.832

6.635 9.210 11.345 13.277 15.086

7.879 10.597 12.838 14.860 16.750

10.828 13.816 16.266 18.467 20.515

6 7 8 9 10

7.841 9.037 10.219 11.389 12.549

10.645 12.017 13.362 14.684 15.987

12.592 14.067 15.507 16.919 18.307

14.449 16.013 17.535 19.023 20.483

16.812 18.475 20.090 21.666 23.209

18.548 20.278 21.955 23.589 25.188

22.458 24.322 26.125 27.877 29.588

11 12 13 14 15

13.701 14.845 15.984 17.117 18.245

17.275 18.549 19.812 21.064 22.307

19.675 21.026 22.362 23.685 24.996

21.920 23.337 24.736 26.119 27.488

24.725 26.217 27.688 29.141 30.578

26.757 28.300 29.819 31.319 32.801

31.264 32.909 34.528 36.123 37.697

16 17 18 19 20

19.369 20.489 21.605 22.718 23.828

23.542 24.769 25.989 27.204 28.412

26.296 27.587 28.869 30.144 31.410

28.845 30.191 31.526 32.852 34.170

32.000 33.409 34.805 36.191 37.566

34.267 35.718 37.156 38.582 39.997

39.252 40.790 43.312 43.820 45.315

21 22 23 24 25

24.935 26.039 27.141 28.241 29.339

29.615 30.813 32.007 33.196 34.382

32.671 33.924 35.172 36.415 37.652

35.479 36.781 38.076 39.364 40.646

38.932 40.289 41.638 42.980 44.314

41.401 42.796 44.181 45.558 46.928

46.797 48.268 49.728 51.179 52.620

26 27 28 29 30

30.434 31.528 32.620 33.711 34.800

35.563 36.741 37.916 39.087 40.256

38.885 40.113 41.337 42.557 43.773

41.923 43.194 44.461 45.722 46.979

45.642 46.963 48.278 49.588 50.892

48.290 49.645 50.993 52.336 53.672

54.052 55.476 56.892 58.302 59.703

40 50 60

45.616 56.334 66.981

51.805 63.167 74.397

55.758 67.505 79.082

59.342 71.420 83.298

63.691 76.154 88.379

66.766 79.490 91.952

73.402 86.661 99.607

70 80 90 100

77.577 88.130 98.650 109.141

85.527 96.578 107.565 118.498

90.531 101.879 113.145 124.342

95.023 106.629 118.136 129.561

100.425 112.329 124.116 135.807

104.215 116.321 128.299 140.169

112.317 124.839 137.208 149.449

Alpha

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The Chi-Square Distribution

92

df 1 2 3 4 5

.995 .000039 0.010 0.072 0.207 0.412

.990 .000160 0.020 0.115 0.297 0.554

.975 .000980 0.051 0.216 0.484 0.831

.950 .003930 0.103 0.352 0.711 1.145

.900 .015800 0.211 0.584 1.064 1.610

.750 .101500 0.575 1.213 1.923 2.675

.500 .455000 1.386 2.366 3.357 4.351

6 7 8 9 10

0.676 0.989 1.344 1.735 2.156

0.872 1.239 1.646 2.088 2.558

1.237 1.690 2.180 2.700 3.247

1.635 2.167 2.733 3.325 3.940

2.204 2.833 3.490 4.168 4.865

3.455 4.255 5.071 5.899 6.737

5.348 6.346 7.344 8.343 9.342

11 12 13 14 15

2.603 3.074 3.565 4.075 4.601

3.053 3.571 4.107 4.660 5.229

3.816 4.404 5.009 5.629 6.262

4.575 5.226 5.892 6.571 7.261

5.578 6.304 7.042 7.790 8.547

7.584 8.438 9.299 10.165 11.036

10.341 11.340 12.340 13.339 14.339

16 17 18 19 20

5.142 5.697 6.265 6.844 7.434

5.812 6.408 7.015 7.633 8.260

6.908 7.564 8.231 8.907 9.591

7.962 8.672 9.390 10.117 10.851

9.312 10.085 10.865 11.651 12.443

11.912 12.792 13.675 14.562 15.452

15.338 16.338 17.338 18.338 19.337

21 22 23 24 25

8.034 8.643 9.260 9.886 10.520

8.897 9.542 10.196 10.856 11.524

10.283 10.982 11.688 12.401 13.120

11.591 12.338 13.091 13.848 14.611

13.240 14.041 14.848 15.659 16.473

16.344 17.240 18.137 19.037 19.939

20.337 21.337 22.337 23.337 24.337

26 27 28 29 30

11.160 11.808 12.461 13.121 13.787

12.198 12.879 13.565 14.256 14.953

13.844 14.573 15.308 16.047 16.791

15.379 16.151 16.928 17.708 18.493

17.292 18.114 18.939 19.768 20.599

20.843 21.749 22.657 23.567 24.478

25.336 26.336 27.336 28.336 29.336

40 50 60

20.707 27.991 35.535

22.164 29.707 37.485

24.433 32.357 40.482

26.509 34.764 43.188

29.051 37.689 46.459

33.660 42.942 52.294

39.335 49.335 59.335

70 80 90 100

43.275 51.172 59.196 67.328

45.442 53.540 61.754 70.065

48.758 57.153 65.647 74.222

51.739 60.391 69.126 77.929

55.329 64.278 73.291 82.358

61.698 71.145 80.625 90.133

69.334 79.334 89.334 99.334

Alpha

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The Statistical Test (continued)

93

The 5% risk column in the table already tells us there is a difference. Alternately, a p-value (the probability of being wrong if accepting the alternative hypothesis) can be computed in EXCEL as follows: = CHIDIST(statistic,dof) = CHIDIST(6.76,1) Excel will return the p-value, in this case 0.0093. Since the probability of being wrong is less than 0.05, we accept the alternative hypothesis: we are confident that we saw unusual behavior with that penny.

Minitab does not have a Macro to accommodate the Goodness-of-Fit test. It is most convenient to compute the chi-square value in Minitab and then evaluate the corresponding p-value in Excel. One can obtain the p-value in Minitab, but it takes a little work.

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Test Of Independence

94

Suppose a bill has been introduced in the Government to raise the speed limit. A polling organization polls 45 members of Political Party 1 and 55 members of Political Party 2, and finds 30 Party 1 and 35 Party 2 members oppose the proposal. Is there a significant effect of party affiliation on preference for the proposal? Ho = no difference between parties Ha = one party likes the proposal significantly more than the other We organize the data in a “contingency table” Oppose

Favor

Party 1

Party 2

fo = 30

fo = 35

Total = 65

fo = 15

fo = 20

Total = 35

Total = 45

Total = 55

Use this example to demonstrate the test for independence and contingency tables. The test for independence asks the question: Does some factor have an effect on the output? For example, does car brand affect injury severity? To test independence, we put the data in a contingency table. We then test to see if the row and column method for classification are independent.

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Test Of Independence (continued)

95

Now calculate the expected distribution, given there is no party preference. For example, the expected frequency of Party 1 opposing the proposal would be:

fe

=

Row Total

x

Column Total

Grand Total

= (65/100) x 45 = 29.25 Note that for each cell, this is the total frequency for the row, times the total frequency for the column, divided by the total population (see chart on following page).

You will be determining your expected frequency on the ratio of number of people who oppose the proposal to the number of people who favor the proposal (regardless of party affiliation). Out of the total 100 (party affiliation unknown) people, 65 oppose the proposal and 35 favor the proposal. Expected ratios: 65/100 oppose; 35/100 favor. When you multiply these ratios by the total in a party, you get the expected frequency. If the population of Party 2 (or Party1) has a statistically different (p < α) observed frequency than the expected frequency (total or average) accept Ha–one party likes the bill significantly more than the other.

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Expected Frequency And Degrees Of Freedom

96

fe = frow x fcol N Party 1

Party 2

Oppose

fe = 29.25

fe = 35.75

Total = 65

Favor

fe = 15.75

fe = 19.25

Total = 35

Total = 45

Total = 55

When performing a chi-square test on a contingency table, the number of degrees of freedom equals the number of rows in the table minus one, times the number of columns in the table minus one. df = (2-1) x (2-1) = 1

Expected frequencies are calculated using the methodology from the previous page. We could use the expected and observed frequencies to calculate the Chi-Square statistic like we have seen before, and then compare it to the critical Chi-Square value from the table using (alpha) and df. But, as usual, we will have Minitab do this for us. See the next pages.

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Minitab Example

97

MINITAB FILE: (Create Your Own)

H o:

There is no difference between party affiliation and preference on the proposal.

H a:

There is a difference between party affiliation and preference on the proposal.

For this example, Party 1 = Republicans Party 2 = Democrats

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Minitab Input And Results

98

1. Double click on both columns.

2. Click OK.

Minitab calculates the expected frequency (fe)

Minitab calculates the expected frequencies. The calculated chi-square is less than the critical value of 3.841, so we accept Ho. The p-value is greater than .05, so we are within our 95% confidence zone of good fit. There is no apparent relationship between political party affiliation and preference on the speed limit proposal.

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Chi-Square Test–Case Study Example

99

Minitab File: GB case study.mtw Ho: There is no difference between Driver types and their on-time delivery performance. Ha: At least one driver type is better or worse at on-time delivery performance. Minitab Command: Stat > Tables > Cross–Tabulation

In our familiar case study example, with our data in rows, we will let Minitab build the contingency table.

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Chi-Square Test

100

MINITAB FILE: GB case study.MTW

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Chi-Square Test

101

1. Double click on both columns C2 & C7..

2. Check the ChiSquare Analysis and Show Count buttons. 3. Click OK.

Since our discrete data is in columns and not tabled, we will first cross-tabulate and then calculate Chi-Square. Since our p-value is less than .05, we reject the Ho and accept it’s alternate, Ha. Compare this p-value with the one done on the ANOVA test for driver type & time. Are they the same?

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Chi-Square Test–Summary

102

Goodness of Fit Test – Does our data fit an expected distribution?

Test of Independence – Does some factor have an effect on the output? 2

χ statistic – χ ≤critical value Accept H o – χ > critical value Reject Ho 2

2

p-value – p < 0.05 Reject Ho – p ≥ 0.05 Accept Ho

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Hypothesis Testing–Breakout Activity (20 minutes)

103

Desired Outcome: Select and perform the appropriate statistical test for a given project situation What

How

Who

Timing

Review Scenarios

Review the hypothesis testing scenarios recruitment cycle time case study that was introduced in the Minitab and Graphical Analysis module.

All

5 mins.

Select Test

For the scenario(s) assigned to your team, complete the hypothesis testing worksheet to select the appropriate statistical test

All

5 mins.

Perform Test In Minitab

Perform the test in Minitab

All

10 mins.

Close

Be prepared to share your analysis and results with the class

Write the p-value from the test and your conclusions on the hypothesis testing worksheet All

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Hypothesis Testing Scenarios

104

The following scenarios relate to the HR recruitment cycle time case. In each case, perform the appropriate statistical test. (Data File: fill_time.mtw) 1. The project team wants to determine if there is a statistical difference in mean cycle time to fill technical positions depending on the type of resource requested. 2. The project team wants to determine if there is a statistical difference in cycle time variation, depending on the type of resource requested. 3. The project team wants to determine if there is statistical difference between the number of cycle time defects for each type of resource. 4. The project team wants to determine if recruitment cycle time increases as the number of years of experience of the person hired increases.

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Hypothesis Testing Worksheet

105

1. State the H0 2. State the Ha 3. State α level 4. What test should we use? 5. Will you reject or accept H0? 1. H0: ___________________________________________________________________

2. Ha: ___________________________________________________________________

3. α level: ________________________________________________________________

4. Test: _________________________________________________________________

5. Accept or Reject H0? _____________________________________________________

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Hypothesis Testing Worksheet

106

1. State the H0 2. State the Ha 3. State α level 4. What test should we use? 5. Will you reject or accept H0? 1. H0: ___________________________________________________________________

2. Ha: ___________________________________________________________________

3. α level: ________________________________________________________________

4. Test: __________________________________________________________________

5. Accept or Reject H0? _____________________________________________________

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Improve Phase Flowchart

D

M

1

A

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IMPROVE PHASE OVERVIEW

Improve 7: Screen Potential Causes

Improve 8: Discover Variable Relationships & Propose Solution

Improve 9: Establish Operating Tolerance & Pilot Solutions

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Improve Phase Overview

2

What is the Improve phase? The Improve phase is when your team: Selects those product performance characteristics that must be improved to achieve the improvement goal by identifying the major sources of variation in the process Develops and pilots process improvements

Why is the Improve phase important? This phase is important because it specifically identifies how the process should be improved. Steps involved in the Improve phase: Improve 7: Screen Potential Causes Improve 8: Discover Variable Relationships & Propose Solution Improve 9: Establish Operating Tolerances & Pilot Solution

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The12-Step Process Step Define

Description

Focus Tools

Deliverables

A

Identify Project CTQ’s

Project CTQ’s

B

Develop Team Charter

Approved Charter

C

Define Process Map

High Level Process Map

Measure 1 2 3

Select CTQ Characteristics Define Performance Standards Measurement System Analysis

Analyze 4 Establish Process Capabilities 5 Define Performance Objectives 6 Identify Variation Sources

Improve 7 Screen Potential Causes 8 Discover Variable Relationships 9 Establish Operating Tolerances Control 10 Define & Validate Measurement System on X’s in Actual Application 11 Determine Process Capability 12 Implement Process Control

Y Y Y

Customer, QFD, FMEA Project Y Customer, Blueprints Performance Standard for Project Y Continuous Gage R&R, Data Collection Plan & MSA test/Retest, Attribute Data for Project Y R&R

Y

Capability Indices

Y

Team, Benchmarking

X

Process Analysis, Graphical Analysis, Hypothesis Tests

X X

DOE-Screening Factorial Designs

Y, X Simulation

Process Capability for Project Y Improvement Goal for Project Y Prioritized List of all X’s

List of Vital Few X’s Proposed Solution Piloted Solution

Y, X Continuous Gage R&R, MSA Test/Retest, Attribute R&R Y, X Capability Indices Process Capability Y, X X

Control Charts, Mistake Sustained Solution, Proofing, FMEA Documentation © GE Capital, Inc., 1999

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Improve 7–Screen Potential Causes

4

What does it mean to Screen Potential Causes? Potential Causes are the possible Vital Few (or Critical) X’s discovered during Analyze 6 that have a significant effect on the Project Y. The Potential Causes are identified by the improvement team. During this step, the Vital X’s discovered in Analyze 6 will be statistically verified by obtaining more data, if necessary. Why is it important to Screen Potential Causes? Potential X’s are important because they help Green Belt teams focus their identification of root causes. Once potential X’s are verified as having a significant effect on the Project Y, then Green Belt teams will use the identified Vital X’s to focus improvement efforts. What are the project tasks for completing Improve 7? 7.1 Verify Vital Few X’s

IMPROVE STEP OVERVIEW

Improve 7: Screen Potential Causes

Improve 8: Discover Variable Relationships & Propose Solution

Improve 9: Establish Operating Tolerances & Pilot Solution

7.1 Verify Vital Few X’s

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Improve 8–Discover Variable Relationships and Propose Solution

5

What does it mean to Discover Variable Relationships and Propose a Solution? A Final Solution is the improvement strategy that the team develops based upon the root causes verified in the previous step.The final solution will address the Vital X’s while maintaining customer focus. Why is it important to Discover Variable Relationships and Propose a Solution? A Final Solution will eliminate or reduce the effect of the Vital Few X’s, thus improving the process capability of the Project Y. The Final Solution must not only address the Vital Few X’s, but you must also consider whether the solution satisfies the customer’s CTQ’s. By using the FMEA tool, you can identify possible Failure Modes within the Final Solution, identify what effect the Failure Modes would have on either the customer’s CTQ’s or the new process, and create action plans to eliminate or reduce the likelihood of that Failure Mode occurring. What are the project tasks for completing Improve 8? 8.1 Generate a transfer function to optimize the changes in Vital X’s (if necessary) 8.2 Propose solution 8.3 Refine solution

IMPROVE STEP OVERVIEW

Improve 7: Screen Potential Causes

Improve 8: Discover Variable Relationships & Propose Solution

Improve 9: Establish Operating Tolerances & Pilot Solution

8.1 Generate a transfer function to optimize the changes in vital X’s (if necessary) 8.2 Propose solution 8.3 Refine solution

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6

Improve 9–Operating Tolerances & Pilot Solution

6

What does it mean to establish Operating Tolerances and Pilot Solutions? An Operating Tolerance is established when the X-Y transfer function is known and the required specification for Y is known. The tolerance for X can be set by using the specification for Y in the transfer function. A pilot is a test of all or part of a proposed solution on a small scale in order to better understand its effects and to learn about how to make the full scale implementation more effective. Why is it important to establish Operating Tolerances & Pilot Solution? Operating tolerances allow you to control the settings of Vital X’s so that you can better predict/control the output of the process – the Y. A pilot allows you to improve a proposed solution to better meet customer CTQ’s, lower the risk of failure of a proposed solution, confirm expected results of a proposed solution, and increase the opportunity for feedback and buy-in for a proposed solution. What are the project tasks for completing Improve 9? 9.1 Establish operating tolerances for Vital X’s 9.2 Pilot solution

IMPROVE STEP OVERVIEW

Improve 7: Screen Potential Causes

Improve 8: Discover Variable Relationships & Propose Solution

Improve 9: Establish Operating Tolerances & Pilot Solution

9.1 Establish operating tolerances for Vital X’s 9.2 Pilot solution

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Statistical Thinking

D M Practical Problem

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A Statistical Problem

Statistical Solution

Characterize the Root cause process analysis – Stability – Critical X’s – Shape Measure the influence of the – Center critical X’s on – Variation Data Integrity the mean and variability – MSA Capability – Test – Brainstorm – ZBench ST & LT potential X’s – Model – Sampling plan – Estimate

Problem statement – Project Y – Magnitude – Impact

I C Practical Solution

Verify critical X’s and ƒ(x) Change process Control the gains – Risk analysis – Control plans

Collect data The Practical-To-Statistical-To-Practical Transformation Process

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Design Of Experiment: Learning Objectives

Define the purpose & benefits of conducting a Design of Experiment Describe screening DOE and optimization DOE and how they are used in the Improve phase Review full factorial DOE design Describe the 5 steps in analyzing DOE data, the key components of each step and the use of Minitab to analyze the data – – – – –

Plot the raw data Plot the residual* Examine the factor effects Confirm impression with statistical procedures Summarize conclusions

Describe the use of fractional factorial design and explain the benefits & the trade-off over full factorial design

* We don’t discuss residuals here, but to fully analyze your DOE, seek assistance from your BB/MBB and/or the “Book of Knowledge”

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Design Of Experiments

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With the use of Design of Experiments (DOE), we will be able to: Verify the “Vital Few” X’s that impact the quality of the Project Y Identify the best combination X–values to optimize process performance and meet customer CTQ’s

DOE is powerful in isolating the Vital Few causes from the many factors affecting a process. In identifying and testing solutions, a team can apply DOE to compare the results of several possible solutions. The team can develop a more effective final solution by measuring effectiveness of the improvements in action.

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DOE Terminology

Independent Variables–X’s

Also called factors Factors or variables we select in advance The causes

Dependent Variables–Y

Also called responses The quantity (Y) that we measure to determine the impact of the X’s The effect

Project Y Dependent Independent X (5 M’s and 1 P)

(x) (x) (x)

M M M Project Y P

(x)

M M

(x) (x)

Remember that the dependent variable (Y) is measured from the customer’s perspective. DOE allows us to identify the X’s that are the key drivers of variation in the Y.

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DOE Terminology (continued) Levels

For example: In our Capital Logistics GB Case Study: Y = On-Time Delivery of Shipments X1 = Truck Size Levels = 62 ft. & 66 ft. truck

The test settings for X

X2 = Tire Type Levels = Brand X & Brand Y

Main Effects Differences between each factor level Interactions Differences between two or more factor level combinations

For example: Is the On-Time Delivery different for: a) 62 ft. trucks vs. 66 ft. trucks? b) Brand X or Brand Y tires?

For example: Is On-Time Delivery different when: a) 62 ft. truck, Brand X tire b) 62 ft. truck, Brand Y tire c) 66 ft. truck, Brand X tire d) 66 ft. truck, Brand Y tire

Deviation from required delivery time. Y

X 62

66

62 ft. truck 66 ft. truck

X

Truck Size Deviation from required delivery time. Y

Deviation from required delivery time. Y

Interactions

Main Effects

Tire Type

Y

X X

Tire Type

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Strategy For Choosing The Appropriate Design The Knowledge Line Current State of Process Knowledge Low

Type of Design

High

Main Effect /Screening

Fractional Factorials

>5

4-10

Usual # of Factors Purpose: Identify

Main effect critical factors - vital few

Estimate

Full Factorials

Response Surface

1-5

2-3

Some Relationships interactions among factor

Crude direction Some All main effects for improvement interactions and interactions

Step 7

Screening DOE

Step 8

Optimal factor settings Curvature in response, empirical models

Optimization DOE

Types of Experimental Design

Types of Experimental Design

Screening DOE–experiments which are used to screen out the vital few X variables out of many at a very low cost.

Fractional Factorials–provide a middle ground. They are used to expand on the study of the vital few X variables at a low cost.

Can study the main effects

Can’t study the interactions

Optimization DOE–Experiments which are used to determine the proper settings for each vital X.

Can study main effects Can study selected (and few in number) interactions Full Factorials–are used to study the vital few X variables and all possible interactions. They can be quite costly when the number of vital few X’s are large.

Can study main effects Can study all interactions

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DOE Benefits Benefits of Design of Experiment (DOE) Can be used to identify “Vital Few” sources of variation Defines the relationship between the inputs & outputs Allows you to measure the influence of the “Vital Few” variables on a response variable – Also allows you to measure the interactions between the “Vital Few” variables

Is more effective & efficient than testing one factor at a time Minimizes the number of test runs you have to make to draw valid conclusions about X & Y linkages Provides knowledge of best set-up conditions of X’s for improved Y performance

Statistical Design Of Experiment Raises Your Batting Average

Design of Experiment is an approach for effectively & efficiently exploring the cause and effect relationship between numerous process variables (X’s) and a process performance variable (Y).

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The Process Of Experimentation 1. Define Project Identify responses

2. Establish Current Situation 3. Perform Analysis

4. Determine Solutions 5. Record Results 6. Standardize 7. Determine Future Plans

Identify factors Choose factor levels Select design Randomize runs Collect data Analyze data Draw conclusions Verify results

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The Process Of Experimentation 1. Define Project (problems) The mileage on my new car is not up to advertised standards. I want to improve my car’s mileage.

2. Establish Current Situation (& state hypothesis) I currently do not get the manufacturer’s advertised gas mileage on my car Some combination of speed, gas octane, and tire pressure will provide me with the optimum gas mileage

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The Process Of Experimentation (continued) 3. Perform Analysis Dependent Variable–Gas Mileage (Y) Identify Factors (independent variables) – Tire Pressure (X) – Octane (X) – Speed (X)

Choose Factor Levels

Independent Variables (X’s) (Factors) Tire Pressure (psig) Octane Speed (mph)

Level -

Level +

30 87 55

35 92 65

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The Process Of Experimentation (continued) 3. Perform Analysis (continued) Select Design – Number of test levels

Tire Pressure + + + +

(Number of factors)

Octane + + + +

= 23 = trials

Speed + + + +

Gas Mileage

How many trials would be necessary if there were 4 variables each at 2 levels? How many variables would there be before the cost became prohibitive? What would be a different type of experiment that would not require all possible runs? The experimental trials tables represent all possible combinations of the 3 factor levels. Note: The table above shows the “standard order” for a 2-level, 3-factor design.

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The Process Of Experimentation (continued) 3. Perform Analysis (continued) Randomize Runs Tire Pressure - (30) + (35) - (30) + (35) - (30) + (35) - (30) + (35)

Octane - (87) - (87) + (92) + (92) - (87) - (87) + (92) + (92)

Speed - (55) - (55) - (55) - (55) + (65) + (65) + (65) + (65)

Gas Mileage 26 27 30 33 18 21 19 22

What effects (main and interaction) seem to be significant? – Main effect is the effect of one X on the Y – Interaction effects are the combined effects of two or more X’s on the Y

In this experiment, only one run of each experimental trial was conducted. Additional runs would increase the confidence level for the results. Replication is a repeat of all experimental trials to obtain additional data to increase the degree of belief in the experimental results. Replications are used when:

The interactions are of critical importance

Data is tricky to get. Replications will supply an extra data point when data from an experimental trial is lost

You need to increase the degree of confidence in the experimental results

You need to reduce the risk when implementing solutions

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The Process Of Experimentation (continued) 3. Perform Analysis (continued) Collect & Analyze Data Pareto Chart of the Effects (Response is Mileage, Alpha = .05)

C B

A: Pressure

A

B: Octane

BC

C: Speed

AC ABC AB 0

1

2

3

4

5

6

7

8

9

Effect Size

What factor has the biggest effect on gas mileage?

The Pareto Diagram bars show the relative importance of each main effect and interaction in the experiment. The length of each bar shows relative impact. Bars that cross the dashed line have statistically significant impact on the Y. The dashed line is called the “reference line”. Any effects that extend past this reference line are statistically significant within our chosen confidence level.

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The Process Of Experimentation (continued) 3. Perform Analysis (continued) Collect & Analyze Data (continued)

Main Effects Plot (data means for Mileage) -

+

+

–

+

–

28

Mileage

26 24 22 20 30

Pressure

35 87

Octane

92 55

Speed

65

What is the best speed to get the best gas mileage?

The Main Effects Plot show the average value for each of the levels of the three independent variables. Each average is based on 4 data points. Extra credit: Can you look at the experimental trials table and say why each level has a total of 4 data points?

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The Process Of Experimentation (continued) 3. Perform Analysis (continued) Collect & Analyze Data (Continued) Cube Plot (data means) for gas mileage 19 -, +, + Pressure, Octane, Speed -, +, -

+, +, + 22 +, +, -

30

33

+ -, -, +

+, -, + 21

18

Octane

+

Speed –

-, -, -

27 26 –

Tire Pressure

+

–

+, -, -

Each corner of the cube represents an experimental trial from the trial table For example, when tire pressure is negative (-), octane is negative (-) and speed is negative (-), the gas mileage is 26 (x,y,z is the convention) Can you tell which combination of tire pressure, octane and speed is the best by looking at the cube? The cube shows the result of the interaction between tire pressure, octane and speed.

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The Process Of Experimentation (continued)

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3. Perform Analysis (continued) Draw Conclusions - Speed has an important effect on gas mileage - Tire Pressure doesn’t significantly affect gas mileage - Octane doesn’t significantly affect gas mileage Verify Results - Run additional trials at optimum settings - Conduct MSA on data results

4. Determine Solutions Drive at 55 mph to get the best gas mileage Set tire pressure for best tire wear results Buy the octane that optimizes cost or engine cleanliness

5. Record Results 6. Standardize 7. Determine Future Plans Any ideas on how the results from this experiment could be used for further experimentation?

Replicate the experiment to get a better indication of the effects and to quantify variability

Test beyond the original limits of the X

Test at midpoint for nonlinear Y responses

Try additional potential X’s

Block by season, tire type, fuel type, etc.

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Full Factorial DOE

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Full Factorial DOE Full Factorial Design of Experiment Is used to study the Vital Few X variables and all possible interactions Can be quite costly when the number of Vital Few X’s is large Can study main effects Can study all interactions

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Full Factorial Layout: 3 Factors, 2 Levels

Std. Order 1 2 3 4 5 6 7 8

Factor 1 – + – + – + – +

Factor 2 – – + + – – + +

Factor 3 – – – – + + + +

For 3 factors, each at 2 levels, there are 23 = 2 x 2 x 2 = 8 combinations of factor settings. (Levels Factors = Combinations) Notice the pattern of factor settings in the standard order.

This is a 3–factor, 2–level full factorial layout arranged in “standard order.” Each row of the full factorial layout represents a set of experimental conditions. There are 8 different experimental conditions in this design layout.

Does this full factorial layout look familiar? Where did you see this before?

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Visualizing The Experimental Space +

2 Factors = A SQUARE Factor 2

– –

Factor 1

+

3 Factors = A CUBE

+

Factor 2

+ –

– –

Factor 1

+

Factor 3

Review how the square is constructed. To add a third factor, you need a three–dimensional cube plot. A cube helps us visualize the experimental space covered by the 3 factors. Each corner represents 1 set of experimental conditions. 23 = (Two Levels)(Three Factors) = 8 experimental conditions.

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The Factorial Pattern Of Experimentation k Factors Order X1 k=1 k=2

k=3

k=4

k=5

k

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 • • • 2k

– + – + – + – + – + – + – + – + – + – + – + – + – + – + – + – +

X2

X3

X4

– – + + – – + + – – + + – – + + – – + + – – + + – – + + – – + +

– – – – + + + + – – – – + + + + – – – – + + + + – – – – + + + +

– – – – – – – – + + + + + + + + – – – – – – – – + + + + + + + +

X5 • • • – – – – – – – – – – – – – – – – + + + + + + + + + + + + + + + +

20

Xk

The number of trials = (2 levels)(k factors)s = 2k . Full factorial layouts can be generated for any number of factors. This table displays factorial designs arranged in standard order. Notice the pattern. A handy way to remember is by thinking how the levels alternate in the columns. For the first column, the levels alternate every 20 = 1 trial. For the second column, the levels alternate every 21 = 2 trials. For the Kth, the levels alternate every 2K-1 trials.

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Replication vs. Repetition Replication: Multiple execution of all or part of the experimental process with the same factor settings – Build different experimental units – In our car mileage example, replicate different experiments at a different time

Repeat tests: 2 or more observations that have the same levels for all factors – Performed on the same experimental unit DESIGN LAYOUT EXAMPLE 2

2 design with 2 replications Std. Order

Response

2

2 design with 2 repetitions Std. Order

Avg

-

-

y1

1

-

-

y11

y21

y1

2

+

-

y2

2

+

-

y12

y22

y2

3

-

+

y3

3

-

+

y13

y23

y3

4

+

+

y4

4

+

+

y14

y24

y4

1

-

-

y5

2

+

-

y6

3

-

+

y7

4

+

+

y8

It allows an experimenter to obtain an estimate of experimental error. This estimate becomes the basic unit of measurement for determining whether observed differences are statistically significant. It yields more precise estimates of factor effects

Repetition

Obs 2

1

Replication has 2 important properties:

Obs 1

May affect the precision of the measured response, but it does not affect the logical structure of the experiment

Why Replication? To measure experimental variability. So we can decide whether the difference between responses is due to the change in factor levels (an induced special cause) or to common cause variability. To see more clearly whether or not a factor is important. Replication provides the opportunity for factors that are unknown or uncontrollable to balance out. Along with randomization, replication acts as a bias–decreasing effect.

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Randomization: The Experimenter’s Insurance Definition of Randomization: To assign the order in which the experimental trials will be run using a random mechanism. – It is not the standard order – It is not running in an order that is convenient – Minitab will randomize for us

Why Randomization? – Averages the effect of any lurking variables over all of the factors in the experiment

What is a Lurking variable? – A variable that has an important effect and yet is not included among the factors under consideration

How and why should we randomize the order in which we conduct an experiment? Randomization reduces the introduction of a systematic bias into an experiment. We call this bias a “lurking variable.” Lurking Variables:

Safeguard: Randomize the order of the experimental trials to protect against the effect of lurking variables Action: If the lurking variable creates a trend, it can be compensated for in the numerical analysis Conclusions can then be drawn from the original factors that are not affected by such lurking variables

Definition

A variable that has an important effect and yet is not included among the factors under consideration because: – Its existence is unknown – Its influence is thought to be negligible – Data on it is unavailable © GE Capital, Inc., 2000

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Design Of Experiment Summary Provides process performance data under different types of operating parameters Establishes cause and effect relationships between a process Y and possible X’s: – Verify the Vital Few X’s – Determine X values for optimal performance – Predict future process performance

Can be used in both incremental and exponential process improvement studies

Caution: Prior To Implementing Solutions, Understand The Difference Between Experimental And Actual Business/Process Conditions

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Reference Material– Analyzing DOE Data

The following pages are reference only and will become helpful if you are contemplating the use of a DOE in your project. Sit down with your mentor after you review this section and determine feasibility.

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The Process Of Experimentation 1. Define Project Identify responses

2. Establish Current Situation 3. Perform Analysis 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8

4. Determine Solutions 5. Record Results 6. Standardize 7. Determine Future Plans

Identify factors Choose factor levels Select design Randomize runs Collect data Focus of this module Analyze data Draw conclusions Verify results

For review: The steps in Designing an Experiment. In this module, we will focus on Step #3–Perform Analysis. We will investigate how you analyze the data collected from the experiment. You saw in the car gas mileage example how we analyzed the data from that full factorial experiment. Now we will use the Capital Logistics Case Study on “On-Time Delivery” to see how they used Design of Experiment to identify the vital few X’s.

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Steps in Analysis: Full Factorial, Replicated Designs

26

3.6 Analyze Data: Diagnostics:

3.6.1. Plot the raw data.

Is data OK? 3.6.2. Plot the residuals*.

Minitab will provide this for you.

3.6.3. Examine factor effects. Analysis:

3.6.4. Confirm impressions with statistical procedures.

Make inferences

3.6.5. Summarize conclusions.

This is the “Analyze Data” step, which is one step in the process of experimentation on the previous page.

After using Minitab to check the data, the next step is to plot the residuals.

Steps in analyzing the data:

Residuals are the “leftover” variation in the data after you have accounted for the main cause of variation. Plotting the residuals should show a normal distribution. If the residuals are not normally distributed, it is a sign that there is another variable present that has not been accounted for (a “lurking” variable).

In steps 1 & 2, we begin by checking for problems with the data before doing the DOE analysis on the data. Minitab will plot the data for you. This will help to:

Find defects, outlier or patterns in the data

Get a feel for the actual data

Get impressions of what the data is going to tell us, to guide our analysis

* We don’t discuss residuals here, but to continue to Step 3, seek assistance from someone who knows how. Once the data has been validated and looks acceptable, you are ready to examine the factor effects. Let’s look at our Capital Logistics GB Case Study.

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Background For DOE: Capital Logistics GB Case Study

27

In Step 6 of the Analyze Phase, the Green Belt and the project team at Capital Logistics determined, based on the results of their Hypothesis Testing, that there were 2 X’s that had an impact on the ontime delivery of shipments to customers. The 2 X’s were: – Drivers – Distance The team determined that there wasn’t anything that they could do to change the distance that each truck traveled to make their deliveries–the routes were automated by the system and were determined to be the shortest routes. They decided to focus on Driver as a factor, as this was under their immediate control. The team used the Cause & Effect diagram to brainstorm potential root causes as to why Driver/Trucking company influenced Time. The resulting list included: – size of the vehicle – type of tire – dispatch method – fuel capacity – type of engine After reviewing their data further, the team decided to conduct a Design of Experiment. They would use Size of Vehicle and Tire Type as possible Vital X’s in their DOE. Each of these factors has 2 levels: – Size of Vehicle is either 66 or 62 feet – Tire Type is either X or Y The DOE was set-up and conducted to determine the Vital X that would have the greatest impact on the timeliness of shipment deliveries to their customers.

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Examine Factor Effects The 3rd Step in “Analyze Data”: Y = f (X1, X2, X3, …, Xn) Y (Response) = On-Time Delivery of Shipment Xi (Factors) = Size of Truck, Tire Type How do the factors affect the response? How do the combinations (interactions) of factors affect the response? – We can write the equation that answers these questions

This is your Y = f(X) Transfer function: On-Time Delivery = Constant +(-) Size of Truck + Tire Type +(-) Size of Truck *Tire Type Interaction Effect.

We can simplify the factor names with abbreviations in our DOE (see next page).

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Factor Names And Interaction Symbols

It is useful to abbreviate factor names. There are several ways to do this: – Choose the first letter or first two letters of each factor – Assign factors a letter: A, B, C, D, . . .

Denote the interaction between Factor A and Factor B as: – A x B or AB

For two factors (A and B) there is one interaction: AB For three factors there are – Three two-way interactions: AB, AC, BC – One three-way interaction: ABC

How many interactions are there for four factors (A,B,C,D)?

Interactions for 4 factors: 2-way: AB, AC, AD, BC, BD, CD, (6) 3-way: ABC, ACD, BCD, ABD (4) 4-way: ABCD (1) Total (11) Higher level interactions (3-way or more) are hard to plot and explain. They are also not very likely to occur.

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Examine Factor Effects–In Minitab Create Factorial Design–in Minitab

30

Data File: GB Case Study.mtw

Type of design = full factorial

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Examine Factor Effects–In Minitab

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Select Two Replicates

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Examine Factor Effects–In Minitab

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Name Factors

Stat > DOE > Create Factorial Design Click on Factors. Enter “Name”. Click “OK” twice.

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Examine Factor Effects–In Minitab Inputting Responses into Minitab

Note: Ensure that when you enter this data into your Minitab Worksheet, you put the times in the correct rows, based on the correct truck & tire combination of (+) and (-).

Note: Ensure that when you enter this data into your Minitab Worksheet, you put the times in the correct rows. Your experiment may have run in a different order and you may have coded your factors differently.

(+)

(-)

Truck Size 66 66 66 66 62 62 62 62

Tire Size X (+) X Y (-) Y X (+) X Y (-) Y

Time 126 140 30 60 -50 -80 -30 -50

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Examine Factor Effects–In Minitab Analyze Factorial Design In Minitab: Stat > DOE > Analyze Factorial Design

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Examine Factor Effects–In Minitab

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Analyze Factorial Design

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Examine Factor Effects–In Minitab

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What does the Pareto Chart tell you about the factors & interactions?

Is Truck Size significant? Is Tire Type significant? Is the interaction of Truck Size & Tire Type significant?

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Examine Factor Effect–In Minitab

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Analyze Factorial Plots

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Examine Factor Effects–In Minitab

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Set-up Main Effects

Stat > DOE > Factorial Plots Click OK.

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Examine Factor Effects–In Minitab

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Set-up Main Effects

Stat > DOE > Factorial Plots Click OK twice.

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Main Effect Plots In our GB Capital Logistics On-Time Delivery Case Study: Main Effects Plot (data means) for Time

1

-1

1

-1

90

Time

60

30

0

-30

Truck Size

Tire Type

How do Truck Size & Tire Type affect Time?

A useful way to graphically show factor effects is by using Main Effects Plot. Simply plot the average response for each level (+ or -). The steeper the line, the more significant the effect. The slope of the line determines whether the effect is positive or negative. A positive slope is a positive effect and vice versa.

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Interaction Effect Differences between 2 or more factor level combinations In our Capital Logistics GB Case Study: On-Time Delivery If we are looking at 2 factors: Truck Size Tire Type Is On-Time Performance different when: Truck Size Tire Type 62 ft. X 62 ft. Y 66 ft. X 66 ft. Y Question: Which of the following indicates Interactions between factors? –

–

Factor B

+ –

+

Factor B

+ Factor A –

Response

Factor A

Response

Response

– Factor A +

–

+

Factor B

+

Adapted from Lawson, John and John Erjavac, Basic Experimental Strategies and Data Analysis. Provo, UT: Brigham Young University, p. 104.

We use the same calculation for Interaction Effects as we did for Main Effects. The only difference is we first need to generate the interaction column. We then use this column for the calculation of the Interaction Effect.

If the lines are not parallel, there is interaction between the factors (variables).

Why are interactions important? Why is it important to determine the effect of interactions?

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Interaction Effect In our GB Capital Logistics On-Time Delivery Case Study: Interaction Plot (data means) for Time Truck Size -1 1 100

Mean

Late

On-Time

Early

50

0

-50

-1

1

Tire Type

How do Truck Size & Tire Type interact? How do the interactions affect time? What does this tell us? In this case, our goal was On-Time-Delivery. None of the points give us OTD for mean=0. Therefore, we should go with the (-) Tire Type and the (-) Truck Size (X Tire Type and Truck Size of 62.) This will get us closest to a mean of zero.

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Steps In Analysis: Full Factorial, Replicated Designs

Diagnostics: Is data OK?

43

3.6.1. Plot the raw data. 3.6.2. Plot the residuals. 3.6.3. Examine factor effects.

Analysis: Make inferences

3.6.4. Confirm impressions with statistical procedures. 3.6.5. Summarize conclusions.

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Confirm Impressions

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The 4th Step in “Analyze Data”: By now you have a good idea about the influence of the factors in the experiment. You can confirm these impressions statistically by performing a Hypothesis Test. Ho: Factor has no effect on the results Ha: Factor has an effect on the results p α: Accept Ho p α: Reject Ho

Statistical Analysis Confirms The Results Of The Graphical Analysis

Now we are determining the statistical significance of the effects.

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Confirm Impressions With Minitab

45

In our GB Case Study: What does the Minitab Session Window tell you ?

What do the p-values for:

Truck Size

Tire Type

Truck Size * Tire Type

Indicate? Does this statistical analysis confirm the graphical analysis?

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Steps In Analysis: Full Factorial, Replicated Designs

Diagnostics: Is data OK?

46

3.6.1. Plot the raw data. 3.6.2. Plot the residuals. 3.6.3. Examine factor effects.

3.6.4. Confirm impressions with Analysis: statistical procedures. Make inferences 3.6.5. Summarize conclusions.

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Summarize Conclusions The 5th Step in “Analyze Data”: List all the conclusions you have made during the analysis Interpret the meaning of these results – For example, relate them to known physical properties or an expert’s personal knowledge of the process

Make recommendations Formulate and write conclusions in simple language

What conclusions would you make from the Capital Logistics DOE study?

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Summarize Conclusions (continued)

From our Capital Logistics GB Case Study on On-Time Delivery: The Green Belt and the project team reviewed the results of the DOE. They saw that there seemed to be a link between on-time performance and the size of the truck unit, as well as an interaction effect between Tire Type and Size of Truck on on-time performance. They returned to their Fishbone (Cause & Effect) Diagram with greater granularity, and asked why these factors would influence on-time performance. They validated these reasons through field observations. The team validated that the larger size trucks took longer at some locations. In addition to the time involved with maneuvering in a cramped environment, on certain routes these trucks had a higher incidence of tire failure (lateral movement caused by tight turns increased the stress on the tires, increasing the number of flat tires). By using the data & results from the DOE, the team had determined the root causes of the on-time performance problem and were ready to start to brainstorm solutions to address/control these “Vital X’s”.

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Reducing the Size of Experiments– Fractional Factorial DOE

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Reducing The Size Of Factorial Experiments Many factors potentially impact

the quality of any process/product The factorial strategy is an efficient approach to experimentation, compared to “one-at-a-time” When factors are investigated at 2 levels, the number of experimental runs is 2k (note: the “k” needs to be raised, because it is 2 to the power of k - “k” is the exponent) This can result in a large number of runs, even with a relatively small number of factors

For a 2–Level Factorial with k Factors….. Number of runs = 2k

Limited resources allow you time to run only 4 trials in the allotted time.

Number of Factors

Number of Runs

1 2 3 4 5 6 7 8 9 10 • • • 15 • • • 20

2 4 8 16 32 64 128 256 512 1024 • • • 32,768 • • • 1,048,576

Which 4 trials will you choose? Full factorial is time-consuming and costly as the number of factors increase.

From a Full Factorial (4 factors): Number

Also consider the number of 2-way and higher order interactions as the number of factors increases. For 4 factors, let’s look at every possible effect (main & interaction) and the overall average. Evaluating the average is what the extra run is used for.

Overall Average

1

Main Effects: A B C D

4

2-way interactions

6

(AB, AC, AD, BC, BD, CD) 3-way interactions

4

(ABC, ABD, ACD, BCD) 4-way interactions

1

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Fractional Factorials

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Fractional Factorials*: Provide a middle ground for design of experiment Are used to expand on the study of the Vital Few X variables at a low cost Can study main effects Can study selected (and few in number) interactions

Fractional Factorials Allow You To Reduce The Size Of An Experiment And Select Certain Runs

*Fractional Factorials are beyond the scope of this course. Consult your BB/MBB or refer to the “Book of Knowledge” for further information.

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Strategy For Choosing The Appropriate Design The Knowledge Line Current State of Process Knowledge Low

Type of Design

High

Main Effect /Screening

Fractional Factorials

>5

4-10

Usual # of Factors Purpose: Identify

Main effect critical factors - vital few

Estimate

Full Factorials

Response Surface

1-5

2-3

Some Relationships interactions among factor

Crude direction Some All main effects for improvement interactions and interactions

Step 7

Screening DOE

Step 8

Optimal factor settings Curvature in response, empirical models

Optimization DOE

Types of Experimental Design

Types of Experimental Design

Screening DOE–experiments which are used to screen out the vital few X variables out of many at a very low cost.

Fractional Factorials–provide a middle ground. They are used to expand on the study of the vital few X variables at a low cost.

Can study the main effects

Can’t study the interactions

Optimization DOE–Experiments which are used to determine the proper settings for each vital X.

Can study main effects Can study selected (and few in number) interactions Full Factorials–are used to study the vital few X variables and all possible interactions. They can be quite costly when the number of vital few X’s are large.

Can study main effects Can study all interactions

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Optimization Design Of Experiment Activity (40 minutes)

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Desired Outcome: Practice how to set-up a DOE What Team Preparation

How Choose a facilitator, scribe, timekeeper, and/or note taker

Who

Timing

Team

2 mins.

Facilitator

15 mins.

Facilitator

15 mins.

All

8 mins.

Determine the timing for each activity below Agree on the example you will use for the exercise – Your own project – How to get a great lawn – How to make the best chocolate chip cookies – How to lose weight Set-up the DOE

For the example you selected, identify 3 factors at 2 levels (+/-) each Using the worksheet on the following pages, design the experiment up through Step 6

Set-up Optimization DOE

Discuss what the experiment might demonstrate, were you to execute it

Report Out

Choose a spokesperson to report out on the design of your experiment, and the questions you have about running it

Brainstorm your list of questions for how to run this experiment

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Design Of Experiments–Breakout Activity Worksheet

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1. Define the problem 2. State the hypothesis 3. Identify the dependent (Y) and independent (X) variables Dependent Variable (Y)

=

Independent Variables (X’s)

= = =

4. Determine the test levels for each independent variable (X).

Independent Variables (X’s) (Factors)

Level -

Level +

5. Calculate the number of trials to test all combinations of test levels. # of independent variables

# of trials = # of test levels

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Design Of Experiments–Breakout Activity Worksheet (Continued)

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6. Construct the experimental trials table

Independent Variable (X) #1

Independent Variable (X) #2

Independent Variable (X) #1

Independent Variable (X) #2

Independent Variable (X) #3

Independent Variable (X) #3

Dependent Variable (Y)

Dependent Variable (Y)

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Appendix: Example Of Designed Experiment: GE Card Services

56

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DOE Example: Defining The CTQ Overall Quality EX/VG - 57% .26

.25

.11

Financial & Marketing Info EX/VG - 30%

Authorizations EX/VG - 60%

Impact

Marketing Rep EX/VG - 54%

.12

.16

New Account Approval EX/VG - 34%

*

Card Production EX/VG - 47%

Performance

*

Billing Statements EX/VG - 40%

Impact Overall 13%

0.23 0.2 1

0.8

0.6

0.4

0.28

Amount/ 18% 26% Type Of Info

0.2

Excellent

#1 Speed

Accuracy 20%

0.24

Credit Lines 16% 25% Granted 0 0% 20% 40% 60% 80% 100%

Insert 12% Capability

0.17 1

0.8

0.6

0.4

34%

Timeliness 10% 33% Of Delivery

0.38

Speed Of 24% 25% Approval

Customer Service EX/VG - 44%

Performance

Overall 18% 16% 0.59

.15

Payment Processing EX/VG - 54%

0.2

0

Card Quality

23%

41% 47% 53%

0% 20% 40% 60% 80% 100% Excellent Very Good

Very Good

Inseparable CTQ’s One Experience To The Customer

#1 Speed #2 Accuracy

Speed Is The #1 CTQ Of The New Account And Card Experience

A project team was working to improve customer satisfaction with the process of approval for and issuing of new credit cards. One of the key drivers of satisfaction was identified as time to issue cards, i.e., the cycle time between a consumer’s approval for a credit card, and the time he/she received it.

When examining the process map, it became clear that many faxed and mailed applications needed additional information before they could be processed. This often involved phone or written correspondence with the applicant, which slowed the process considerably.

Through segmentation, the team found that applications mailed or faxed in took considerably longer than other applications where the application information was entered electronically at the store.

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DOE Example: Causes Of Time Consuming Delays

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79% of queuing for non-fraud! Why? Non-Fraud Queue Pareto 50%

Frequency %

40%

30%

20%

10%

0% Msg Home #/AC

Wrng Promo Cd

Msg/Wrng Brnch/Dlr/ Str #

Msg/ Wrng SS#

Unknown

CBR Issues

Msg/ Wrng Zip

Duplicate

Missing and illegible information is a major cause of delays. What can be done to reduce missing and illegible information? Many felt that little could be done to improve the situation for handwritten applications.

The team discovered that 79% if the applications which were “in queue”–i.e., on hold before being processed – were in queue for reasons other than potential fraud issues. The team analyzed the reasons for non-fraud queuing and created a Pareto chart.

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DOE Example: The Designed Experiment

Factor Name

Explanation

Standard Level

New Level

App. Type

Terms of the credit agreement printed on the application

Present (Full)

Absent (Naked)

Instructions

Written instructions on how to complete the form included

No

Yes

Flags

Critical information without which the application can’t be processed is specially noted

No

Yes

Boxes

Delineated boxes to hold numeric information, e.g., phone

No

Yes

(

)-

-

Insurance

Location on the form for the purchase of the optional credit card insurance

Not Body*

Body*

Page Layout

Orientation of the form

Portrait

Landscape

The only influence that the business has on legibility and completeness is through the application itself. The team then decided to study what they could do to the application to make it easier for their customers to fill out. The factors shown above were chosen for study. *Body/Not Body–refers to location of the insurance text on the application form. On a landscape layout, “not body” applications had text to the right of the application. On a portrait layout, “not body” applications had text at the bottom of the application.

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DOE Example: Experimental Complications Complications

The difficulty in tracking many (in this case, 16) different applications through the process Large amount of person-to-person variation with respect to legibility and completeness, making it difficult to assess the effect of changes

Remedies

Test the applications outside the normal process Have each tester fill out two applications

The applications were paired (eight pairs of applications) and customers were asked to fill out a pair of applications and provide feedback regarding the two application versions. The applications were paired so that customers experienced the factors at both levels. Eighty customers filled out a pair of applications in return for a $10.00 gift certificate. The order which each paired application was presented to the customer was randomized throughout the test to balance the effect of order on the results. Customers were asked whether they preferred one application version over another and why. Applicants signing for credit insurance were asked whether they understood that they had requested insurance coverage.

The completed applications were sent for imaging, and the imaged applications were reviewed by an associate to record the legibility and completeness of each field on each application. A legibility score was assigned using a 5-point scale; missing information was given a “0” and fields not relevant to the applicant were recorded as not being applicable. Preferred applications were given a score of “1,” not preferred “0,” and no preference was indicated by a “0.5.”

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DOE Example: Responses

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Two Key Responses Were Studied: A combined completeness and legibility score, which was based on the percent of necessary information that was both present and legible A preference score, which told which of the two applications the customer preferred

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DOE Example: Analysis Main Effects Plot – Means For Legibility And Completeness

Legibility and Completeness

0.849 0.843 0.837 0.831 0.825

Naked

Full No Portrait

App. Type

Yes

No

Instruct

Yes

No

Flags

*

Yes

Boxes

Body

Bottom

Insurance

*

Landscape

Pg. Layout

*

Main Effects Plot – Means For Preference 0.67

Preference

0.59 0.51 0.43 0.35

* Effect was significant

Naked

Full

No

Yes

App. Type

Instruct

*

*

No

Yes

Flags

No

Yes

Body

Bottom

Landscape Portrait

Boxes

Insurance

Pg. Layout

*

*

*

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DOE Example: Results

Factor

Effect On Legibility And Completeness

Effect On Preference

Recommendation

Application Type

Full 82.8%

Naked 84.8%

Full 34%

Naked 66%

Naked

Instructions

H

H

No 57%

Yes 43%

Yes1

Flags

No 82.9%

Yes 84.8%

H

H

Boxes

H

H

No 59%

Yes 41%

No

Not Body 85.3%

Body 82.4%

Not Body 56%

Body 44%

Not Body

H

H

Portrait 36%

Landscape 64%

Landscape

Insurance Page Layout

1

Yes

The data does not show that instructions improve legibility and completeness, but it is felt that instructions should be provided for clarification purposes. Also, consideration should be given to improving the effectiveness of the instructions provided on the application.

+ Effect not significant

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1

Step 9 Step 8 provided the experimental techniques to establish the relationship between the measurable Y characteristics and the controlling X factors. In step 9, those relationships (transfer functions) wil be used to define the key operating parameters and tolerances to achieve the desired performance of the CTQ’s/ One should be able to set the tolerance of X factors if the X-Y relationship and the specifications of Y are given.

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2

Principle Of Tolerancing Tolerance: the allowable range of variation of X while still meeting the requirements of Y. Establish tolerance of X based on the requirements of Y, or often the specification limits via the Transfer function The tolerance should allow the project to reach the project objectives established in step 5 When more than one CTQ is involved, be aware of the tradeoffs among CTQ’s Be aware of the variations due to the measurement of X’s and Y Y’s USL T LSL

Y = f (X)

Tolerance: the allowable range of X X

Lower Limit of Tolerance

Upper Limit of Tolerance

It is complicated to calculate tolerance for ƒ (X) with multiple X’s. Use:

Crystal Ball

Calculus

It will be covered in detail in the GE-DFSS course

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Consideration Of Measurement Variations

3

Y

USL The measurement variation of Y

T LSL

New tolerance considering the variation of Y measurement

Y = f (X)

X

Lower Limit of Tolerance

Upper Limit of Tolerance

Y

USL The measurement variation of Y

T LSL

Y = f (X)

New tolerance considering the variation of X + Y measurement X

The measurement variation of X

Lower Limit Upper Limit of Tolerance of Tolerance

Estimate the gage error for Y using the σe from the MSA study in Step 3. The width of the measurement error distribution is 5.15σe Establish the gage error for X in Step 10. Use the 5.15σe from the MSA of X.

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Example: Weight Loss Wellness Program

4

lbs. week 3

Weight 2 Loss 1

USL

Target

Transfer Function

LSL

0 1

1.4

2

2.7

3 hrs./week

CTQ requirements: 4 Target to lose 2 lbs/week At least need to lose 1 lb/week No more than 3 lbs/week due to health concerns These goals do not take into consideration any error in the Y or X due to measurement error (MSerror) Since we have performed a Gage R&R on both the Y and X measurement system we know the GRR % Tolerance for Y and X Lets use the information to develop the operating limit for our actual X

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Example: Weight Loss Wellness Program (continued)

The measurement variation of Y

lbs. week 3

USL

Target

Weight 2 Loss 1

LSL

0 1

2

1.55

Exercise

hr/week

New operating limits on X due to variability in the Y and X measurements

2.55

To get a more conservative tolerance for X, taking into account measurement error (MSerror) on Y, we center the width of the 5.15 MSerror distribution on both the USL and LSL for Y. Q: Why center the measurement error distribution on the spec? A: The error in measurement system will effect us most at the ends of the tolerance Q: Why start from within the tolerance? A: This results in a more conservative tolerance for the X factor operating within. The new operating limits of X will ensure you stay in spec for Y.

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Example: Weight Loss Wellness Program (continued) The measurement variation of Y

6

lbs. week 3

Weight 2 Loss 1

USL

Target

LSL

0 1

1.5

2

Exercise

2.6

3 hrs./week

New operating limits on X due to variability in the Y measurements

How to Determine the values of the new Y start points Given Y Tolerance = 2; GR&R = R&R % Tolerance =10% 1. Calculate MSerror in Y units MSerror = (R&R % Tolerance) ‫( ٭‬Tolerance) MSerror = (10%) ‫( ٭‬2) = .2 2. Take ½ MSerror (½) ‫( ٭‬MSerror) = ½ (.2) = .1 3. Calculate new start points for Y axis New Y USL start point Y USL- (½ MSerror) = 3 - .1 = 2.9

New Y LSL start point Y LSL + (½ MSerror) = 1 + .1 = 1.1

Our purpose is to get an operating tolerance on the X but we first should adjust the Y tolerance due to measurement error.

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Example: Weight Loss Wellness Program (Continued) The measurement variation of Y

7

lbs. week 3

USL

Target

Weight 2 Loss 1

LSL

0 1

1.5

2

Exercise

2.6

3 hrs./week

New operating limits on X due to variability in the Y measurements

Given: X is R&R % Tolerance = 20% New X Tolerance = USL – LSL (from last page) New X Tolerance = 2.6 –1.5 = 1.1 Calculate MSerror in X units 1. MSerror = (20%) ‫(٭‬1.1) = .22 2. Take (½) ‫(٭‬MSerror) = (½) ‫(٭‬.22) = .11 3. New X USL = USLx - (½ (MSerror)) = 2.6 - .11 = 2.49 New X LSL = LSLx - (½ (MSerror)) = 1.5 + .11 = 1.61

Correct X USL and LSL for the MSerror of the MSA system used to measure X using same methods as with Y. This has the effect of further tightening the X Tolerance If you operate in these new operating limits of X you should be ensured of staying in spec on Y. That means no defects.

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Summary

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C

8

Set the process tolerances based on product specifications (exercise time needed to achieve desired weight loss goal). Adjusted our process tolerances to account for product measurement variation The tolerance principle is relatively simple and the application is relatively straightforward when: 1) The measurement variation of of Y and X are sufficiently small to be ignored 2) Only one X factor involved However, when measurement variations of Y and X needs to be considered and multiple X factors are involved, the math techniques could be more complicated. Courses on DFSS Statistical Design Method or DFSS Statistical Tolerance are offered in various GE businesses.

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Control Phase Flowchart

D

M

1

A

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CONTROL PHASE OVERVIEW

Control 10: Validate Measurement System

Control 11: Determine Process Capability

Control 12: Implement Process Control System & Project Closure

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Control Phase Overview

2

What is the Control phase? The Control phase is when your team: Ensures that the new process conditions are documented and monitored via statistical process control methods After a “settling–in” period, reassesses the process capability Closes the project Why is the Control phase important? This phase is important because it ensures that process improvements are implemented together with appropriate process controls to ensure that the process changes are sustained into the future. It also is an opportunity for the team to “prove” that the project process performance goal has been met. Steps involved in the Control phase Control 10: Validate Measurement System Control 11: Determine Process Capability Control 12: Implement Process Control System & Project Closure

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The12-Step Process Step Define

Description

Focus Tools

Deliverables

A

Identify Project CTQ’s

Project CTQ’s

B

Develop Team Charter

Approved Charter

C

Define Process Map

High Level Process Map

Measure 1 2 3

Select CTQ Characteristics Define Performance Standards Measurement System Analysis

Analyze 4 Establish Process Capabilities 5 Define Performance Objectives 6 Identify Variation Sources

Improve 7 Screen Potential Causes 8 Discover Variable Relationships 9 Establish Operating Tolerances Control 10 Define & Validate Measurement System on X’s in Actual Application 11 Determine Process Capability 12 Implement Process Control

Y Y Y

Customer, QFD, FMEA Project Y Customer, Blueprints Performance Standard for Project Y Continuous Gage R&R, Data Collection Plan & MSA test/Retest, Attribute Data for Project Y R&R

Y

Capability Indices

Y

Team, Benchmarking

X

Process Analysis, Graphical Analysis, Hypothesis Tests

X X

DOE-Screening Factorial Designs

Y, X Simulation

Process Capability for Project Y Improvement Goal for Project Y Prioritized List of all X’s

List of Vital Few X’s Proposed Solution Piloted Solution

Y, X Continuous Gage R&R, MSA Test/Retest, Attribute R&R Y, X Capability Indices Process Capability Y, X X

Control Charts, Mistake Sustained Solution, Proofing, FMEA Documentation

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Control 10–Validate Measurement System

4

What does it mean to Validate Measurement System? In the Measure phase, you focused on validating the measurement system for the Project Y. In this step, you should now validate the measurement system for the Vital X’s. A Measurement System Analysis (MSA) is the overall process to test your data for its validity. Before actually performing the MSA, you will have to develop a data collection plan for the Vital X’s. You should focus on the Vital X’s at this point because you want to develop Control Plans for each Vital X. Why is it important to Validate Measurement System? Validating the Measurement System is important because you need to have data that you can trust in order to make decisions with that data. If your data is not telling you the truth, you are likely to make a decision with that data that will add more variation to the process. As part of your Process Control System, you will monitor the Vital X’s to make sure they stay in control. Therefore, you must validate the Measurement system used to collect the Vital X data. What are the project tasks for completing Control 10? 10.1 Validate Measurement System 10.2 Determine whether Measurement System is adequate to measure Vital Few X’s

CONTROL STEP OVERVIEW

Control 10: Validate Measurement System

Control 11: Determine Process Capability

Control 12: Implement Process Control System & Project Closure

10.1 Validate Measurement System 10.2 Determine whether Measurement System is adequate to measure Vital Few X’s

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Control 11–Determine Process Capability

5

What does it mean to Determine Process Capability? Process Capability is the measure of process performance relative to the Customer’s CTQ. It is measured again at this point in the process in order to see if there was a process improvement. If a pilot is conducted, the improvement team should measure process capability from the pilot and then, once full implementation takes place (after Step 12), measure process capability again. Why is it important to Determine Process Capability? Process Capability is important at this stage of the project because you want to be able to compare baseline performance before improvements to the new Process Capability once improvements have been implemented. It is also important to statistically validate the improvement in the process through the use of a Hypothesis Test, such as the 2-Sample t-Test. What are the project tasks for completing Control 11? 11.1 Evaluate Process Capability of the improved process 11.2 Confirm statistically that the improvement goal has been met

CONTROL STEP OVERVIEW

Control 10: Validate Measurement System

Control 11: Determine Process Capability

Control 12: Implement Process Control System & Project Closure

11.1 Evaluate Process Capability of the improved process 11.2 Confirm statistically that the improvement goal has been met

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Control 12–Implement Process Control Systems

6

What does it mean to Implement Process Control System? A Process Control System is a system of activities whose purpose is to maintain process performance at a level that satisfies customers’ needs and drives the ongoing improvement of process performance. A Process Control System consists of three parts: Documentation, a Monitoring Plan and a Response Plan. During this step of the project, you are also ready for project implementation. Once the improvement is implemented and the process improvement is verified, the final step of the project is Project Closure. During Project Closure, you will finalize project documentation, leverage learning to other areas of the business and celebrate project completion with your team. Why is it important to Implement Process Control? A Process Control System will help maintain the gain that occurred with the process improvement. Without control of an improved process, the process tends to revert to its old performance. What are the project tasks for completing Control 12? 12.1 Implement a Control strategy for each Vital X 12.2 Prepare Process Control plan 12.3 Implement a solution 12.4 Close the project

CONTROL STEP OVERVIEW

Control 10: Validate Measurement System

Control 11: Determine Process Capability

Control 12: Implement Process Control System & Project Closure

12.1 Implement a Control strategy for each Vital X 12.2 Prepare Process Control plan 12.3 Implement a solution 12.4 Close the project © GE Capital, Inc., 1999 DMAIC GB U TX PG

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Statistical Thinking

D M Practical Problem

7

A Statistical Problem

Statistical Solution

Characterize the Root cause process analysis – Stability – Critical X’s – Shape Measure the influence of the – Center critical X’s on – Variation Data Integrity the mean and variability – MSA Capability – Test – Brainstorm – ZBench ST & LT potential X’s – Model – Sampling plan – Estimate

Problem statement – Project Y – Magnitude – Impact

I C Practical Solution

Verify critical X’s and ƒ(x) Change process Control the gains – Risk analysis – Control plans

Collect data The Practical-To-Statistical-To-Practical Transformation Process

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Refer To Diagram That Illustrates Process Steps Separated By Function. Shows Transfers Between Functions, And Which Function Is Responsible At Each Step.

Key Process & Output Measures

Root Cause X’s Refers To Document That Project Y’s Describes How The Task Should Process Sigma For Each Be Done, Or Project Y Refers To A Document That Describes The Step.

Procedure (From SOPs) For Each Measure, Describes Any Target, Numeric Limits, Or Tolerances To Which A Process Should Conform

Monitoring Standards For Each Measure, Describes How The Monitored Data Should Be Recorded, Who Should Record The Data And How.

Response Plan

Describes What Should Be Done For Those IllServed By These Defects.

Identifies Who Should Do What With The Defective Output.

Describes What Must Be Done To Prevent Special Causes That Worsen Performance Or To Incorporate These Special Causes That Improve Performance.

Describes What Must Be Done When We Fail Process Sigma Standard.

Preventive Action Procedure For Process Improvement

Response ResponseTo ToSignals Signalsof ofChange Change

Method For Corrective Action Recording For Containment Data

Checking CheckingThe TheWork Work

Plan PlanFor ForDoing DoingThe TheWork Work

Process Step (From Process Map Attached)

Monitoring

Documentation

Process Control Plan Worksheet 8

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Forms Of Intellectual Property

9

Patent Best Protection against independent development by others Gives right to exclude others from making, using selling, the invention or 20 years from filing Can wait 2-3 years for patent to issue Right granted by the government for new, useful, nonobvious inventions Trade Secret Rights exist only so long as actually kept secret Protects against theft or misappropriation, not independent development Does not require inventiveness in the patent sense Copyright Protects original works of authorship fixed in a tangible medium Does not protect against independent development Trademark Defines source of goods or services Arbitrary, fanciful marks get stronger protection

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Intellectual Property Infringement Avoidance Clearance And Assessment

10

It is critical to assure that improvement or new designs developed in the course of the project do not infringe on the Intellectual Property of others, external to GE. GE has a clear policy on infringement avoidance. “Intellectual Property Infringement Avoidance Process”. The team must conduct the necessary reviews to assure no infringement (consult the IP Business Champion for guidance). In general, if the answer is “yes” to any of the questions below, consult with the IP Business Champion and IP Designee for your business to obtain clearance before proceeding. 1) Is the team aware of any non-GE businesses who use substantially the same process or sell substantially the same process? 2) Will the project result in a product or process that is significantly different than a current GE product or process, and will it be commercially significant? 3) Have or will any services or products been obtained from an outside party I connection with this project, and is the project result commercially significant? 4) Will the product or process be exposed to non-GE parties, and be commercially significant? 5) Will the product or process be exposed to the public, and be commercially significant?

If the project obtained clearance from the Infringement Avoidance screen, then consider whether there is Intellectual Property to Capture and Protect, via Patent, Trade Secret, Copyright or Trademark. If the project results in a process or product that is new, non-obvious and useful and will be of significant commercial value. It may be patentable. Consult the IP Business Champion and IP Designee for your business and submit the new process or product for evaluation through the IDEAS website.

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1

Statistical Process Control– Overview

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Statistical Process Control: Learning Objectives

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Describe the two types of Control Charts Describe and use Variable and Attribute Control Charts Select the appropriate Control Chart for a given process based on data type Define the control limits and how they differ from specification limits Explain the decision errors in SPC Explain the rules (Minitab and Western Electric) to determine whether a process is out of control Describe and practice the use of Minitab to generate I&MR, X & R, U, C, P and NP chart

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Statistical Process Control

3

“The Application of Statistical Techniques for Measuring and Analyzing the Variation in Processes”

Control Charts Are The Primary Tools In SPC

First developed by Dr. Walter Shewhart, control charts serve as the best way to determine if a process is “in control.” By “in control,” we mean that the process is consistent and predictable. When a process is out of control, something about the process has changed. A cause for the change in the process should be sought.

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Five Main Uses Of Control Charts

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To reduce scrap and rework and for improving productivity Defect prevention. In control means less chance of nonconforming units produced. Prevents unnecessary process adjustments by distinguishing between common cause variation and special or assignable cause variation Provides diagnostic information so that an experienced operator can determine the state of the process by looking at patterns within the data. The operator can then make the necessary changes to improve the process performance. Provides information about important process parameters over time

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Process States The Four States of a Process 1. Chaos

Process out-of-control, producing non-conforming product Even the level of nonconformance is unstable Assignable causes dominate the output Fixes don’t work for very long

How To Begin To Sort Out The Problems To Be Solved?

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Process States (continued) The Four States of a Process 2. The Brink of Chaos

Process unstable, some nonconforming product is being produced Instability will continually change product characteristics Process output is influenced by assignable causes No assurance the next piece produced will be conforming

How To Determine Existence Of Assignable Causes?

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Process States (continued) The Four States of a Process 3. The Threshold State Process inherently stable over time, but producing some nonconforming product (process sigma is less than process sigma goal/standard Proportion nonconforming predictable Some non-conformances will be shipped If process natural spread is greater than the tolerance, common causes must be reduced/removed Process must be monitored to assure desired effect is achieved

How To Be Certain That The Process Has Improved?

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Process States (continued)

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The Four States of a Process 4. The Ideal State The process is inherently stable over time (process sigma > process goal/standard) Operating conditions are not changed arbitrarily (follow the process plan) The process average is set and kept at the proper level The natural spread of the process is less than the specified tolerance

How To Be Certain That None Of These Conditions Change Or Degrade?

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Variation And Control Charts

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40

Upper Control Limit* (UCL)

Measurement

30

Average

20

10

Lower Control Limit* (LCL)

0 0

10

20

Time Order of Sample

Control charts are used to distinguish between common and special causes of variation and use that understanding to control and improve processes. Control charts are characterized by two things: 1. The average (mean), or centerline, which represents the middle point about which plotted measures are expected to vary randomly. 2. Control limits, both upper and lower, which represent the performance boundaries you can expect for the process. Although measures vary, one would not expect to see plotted measures outside of these boundaries if the process operated predictably. *Note: Minitab displays UCL as 3.0SL (Three sigma limits) Minitab displays LCL as–3.0SL © GE Capital, Inc., 2000 DMAIC GB V TX PG

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Determining If Your Process Is “Out Of Control”

Zone A

10

Upper Control Limit (UCL)

Zone B Zone C Zone C

Average

Zone B Zone A

Lower Control Limit (LCL)

Source: Memory Jogger Plus, ©1994 GOAL/QPC

Dividing the control chart into zones can aid in detecting special cause variation. Each of the zones represent standard deviations from the mean. Zone C, for example, is + and - one standard deviation from the average.

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Minitab Rules

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1. One point beyond zone A (Western Electric) 2. Nine points in a row in zone C or beyond (All on one side.) (Western Electric) 3. Six points in a row, all increasing or decreasing 4. Fourteen points in a row, alternating up and down 5. Two out of three points in a row in zone A or beyond (Western Electric) 6. Four out of five points in a row in zone B or beyond (Western Electric) 7. Fifteen points in a row in zone C, above or below center 8. Eight points in a row beyond zone C, above or below center

+3σ

A

+2σ +1σ -1σ -2σ -3σ

B C C B A

These are the rules available in Minitab. You can find these rules under the “TESTS” button inside the Control Chart screen. GE has standardized on the abovementioned rules to identify special cause variation.. You can select the rules you want Minitab to use. One thing to be careful with all these rules is that you may not want to react too quickly. Several factors need to be considered: Are consequences high (i.e. cost, safety, etc) if we do not react to a potentially unstable system using the 8 rules? Can we potentially make a process unstable if we react too quickly to the control chart, when in reality the process is not out of control (i.e., “Do not fix it, if it is not broken”)?

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Control Limits vs. Specification Limits Control Limits Defined based on process performance (+/- 3 estimated standard deviations from the mean) Help determine if your process is “in control” (without special cause variation) Plotted on control charts Change when there is a verified, significant change to your process Represent the voice of the process

Control limits are not the same as tolerances.

Control limits are what you have

Tolerances are what you want

Example:

12

Customer Specification Limits Defined based on feedback from the customer(s) Help determine if your process is producing defects Plotted on histograms (not control charts) Change when your customers say they do! Represent the voice of the customer

While the data collected for the control charts demonstrates: Mean = 40 days UCL= 46 days

Customer may define the following for shipment delivery from time of order:

LCL= 39 days

Target= 20 days

The UCL and LCL are calculated based on the data collected–the UCL and LCL are NOT related at all to spec. limits.

USL= 45 days

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Control Limits vs. Specification Limits (continued)

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It is possible to have a stable (in control) process that has unacceptable variation Assume both process A and B are statistically performing “in control”

PROCESS A Lower Spec. Limit

PROCESS B Upper Spec. Limit

Process A has acceptable variation when evaluated against customer specification limits

Lower Spec. Limit

Upper Spec. Limit

Process B has unacceptable variation when evaluated against customer specification limits

When a process is in statistical control and has unacceptable variation, work on the reduction of variation due to common causes To reduce common cause variation, make improvements to the Vital Few X variables

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Selecting Measures For Control Charts What Do I Monitor?

14

Process

Output (Y’s)

Input Variables (X’s)

Key input and process measures (X) that track variables identified in your project as key drivers of Project (Y) variables

X

X

X

X

Key output measures (Y) from the customer’s perspective

Process Variables (X’s)

Measure The Process And Not The People

The measures that you choose to monitor in the control plan are the critical measures for your process. These are the process management measures that the process owner will rely on to track process performance over time.

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Selecting Measures For Control Charts (continued)

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How Do I Monitor The Control Plan?

Establish Data Collection Goals

Develop Operational Definitions & Procedures

Ensure Data Consistency & Stability

Collect Data & Monitor Consistency

Use the 4-step data collection plan in order to develop a process that will protect the integrity of the data.

Following the 4-step data collection plan will ensure that the data collected on an ongoing basis will accurately reflect the variation in the process. Since this data will be collected over a long period of time, measurement systems analysis to ensure consistency should be a major concern for both the project team as well as the process owner after the hand-off. Make sure that periodic audits of the data collection are an integral part of the overall control plan.

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Types Of Errors In Control Charts

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3 σ-level Control Limits – Created by Dr. Walter Shewhart to minimize two types of mistakes – Placed empirically because they minimize the two types of mistakes – Are not probability limits

Two types of Mistakes: – Calling a special cause of variation a common cause of variation (Missing a chance to identify a change in the process) – Calling a common cause of variation a special cause of variation (Interfering with a stable process, wasting resources looking for special causes of variation that do not exist)

Control limits vs. Specification limits – Control limits are determined by process data – Specification limits are determined by customer needs

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Two Types Of Control Charts

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VARIABLE CHART

Uses Measured Values – Cycle Time, Lengths, Diameters, etc. Generally One Characteristic Per Chart More Expensive, But More Information

ATTRIBUTE CHART

Pass/Fail, Good/Bad, Go/No-Go Information Can Be Many Characteristics Per Chart Less Expensive, But Less Information Variable = continuous data Attribute = discrete data

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Selecting the Appropriate Control Chart

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Variable or Attribute Data?*

Variable Variable

No

Attribute Attribute

Rational Subgrouping Possible?

No

Yes

Yes

Constant Lot Size?

Defects or Defective

Individuals Individuals & & Moving Moving Range Range

Xbar Xbar & & Range Range

uu

There are many different types of control charts. The chart pictured here is a helpful guide to decide which type of chart to use and when. The primary determinant of which type of control chart to use is the type of data being analyzed. If the data being analyzed is continuous (variable), you would use either:

The “Individuals & Moving Range” (I-MR): use if Rational Subgrouping is not possible (you want to see each transaction on the control chart) The Xbar & Range (X - R) use if Rational Subgrouping is possible. Typically subgroup size will be between 3 - 5. Use (X - S) if subgroup size is 7 or greater

Defects or Defective

pp

cc

np np

If the data being analyzed is discrete (attribute), you would need to determine: If you have a constant lot (sample) size or if the lot (sample) size is not constant If you are counting defects, you may have multiple defects per unit. If you are counting defectives, the unit either is or is not defective. In this module we will study the different types of control charts and when to use each one. What you want the Control Chart to tell you is: Is my level of non-conformance consistent? Am I controlling my significant X’s?

* Refer to Memory Jogger

TM

for further details.

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Interpreting Control Charts–Activity (20 minutes)

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Desired Outcome: Practice deciding which control chart is the appropriate choice for given data examples What

How

Who

Timing

Preparation

Choose a partner for the exercise

All

1 min.

Review and Feedback

For each of the examples listed on the following page

Partners

9 mins.

Partners

10 mins.

– Determine the appropriate type of control chart – Determine how you would label the X and Y axes Close

Keep notes on your responses for report-out

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Selecting Control Charts-Partner Activity (continued)

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1. A team from Marketing is tracking response rates (yes, no) on telemarketing calls. Each day, they randomly sample 100 responses from their outgoing calls. The number of positive responses is plotted on the chart. 2. The technical support area is monitoring average response time on help requests. Each hour, 5 calls are sampled. 3. A team is monitoring the number of applications received each day with incomplete fields. All applications are being audited. Each day, 200-250 applications are received. 4. A team is monitoring the cycle time for the underwriters’ loan decisions. The data comes in slowly; that is, one loan is completed daily. 5. A team is tracking the number of fields left blank on an application. Each day, a sample of 100 applications is audited. 6. Another team is doing the same thing as the team in example 5 (counting the number of fields left blank on an application), only they are looking at all the applications that come in daily. Each day, 50-100 applications are turned in. 7. The team is tracking the number of abandoned calls to a customer call center in a shift. Each shift takes from 200-400 calls.

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Variable Control Charts– Xbar R-Chart

In class we will show you how to construct in Minitab two continuous Control Charts (Xbar and R Chart and I/MR Chart) and one Discrete Chart (p Chart). The remainder will be reference material. Note: All Control Chart interpretation is identical.

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Selecting The Appropriate Control Chart

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Variable or Attribute Data?*

Variable Variable

No

Attribute Attribute

Rational Subgrouping Possible?

No

Yes

Yes

Constant Lot Size?

Defects or Defective

Individuals Individuals & & Moving Moving Range Range

Xbar Xbar & & Range Range

uu

Defects or Defective

pp

cc

np np

We will now focus on the Variable Control Chart with Rational Subgrouping: the Xbar & Range Chart.

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A Valid Variable Control Chart Has…

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Data in time or production sequence – To show stability, time-to-time variation

A measure of central tendency – To portray behavior of process center

A measure of variability Control limits – To allow separating common cause from assignable (special) cause

Xbar & Range Charts Xbar Chart: a plot of the sample means over time R-Chart: a plot of the range (difference between highest and lowest values) of a sample over time

General Comments on Xbar & Range Charts:

Cluster or periodic measurements of characteristic

Frequency depends on speed and stability of process.

Subgroup averages are plotted on Xbar chart

Xbar chart monitors central tendency of a process over time

Subgroup ranges plotted on Range Chart

R-Chart monitors the variability of a process over time

Provides data-smoothing effect

In Minitab: Stat > Control Charts > Xbar-R

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Variable Control Charts– I & MR Chart

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Selecting The Appropriate Control Chart

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Variable or Attribute Data?*

Variable Variable

No

Attribute Attribute

Rational Subgrouping Possible?

No

Yes

Yes

Constant Lot Size?

Defects or Defective

Individuals Individuals & & Moving Moving Range Range

Xbar Xbar & & Range Range

uu

Defects or Defective

pp

cc

np np

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Individuals & Moving Range Charts

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Can use in intermittent operations Similar to Xbar & R-Charts, Except... – – –

Single Values, Not Subgroups Range Values must be artificially constructed Somewhat “Noisier”, since you track each individual value (transaction,etc.)

Individuals Chart: a plot of the individual values over time Moving Range Chart: a plot of the moving range (for two samples |Xi –( Xi-1)|over time)

General Comments on I & MR Charts:

Range value artificially constructed from successive readings

Subgroup size for X is n = 1; for MR is usually 2

Some correlation between charts is possible

More “noise” in chart–tougher to spot true process shift

Displays the variability between individual observations over time

Assumes that past and present data is equally important

In Minitab: Stat > Control Charts > I-MR

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Building An Individuals And Moving Range Chart

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Individual Data Moving Range 55

N/A

56

ABS(55-56) = 1

59

ABS(56-59) = 3

55

ABS(59-55) = 4 Individuals

4

Moving Range

3 2 1 0

An Individuals chart plots actual data–each transaction. A Moving Range chart calculates ranges between consecutive data points (absolute value). You lose one data point, since the range is not calculated for the first point.

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Take Aways–Variable Control Charts

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Variable control charts can be used with continuous data to tell when a process is: – Experiencing only common cause variation and working at its intended best – When the process is disturbed and needs corrective action

Control charts: – Time ordered plot of data – Reflect the expected range of variation of the data – Identify when a special cause appears to be influencing the data

Xbar & R-Charts are used for plotting means and ranges of subgroups over time I & MR charts are used for plotting individual values and moving ranges over time

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Take Aways–Variable Control Charts

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Control limits are typically calculated as + 3 standard deviations away from the mean of the process Control limits and specification limits are not the same – Control limits are calculated from the sample data; they are internal to the process – Specification limits are determined by your performance standard; they are external to the process (generally come from the customer)

Know when a process is out of control: Western Electric Rules Control charts are only as good as the actions that you take to keep the process in control

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Variable Control Charts: Activity (10 minutes) Objective

Instructions

30

Practice using Minitab to generate an Xbar and R Chart. Think about the correct Data File: Variable Control Charts.mtw rational subgroup. The quality team has 25 weeks of historical data, contained in the file listed above. You have been asked to examine their data and believe an Xbar and R Chart, or an I/MR Chart would be the appropriate tool to use. 1. Plot the data using an I and MR chart. 2. Plot the data as Xbar/R-charts, forming subgroups by shift, day, and week. 3. For each chart created in 1 and 2 above, answer the following: A. Is the chart for spread stable? B. Is the chart for center stable?

Time

10 minutes

Stat > Control Charts > Xbar-R.

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Minitab Output Stat > Control Chart > I-MR Variable: Response Time Click on TESTS: Perform “All 8 Tests” Response Time

I and MR Chart for Response Individual Value

600

1

500 400 300 200

1 2

100 0

1 1 1 11 5 44 4

11 1 11 1 5 55

1 1 1 5

1 1 1

11 7 7

6

1 1 1 4 44 4

2

3.0SL=205.2 X=84.00 77 7

2

-3.0SL=-37.19

-100

Moving Range

Subgroup

0

500

1000

1 1

500 400 300 200

1 11

1 2

1

1 1 1

1

11 11 1

1

1 1

1 1 111

11 1

1 1

1

3.0SL=148.9

100 0

2

2

22 22

2

2

2 22 22 2

2

R=45.57 -3.0SL=0.00E+00

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Minitab Output

(continued)

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Stat > Control Charts > Xbar-R Single Cause: Response Time Subgroup Size: Day Click on > Tests: “Perform All 8 Tests” SUBGRP.MTW: Xbar/R for Response Time

Xbar/R Chart for Response Time: Day

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Attribute Control Charts

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Selecting The Appropriate Control Charts Attribute Data

Variable or Attribute Data?*

Variable Variable

No

34

Attribute Attribute

Rational Subgrouping Possible?

No

Yes

Yes

Constant Lot Size?

Defects or Defective

Individuals Individuals & & Moving Moving Range Range

Xbar Xbar & & Range Range

uu

Defects or Defective

pp

cc

np np

If the data being analyzed is discrete (attribute), you would need to determine:

If you have a constant lot (sample) size

or if the lot (sample) size is not constant

If you are counting defects you may have multiple defects per unit. If you are counting defectives, the unit either is or is not defective. In this module, we will study the different types of control charts and when to use each one. What you want the Control Chart to tell you is:

Is my level of non-conformance consistent?

Am I controlling my significant X’s? TM * Refer to Memory Jogger for further details.

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Important Definitions

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A Defect A single characteristic that does not meet requirements

A Defective A unit that contains one or more defects

Attribute Charts Can Consider Either Case, Depending On The Chart Type Chosen Other terminology may also be used:

A defect is also known as a nonconformance

A defective is known as a nonconforming

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Classification Of Attribute Chart Types

Constant Sample Size

Defects

Defective

c

np

36

Variable Sample Size

u

Can not count non-occurrences

Can count occurrences

p

To choose the appropriate attribute control chart, use the following factors: 1. Is it defects or defectives that you are investigating in the data you are collecting? For example:

Is it pass/fail for the part or process?

Or is it several sub-components or sub-processes passed/failed for the part or process)?

2. Is it a constant lot (sample) size or variable lot (sample) size?

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Attribute Control Charts P-Chart

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Selecting The Appropriate Control Chart P-Chart

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Variable or Attribute Data?*

Variable Variable

No

Attribute Attribute

Rational Subgrouping Possible?

No

Yes

Yes

Constant Lot Size?

Defects or Defective

Individuals Individuals & & Moving Moving Range Range

Xbar Xbar & & Range Range

uu

Defects or Defective

pp

cc

np np

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P-Chart

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Chart of proportion defective Variable subgroup/lot size (n)

P–chart shows the Proportion Defective–the proportion that do not conform

The units may have one or more defects

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Interpreting Control Charts–Activity (15 minutes)

40

Desired Outcome: Practice interpreting P-Chart What

How

Who

Timing

Preparation

In your team, read background information on the next page

Team

5 mins.

Interpret Control Charts

Interpret P-Chart results and answer questions

Team

5 mins.

Close Exercise

Choose a spokesperson to report out on your responses to the questions

All

5 mins.

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Interpreting Control Charts–Activity

41

P-Chart Of Loan Approval Rate May 1 To November 5

% Applications Approved

The loan department has made a change to the loan application process. They think the change will help weed out the bad loan risks before the applications are actually submitted. If they are right, the approval rate for submitted applications should increase. They want to check to see if this change in the process has had the desired effect. 1. Is there evidence that the new process made a difference? 2. What is the number of opportunities for defect in this process measure? 3. Is this an input, process, or output variable? Why?

•

90

•

•• •

80

•

New Process Implemented

• • • •• •

••

• • •

•

•

93.79 89.86

•

• •

•

•

3.0SL = 97.71

•

P = 85.94 82.02

•

78.09

•

-3.0SL = 74.18 70 0

10 20 Week (Time Order)

30

Note: “SL” is the standard Minitab notation for “Sigma Limits” which are the same as Control Limits.

To create a p-chart in Minitab: STAT > CONTROL CHARTS > P

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Reference Materials–Attribute Control Charts C-Chart

42

Reference Materials– Attribute Control Charts C-Chart

Pages 43-60 cover c, np and u charts. All Attribute Charts are interpreted as discussed in the previous pages for p-charts. Review these charts with your mentor for additional exercises. Proceed to page 61

Stat > Control Charts: All 4 Attribute Charts: (p,np,c,u) can be generated from this menu.

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Selecting The Appropriate Control Chart Attribute Data

Variable or Attribute Data?*

Variable Variable

No

43

Attribute Attribute

Rational Subgrouping Possible?

No

Yes

Yes

Constant Lot Size?

Defects or Defective

Individuals Individuals & & Moving Moving Range Range

Xbar Xbar & & Range Range

uu

Defects or Defective

pp

cc

np np

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C-Chart

44

Chart for counts Based on Poisson distribution – High probability of finding defect of some type. Large samples are needed if defect probabilities are low. – Lower probability of a defect of a given type

Works best on complex unit of product Constant subgroup/lot size

C bar = DPU = number of defects detected/subgroup A subgroup may contain one or more “physical” units. You need C bar up around 5. If it is less than 5, your distribution will be skewed because it will be truncated by 0. Increase your subgroup size if you need to increase C bar or collapse existing categories into meaningful groups. More specifically, combine two or more categories so that the frequencies are greater than 5.

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Interpreting Control Charts–Activity (15 minutes)

45

Desired Outcome: Practice interpreting C-Chart What

How

Preparation

In your team, read background information. Review chart on next 2 pages

Interpret Control Charts

Interpret C-Chart by answering the questions on the page

Close Exercise

Choose a spokesperson to report out on your responses to the questions

Who

Timing

All

5 mins.

Facilitator

5 mins.

(Sub-group)

All

5 mins.

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Interpreting Control Charts–Activity (continued)

46

An applications group of a large insurer recently made some changes to the design of their application. The old applications had 10 fields for the customer to fill out; the new application has 5 fields for the customer to fill out. They are now monitoring the incoming applications to ensure the new design has had an impact on completeness. A random sample of 100 applications are reviewed each day and the total number of incomplete fields are plotted. The chart for this data is on the following page. 1. Why is the control chart a C-Chart? 2. Is the number of errors in a sample stable over the 20–day sample? 3. What questions does the chart raise? Extra Credit!! Calculate baseline sigma for the first 20 days of service for the new application. Day

Data

Day

Data

Day

Data

Day

Data

1

5

6

9

11

6

16

7

2

5

7

9

12

6

17

7

3

11

8

8

13

7

18

8

4

5

9

8

14

5

19

12

5

8

10

7

15

6

20

13

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Interpreting Control Charts–Activity (continued)

47

3.0SL=15.87

Number of Incomplete Fields

15

10

C=7.600

5

-3.0SL=0.00E+00

0

0

10

20

Day of Sample

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48

Attribute Control Charts U-Chart

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Selecting The Appropriate Control Chart Attribute Data

Variable or Attribute Data?*

Variable Variable

No

49

Attribute Attribute

Rational Subgrouping Possible?

No

Yes

Yes

Constant Lot Size?

Defects or Defective

Individuals Individuals & & Moving Moving Range Range

Xbar Xbar & & Range Range

uu

Defects or Defective

pp

cc

np np

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U-Chart

50

Chart for defects per unit, with variable lot (subgroup) size Same logic as C-Chart, except variable lot (subgroup) size (n)

Compare to C-Chart

In Minitab: Stat > Control Charts > I

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U-Chart Activity (20 minutes)

51

Desired Outcome: Practice constructing and interpreting U-Chart What

How

Preparation

In your team, prepare to create a U-Chart in Minitab

Construct And Interpret The U-Chart

In the U-Chart.mtw, column errors contains data (in time sequence) of the defects found each day on customer orders. A defect is defined to be inaccurate information found on a customer order. Both the number of defects and the daily number of orders are recorded.

Who

Timing

All

1 min.

Team

10 mins.

Using Minitab, construct a U-Chart of the data What are your observations? Close

Choose a spokesperson to report out your conclusions

All

9 mins.

Note: Do not turn the page until you have completed the activity.

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U-Chart Example Minitab Menu Commands

52

MINITAB FILE: U_Chart.mtw

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U-Chart Minitab Input & Output

53

U Chart for errors

Sample Count

3

3.0SL=2.114

2

U=1.764 -3.0SL=1.415 1 0

10

20

30

Sample Number

CONTROL: The process does not look stable–there are indications pf special cause variations. Why do the control limits vary? Lot (Sample) size varies.

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54

Attribute Control Charts NP-Chart

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Selecting The Appropriate Control Chart NP-Chart

55

Variable or Attribute Data?*

Variable Variable

No

Attribute Attribute

Rational Subgrouping Possible?

No

Yes

Yes

Constant Lot Size?

Defects or Defective

Individuals Individuals & & Moving Moving Range Range

Xbar Xbar & & Range Range

uu

Defects or Defective

pp

cc

np np

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NP-Chart

56

NP-chart: number of defectives (non-conforming items) in subgroup Same logic as the P-Chart, except constant subgroup/lot size (n)

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Interpreting Control Charts–Activity (15 minutes)

57

Desired Outcome: Practice interpreting NP-Chart What

How

Who

Timing

Preparation

In your team, read background information on next 2 pages

Team

5 mins.

Interpret Control Charts

Interpret NP-Chart results and answer questions

Team

5 mins.

Close Exercise

Choose a spokesperson to report out on your responses to the questions

All

5 mins.

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Interpreting Control Charts–Activity (continued)

58

An applications group of a large insurer recently made some changes to the design of their application. They are now monitoring the incoming applications to ensure the new design has had an impact on completeness. 150 applications are chosen randomly and reviewed each day. The number that are incomplete are plotted each day The chart for this data is on the following page. 1. Why is the chart an NP–chart? 2. What questions does the chart raise about the completeness of the insurance application? 3. What is the number of opportunities for defect in this measure? 4. What is the difference between the value plotted on a P–and an NP–Chart? Day

Data

Day

Data

Day

Data

Day

Data

1

12

6

14

11

2

16

11

2

22

7

16

12

15

17

17

3

14

8

19

13

8

18

12

4

15

9

11

14

12

19

11

5

12

10

1

15

12

20

21

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Interpreting Control Charts–Activity (continued)

59

25 3.0SL=23.13

# of Incomplete Applications

20

15 NP=12.85 10

Day of Sample

5 -3.0SL=2.567 0 0

10

20

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Attribute Chart Subgroup Size

60

Rule of Thumb: – Select a subgroup size that will provide an average defect/defective of approximately C, U, NP > 5.0

To Make UCL & LCL Nearly Symmetrical Around the Mean – For NP-charts, to select the appropriate sample size such that 95% of the subgroups will have at least one defective, use the relationship n= 3

p

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Summary Of Attribute Charts

61

Useful when variable data not available Use count/classification data–pass/fail, good/bad Same general rules for interpretation as variable charts Useful as end-to-end overview; use variable charts for further study of problems Can use data gathered for other purposes Generally less expensive to administer, but tell you less Shortcomings Including too many variables makes interpretation difficult Must fit the parameters you are evaluating to theoretical distribution [Poisson (C, U-Charts), Binomial (P, NP-Charts)] Need to evaluate whether constant/non-constant lot size will help you with root cause analysis Sensitivity is dependent on magnitude of defect level

Variable or Attribute Data?*

Variable Variable

No

Rational Subgrouping Possible?

Attribute Attribute

Yes

Constant Yes Lot Size?

No

Defects or Defective

Individuals Individuals&& Moving Moving Range Range

Defects or Defective

Xbar Xbar&& Range Range uu

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Take Aways Attribute Control Charts

62

Attribute control charts are used to monitor the level of nonconformance of a process Select the appropriate attribute control chart based upon – Constant vs. variable lot (sample) size – Defects vs. defectives

Defect – A single characteristic that does not meet requirements

Defective – A unit that contains one or more DEFECTS

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Summary–Control Charts

63

All control charts have the same form – Time plot of data – Statistical limits placed +/- 3s from center line

Choose the control chart according to: – Data type – Sample size

Interpret and act on the control chart – Investigate special causes of variation – Assess baseline sigma in order to understand if we are performing to customer CTQ’s – Shrink common cause variation by making fundamental changes in the Vital Few X variables

Maintain the control chart – Make notes on the control chart to indicate problems, changes, or important events

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64

Calculating Control Limits (Optional)

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Control Limit Calculations

65

The formulas for calculating control limits are shown on the following pages There are different tables for continuous and discrete data Both continuous and discrete data control charts have control limits that are placed +/- 3 estimated sigma from the average line

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Control Limit Calculations–Formulas

66

Continuous Data Control limits are calculated using control chart factors and the Range-Bar (an estimate of short-term sigma) Control chart factors were invented by Shewart in the 1920’s to avoid long-hand calculation Control chart factors are shown in the table according to the sample size for each subgroup Individual control charts are considered to have a sample of size 2, the number of data points make up the moving range Discrete Data Control limits are calculated using a formula that estimates sigma without the necessity to transform the data The normal estimate for sigma (under radical) is then multiplied by three

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Control Limit Calculations–Continuous Data Table Type Control Chart

Sample Size n

Central Line*

Control Limits

X=

(X1 + X2 +…Xk) k

UCLx = X + A2R LCLx = X - A2R

X and R

R=

(R1 + R2 +…Rk) k

UCLR = D4R LCLR = D3R

Average and Standard Deviation

X=

(X1 + X2 + … Xk) k

UCLx = X + A3s LCLx = X - A3s

Average and Range < 10, but usually 3 to 5

Usually ≥ 10 s=

X and s Median and Range

< 10, but usually 3 to 5

X ˜ and R

Individuals and Moving Range 1 X and Rm

(s1 + s2 +…sk) k

UCLs = B4s LCLs = B3s

X ˜=

˜ 1 + X˜ 2 + … X˜ k) (X k

˜ + A2R UCLx = X LCLx = X ˜ - A2R

R=

(R1 + R2 +…Rk) k

UCLR = D4R LCLR = D3R

X=

(X1 + X2 + … Xk) k

UCLx = X + E2Rm LCLx = X - E2Rm

Rm = Rm =

I(Xi+1 - Xi)I (R1 + R2 +…Rk-1) k-1

67

UCLRm = D4Rm LCLRm = D3Rm

˜

k = # of subgroups, X = median value within each subgroup *X =

ΣXi n

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Control Limit Calculations–Table Of Contents Sample Size n

X and R Chart

X and s Chart

A2

D3

D4

A3

B3

B4

c4*

2

1.880

0

3.267

2.659

0

3.267

.7979

3

1.023

0

2.574

1.954

0

2.568

.8862

4

0.729

0

2.282

1.628

0

2.266

.9213

5

0.577

0

2.114

1.427

0

2.089

.9400

6

0.483

0

2.004

1.287

0.030

1.970

.9515

7

0.419

0.076

1.924

1.182

0.118

1.882

.9594

8

0.373

0.136

1.864

1.099

0.185

1.815

.9650

9

0.337

0.184

1.816

1.032

0.239

1.761

.9693

10

0.308

0.223

1.777

0.975

0.284

1.716

.9727

Sample Size n

68

˜ and R Chart X

X and Rm Chart

˜2 A

D3

D4

E2

D3

D4

d2*

2

–

0

3.267

2.659

0

3.267

1.128

3

1.187

0

2.574

1.772

0

2.574

1.693

4

–

0

2.282

1.457

0

2.282

2.059

5

0.691

0

2.114

1.290

0

2.114

2.326

6

–

0

2.004

1.184

0

2.004

2.534

7

0.509

0.076

1.924

1.109

0.076

1.924

2.704

8

–

0.136

1.864

1.054

0.136

1.864

2.847

9

0.412

0.184

1.816

1.010

0.184

1.816

2.970

10

–

0.223

1.777

0.975

0.223

1.777

3.078

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Control Limit Calculations–Discrete Data Table

Type Control Chart

Fraction Defective

Sample Size

Central Line

Variable, usually ≥ 50

For each subgroup: p = np/n For all subgroups: p = ∑np/ ∑n

p-Chart

Number Defective

Constant, usually ≥ 50

np-Chart Number of Defects c-Chart Number of Defects Per Unit

Constant

Variable

u-Chart

np = # defectives c = # of defects n = sample size within each subgroup k = # of subgroups

For each subgroup: np = # defectives For all subgroups: np = ∑np/k

69

Control Limits

*UCLp = p + 3

p(1 - p) n

*LCLp = p - 3

p(1 - p) n

UCLnp = np + 3 LCLnp = np - 3

For each subgroup: c = # defects For all subgroups: c = ∑c/k

UCLc = c + 3

For each subgroup: u = c/n For all subgroups: u = ∑c/ ∑n

*UCLu = u + 3

LCLc = c - 3

*LCLu = u - 3

np(1 - p)

np(1 - p) c c u n u n

* This formula creates changing control limits. To avoid this, use average sample sizes n for those samples that are within ±20% of the average sample size. Calculate individual limits for the samples exceeding ± 20%. If the Lower Control Limit (LCL) is a negative number, set the LCL to zero.

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Dmaic - Book of Knowledge - Green Belt11ea60e023f

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