8668005 Six Sigma Green Belt Exam Study Notes
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Cpk • Cp
 see Natural Tolerance decreases with spec width  see Natural Tolerance
• •
decreases with spec width Cp = 1 for centered process  natural tolerance =spec width
Cause and Effect Diagram  Fishbone Diagrams  Ishikawa Diagrams • • • • • • • •
used to identify and organize potential root causes problem solving analysis done by brainstorming common categories  Measurement, Materials, People, Process, Equipment, Environment ask “Why?” 3 times to get to root cause have detailed problem statement at head of fish  “effect” need corresponding process map should fit on one 8½ x 11 page should have all 6 fishbones and at least 3 levels deep
Cbar •
Cbar is the average of all the subgroup Cvalues in CChart
C – Chart • • • •
 see Attribute Data Control Charts
Count chart a specialized version of U chart used to monitor the number of errors found  occurrences per unit  error count number of units or subgroup size MUST remain constant
Census •
count or measurement of the entire population
Continuous Data • •
measured – weigh, timed, can be measured and broken down into smaller parts and still have meaning. Money, temperature and time are continous.Volume (like volume of water or air) and size are continuous data.
Control Charts •
indicate stability over time
Chart Rules – Control Charts • •
Pchart or NPchart  count number of items in error or defectives Uchart or Cchart  count number of errors or defects in items
Common causes control limits

see variation
• Provide boundaries for a process running in control • based upon process data CTQ  Critical to Quality • • • •
key measurable characteristics of a product or process whose performance standards or specification limits must be met in order to satisfy the customer CTQ’s represent the product or service characteristics that are defined by the customer (internal or external). They may include the upper and lower specification limits or any other factors related to the product or service. the product or service characteristics that are defined by the customer as critical to their needs what the customer expects of a product
DATA Attribute Data Control Charts • • • • • •
Attribute data  qualitative data that can be counted for recording and analysis good/bad, yes/no the average and dispersion are closely related; therefore, only one chart needed PChart – proportions percent defective with variable or constant sample size NPchart– number of defectives with constant sample size CChart – count of defects with constant sample size UChart – defects per unit with variable or constant sample size
Variable Data Control Charts • • • • •
Variable data – measured  two types (Discrete) count data and (Continuous) data X and MR – for financial, mtce costs, efficiency ratings, productivity – (usually 2 charts) Xbar and Range Xbar and S (standard deviation) – Xbar for sample average and “S” to monitor process dispersion
Defect •
nonconformities – a single characteristic not meeting defined requirements
Defective •
nonconformance – contains one or more defects
DET  see FMEA Discrete Data •
counted (usually in whole numbers)
DMAIC • • • •
Define – project charter, problem statement, scope, goals, resources, financial, process maps Measure – collect data, process maps, fishbone, Pareto, QFD, need accuracy & precision Analyze  root cause is verified, hypothesis testing (verifying assumptions and predictions regarding the relationship between process inputs and the CTQ values) Improve – brainstorming for ideas & solutions to problems identified in Analyze phase
• Control – helps to reduce variation in the process and eliminate defects • Control  project responsibilities transition from process improvement team to operations team • Six Sigma Methodology used for process improvement DPMO (defects per million opportunities) • •
defect level for a process number of defects divided by number of opportunities multiplied by one million
DOE  Design of Experiments • • • •
math & statistics used in the design & analysis phase of an experiment to find best settings optimize a process, reduce common cause variation, and maximize ROI organized method for determining the relationship between factors (Xs) affecting a process and the output of that process (Y) experimental methods used to quantify indeterminate measurements of factors and interactions between factors statistically through observance of forced changes made methodically as directed by mathematically systematic tables
Fish Bone
 see Cause and Effect Diagram
FMEA  Failure Mode and Effects Analysis • • • • • •
tool to identify where in the process if the source of failure RPN  Risk Priority Number relative risk of a particular failure mode = SEV x OCC x DET OCC or Likelihood of Occurrence rating  likelihood of the failure occurring DET – detection rating measures likelihood current control system will detect cause or failure SEV – severity rating how significant the impact of the effect is to the customer vital x’s (root causes from lowlevel fishbones) go into potential cause column and can occur in more than one process step
Gauge R&R •
Repeatability & Reproducibility
Gauge Repeatability •
how consistently same operator or measurement system measures same even over time
Gauge Reproducibility •
how consistently several operators or measurement systems measure same even over time
Histogram •
tool used in the Measure phase to illustrate shape, central tendency, and dispersion of data
Leverage • • •
applying proven methods to other projects via lessons learned  share ideas & best practices reduces costs, increase efficiency, improve customer service identifying “spinoff” projects that can benefit
Master Attribute
•
standard or correct answer in an Attribute Gauge R & R study
MR = Moving Range Mean • • • •
arithmetic average the statistic most often used as the measure of central tendency or center of data represented by Greek symbol “μ” (pronounced mu) center line (process average) in a control chart between UCL and LCL
Measurement systems • • • • •
see Gauge Reproducibility and Gauge Reproducibility Accuracy – how close the average are equal to the target Precision – variation in repeated measurement of the same event Linearity – performance over a range of events Stability – performance over time
Measurement system analysis •
used to validate the measurement system
natural tolerance • •
Natural tolerance is also called “6 sigma” because it is defined as 6 times the population standard deviation of the individual observations. 3 sigma on each side of the process mean Cp CpU CpL Cpk
= = = =
Process capability potential = spec width/natural tolerance = (U  L) / 6 sigma Upper capability index = (U  Mean) / 3 sigma Lower capability index = (Mean  L) / 3 sigma Process capability index = Minimum of CpU and CpL
If the process capability potential, Cp, is greater than 1.0, the specification limits are wider than the natural tolerance, and the process has the potential for meeting specifications if held in control at a mean of (U  L)/2. net profit •
selling price minus costs
NPBar •
centerline or process average of all subgroups in NPChart
NP  Chart • • • • •
 see Attribute Data Control Charts
a specialized version of the Pchart used when your sample size is constant used to monitor the number rather than the proportion of items with a defined characteristic subgroups MUST be equal size used to track the actual number of defective items or the actual number of good items average and dispersion are closely related; therefore, only one chart is required
OCC  see FMEA
Pareto Chart • • • • • • • • • •
simple bar chart where the height of each bar represents the frequency of a given category can be used to rank problems by their dollar costs rather than frequency prioritize problems from those that happen most often to those that happen least often cumulative percentage curve added to show ∑% of occurrences up to and including a given category stratification  systematic subdivision of a problem into its subcomponents identifies which opportunity or problem the team should focus on categories are listed in order of frequency – higher on left height of each bar represents the frequency of a given category 8020 rule  80% of occurrences of problems are accounted for by 20% of the categories of problems developed by Italian economist named Vilfredo Pareto
PChart • • • • • •
 see Attribute Data Control Charts
monitor proportion or percentage values plotted will always be a proportion and result in a number from zero to one Pchart is required to monitor the process average and dispersion. With attribute data, the average and dispersion are closely related. Therefore, only one chart is needed. subgroup sample sizes may vary. The control limits will vary but the centerline stays constant. larger subgroup size has narrower limits because larger sample size reduces sampling error With unequal subgroup sizes, pbar is a weighted average of the individual subgroup proportions. A weighted average just means the individual p’s don’t all carry the same weight in the calculation of pbar.
Problem statement •
datadriven statement that does not include opinions on root causes or possible solutions
Process capability • • • • •
the extent to which a stable process is able to meet specifications assessed using either continuous data or discrete data when using attribute data should be expressed as percent, PPM, PPB defective, DPMO, etc. assessed with a histogram with specification limits capable process has a high Cp value and Cpk=Cp
Process Capability Index: distance of mean to near spec Cpk = ―――――――――――― half the natural tolerance) Process Capability Index (if centered): voice of customer (spec width) Cp = ―――――――――――――― voice of process (natural tolerance or 6 sigma) Process outofcontrol  see process shift
process shift • • •
a cluster of eight consecutive data points either all above or below the median a point outside of control limits is indication that process may be shifting process shift makes it inappropriate to calculate the overall average (or standard deviation) of the data
Process maps • • • • • • • • • •
shows the interrelationships of the steps in a process used to discipline teams to produce solutions that are definable, repeatable, predictable and measurable walk the process clearly define the boundaries of the process should include data, sigma level, COPQ, defect rate, flow rate “as is" include rework loops oval – starting or stopping point rectangle – process step or action diamond  decision
projects selecting potential projects consider  resource availability, reward, complexity, risk Project Charter • • • • •
set expectations and obtain buyin on scope, goal, and resources accelerate the acquisition of resources avoid scope creep documentation easy and effective means to document a Six Sigma project
Project selection •
considerations = Complexity, Risk, Reward, Resource availability
Quality Function Deployment  QFD •
tool used to analyze customer requirements
R = Range
Root Causes • • •
often found in lowlevel fishbones during analyze phase easier to find the root cause of a problem that is detected as it is happening see Cause and Effect Diagram
ROI = Return On Investment • • • • • • • •
for Six Sigma project is calculated by dividing the project savings by the project cost used to measure the impact of a Six Sigma project on business results Reduced operating costs Increase in operating efficiencies Improved morale Communicating project savings Sharing ideas and best practices Identifying “spinoff” projects
RPN – see FMEA S = Standard Deviation SChart •
 see standard deviation
 see Variable Data Control Charts
to monitor process dispersion
Sample • • •
subset of the population every element in a sample is also an element of the population Stratified sampling – grouping members into similar subgroups before sampling
Sample Mean • •
used to estimate the population mean sample = subset of the population
Savings • •
soft = nontangible – time, customer satisfaction, morale hard = money, cost, can be counted, direct impact upon the company's bottom line
Scatter Diagram • • •
shows the type of correlation between two variables strength of the relationship between two variables is determined visually by the tightness of the cluster of points on the scatter diagram around the line of best fit drawn through the points extrapolation is used to predict a value outside the range of the data plotted
Scope Creep • •
Tendency for project to expand scope limited by clearly defining boundaries
SEV  see FMEA Sigma 
see standard deviation
SIPOC • Suppliers, Inputs, Process, Outputs and Customers • the system view of a process Six Sigma • • • • • •
∂
a commitment to your customers. a method that uses best management ideas and practices for flexible system for process improvement a means to stretch your thinking with respect to quality and customer satisfaction customer focused factbased strategy focused on process improvement, variation reduction and defect elimination uses two types of data  continuous and discrete
solution design matrix •
used to organize alternative solutions
Spec width = USL – LSL Special causes

see variation
Specification Limits •
used to determine if a product meets customer requirements
Standard Deviation • • • • • • •
=
sigma
measures dispersion from the mean – shows on average how far the values are from the mean “s” represents standard deviation of a sample sigma or Standard Deviation is used in combination with X Bar to describe the "Normal Distribution To find six sigma, calculate sigma, multiply by 6, and add or subtract the result to the calculated mean. 68.27% of normal population lies within +/ one sigma from its average (mean) μ 95.45% of normal population lies within +/ two sigma’s from its average (mean) μ 99.73% of normal population lies within +/ three sigma’s from its average (mean) μ Sigma, (Standard Deviation), Formula = n or (n  1)
Statistics • • • •
Uses Qualitative and Quantitative data types Systematic Sampling  uses a rule or pattern to select elements from the population to form the sample Qualitative = discrete data – counted , Not measured Quantitative data  continuous data  different depending on types of questions
Xbar Chart  see Variable Data Control Charts • used to monitor central tendency Xbar and S Chart
 see Variable Data Control Charts
__ Xbar = X • • •
mean or average of sample typically charted on a line control chart with the center line being X Double Bar, (an average of the averages), and upper control limits and lower control limits We use averages because they are more susceptible to change than single values.
XmR Charts • •
 see Variable Data Control Charts
control chart which uses a moving range. Typically two but can have a larger range usually used when one measurement is available for each subgroup
Upper Control Limit •
control limit for points above the central line in a control chart
U  Chart • • • • • • •
UCL
 see Attribute Data Control Charts
a graph of the number of errors per unit   error rate unit may be time, area, machines, or length value of U could be a number greater than 1 equal sample or subgroup size is NOT a requirement used to track the number of occurrences of some event per unit average and dispersion are closely related. Therefore, only ONE chart is needed larger subgroup size = narrower limits (larger sample size reduces sampling error)
Variable •
a characteristic or property of an individual element in a population or sample
Variation • • •
Common Cause  causes of variation that are inherent in a process over time. They affect every outcome Common cause – variation inside control limits  do NOT adjust process Special Cause  relatively large, unusual variation usually comes from outside the process
Z value • •
Z value is a data point's position between the mean and another location (usually mean) as measured by the number of standard deviations. Z is a measure of process capability and corresponds to the process sigma value that is reported by the businesses. For example, a 3 sigma process means that three standard deviations lie between the mean and the nearest specification limit. Three is the Z value.
Costs
Costs
Costs
appraisal costs • • • • • • • •
inspection costs incurred to identify defective products before the products are shipped to customers Test and inspection of incoming materials Test and inspection of inprocess goods Final product testing and inspection Supplies used in testing and inspection Supervision of testing and inspection activities Depreciation & maintenance of test equipment field testing and appraisal at customer site
COPQ • • • •
(Cost Of Poor Quality)
rework loop cost = (Defect rate) x (Volume) x (Cost of rework per unit) penalty from not performing work correctly the first time or not meeting customer’s expectation cost categories = appraisal, internal failure, prevention, external most often calculated in the design stage of the Six Sigma Methodology
Entitlement cost •
cost of doing the right thing right the first time
Internal failure Costs • •
Internal failure costs result from identification of defects before shipping to customers Costs include scrap, rejected products, reworking of defective units, and downtime
External Failure Costs • •
defective product is delivered to customer costs include warranty, repairs and replacements, product recalls, liability arising from legal actions against a company, and lost sales arising from a reputation for poor quality
Prevention Costs • •
Prevention costs support activities whose purpose is to reduce the number of defects. Examples  statistical process control, quality engineering, training, and tools
Sigma to DPMO to Yield to Cpk Table
Sigma
DPMO
Yield
Cpk
1.5
500,000
50%
0.50
3.00
66,800
93.320%
1.00
3.50
22,700
97.730%
1.17
4.00
6,210
99.3790%
1.33
4.50
1,350
99.8650%
1.50
5.00
230
99.9770%
1.67
6.00
3.4
99.99966%
2.00
Assumptions No analysis would be complete without properly noting the assumptions made. In the above table, we have assumed that the standard sigma shift of 1.5 is appropriate, the data is normally distributed, and the process is stable.
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