Lean & Six Sigma
Manufacturing Black Belt Sample Materials for Licensed Partners
Hypothesis Testing of Categorical Inputs (Xs)*
Output (Y) Input (X)
Continuous
Categorical
1-Proportion Test HO: p1 = Ptarget Ha: p1 ≠ , <, or > Ptarget
1 Sample
Continuous
Continuous “Y” Data
Stat>Basic Stat> 1-Proportion
Categorical “Y” Data
Categorical
2-Proportion Test
Data are Not Normal 2 or More Samples
2 or More Samples
1 Sample
Compare Variances Levene’s Test HO: σ1= σ2 = σ3… Ha: σi ≠ σj for i to j (or at least one is different) Stat>ANOVA> Test for Equal Variances
Compare 2 Medians Mann-Whitney Test
1 Sample
Compare 2 Means
Chi2 Test
Paired t-Test
HO:µ1 = µ2 Ha: µ1 ≠, <, or > µ2
HO: µd = µO Ha: µd ≠ , <, or > µO
Stat>Basic Stat>Graphical Summary
Stat>Basic Stat>Paired t
All Rights Reserved, Juran Institute, Inc.
Chi Square Test HO: FA Independent FB Ha: FA Dependent FB Stat>Tables>Chi2 Test
Compare Variance to Target
Stat>Basic Stat>2-Sample t uncheck: Assume = Variances
Chi2 Test
Compare Variances
1 Sample
Bartlett’s Test (> 2) or F-Test (2)
1-Sample Wilcoxon
Stat>Nonparametrics> Kruskal-Wallis
For 2 or more Samples, Test for Independence
2-Sample t-Test
HO: σ 1 = σ target Ha: σ 1 ≠ σ target
Stat>Nonparametrics> Mann-Whitney
(assumes no outliers; otherwise, use Mood’s Median test) HO: η1 = η2 = η3… Ha: ηi ≠ ηj for i to j (or at least one is different)
Stat>Basic Stat> 2-Proportion
2 Samples
Compare Mean differences
Compare Median to Target
Kruskal-Wallis Test
2 or more Samples
Compare Variance to Target
(if target std dev. falls within 95% CI, then fail to reject HO; otherwise, reject)
Ho: p1 = p2 Ha: p1 ≠ , <, or > p2
Data are Normal
H HOO:: Data Data is are Normal Normal H Haa:: Data Data is are notnot Normal Normal Stat>Basic Stat>Basic Stat>Normality Stat>Normality Test Test or or Stat>Basic Stat>Basic Stat>Graphical Stat>Graphical Summary Summary
HO: η1 = η2 Ha: η1 ≠, <, or > η2
Compare More Than 2 Medians
2 Samples
Normality Normality Test Test
HO: σ1 = σtarget Ha: σ1 ≠ σtarget Stat>Basic Stat>Graphical Summary
HO: σ21 = σ2 2 = σ23… Ha: σ2i ≠ σ2j for i to j (or at least one is different) Stat>ANOVA>Test for Equal Variance
(if target std dev. falls within 95% CI for std dev, then fail to reject HO: reject otherwise)
Equal Variances
Compare Mean to Target
HO: η1 = ηtarget Ha: η1 ≠ , <, or > ηtarget Stat>Nonparametrics> 1-Sample Wilcoxon
Compare More Than 2 Means
Compare 2 Means
1-Way ANOVA
HO: µ1 = µ2 Ha: µ1 ≠, <, or > µ2
(assumes equality of variances) HO: µ1 = µ2 = µ3… Ha: µi ≠ µj for i to j (or at least one is different)
2-Sample t-Test
Stat>Basic Stat>2-Sample t Check: Assume = Variances (uses pooled std dev)
Stat>ANOVA>1-Way (select stacked or unstacked data)
*NOTE: If X is Continuous and Y is Continuous, proceed with Regression and Correlation Analysis.
1-Sample t-Test HO: µ1 = µtarget Ha: µ1 ≠, <, or > µtarget Stat>Basic Stat>1-Sample t
If P-Value P-value ≤≤ alpha, alpha, then then reject reject H Hoo If P-value P-Value >> alpha, alpha, then then fail fail to to reject reject H Hoo Alpha is usually pre-set at 0.05. Use other values as appropriate. If P-value P-Value >> alpha, alpha, ensure ensure sufficient sufficient power and correct sample size if necessary.
Hypothesis Testing Protocol Practical Problem or Theory: State problem or state theory to be proven. Statistical Problem: State Ho and Ha (with the correct test in mind) Statistical Analysis: Analysis: Test to be used, alpha and power. Run test, show printout, results results and pp-value Statistical Conclusion: Based on pp-value, Reject Ho or Fail to Reject Ho. (“ (“If the p is low, the null must go” go”) Practical Conclusion: Answer to your practical problem. Theory is proven true or not. not.
Hypothesis Tests by Data Type
Y Continuous Continuous
X
How does change in X affect change in Y? Statistical: Regression
If Normal: t-tests; ANOVA If Non-Normal: Wilcoxon, MannWhitney, Kruskal-Wallis Graphical: Histograms; Box Plots Variance Different? Statistical: Test for Equal Variances (Bartlett’s, Levene’s) Graphical: Histograms; Box Plots All Rights Reserved, Juran Institute, Inc.
Logistic Regression (out of scope)
Graphical: Scatter Diagrams Means or Medians Different? Statistical:
Categorical
Categorical
Are the outputs different? Statistical: Chi Square, Proportions tests Graphical: Pareto Diagrams; Stratification
Calculating Sigma Level: Process Capability Using Continuous Data Learning Objectives .......................................................................18 How Do You Perform a Process Capability Study? .......................20 Prediction of Defect Levels ............................................................21 Capability Indices (Long-term vs. Short-term)................................25 Calculating Sigma â&#x20AC;&#x201C; Continuous Normal Data ...............................27 Long Term vs. Short Term Capability ............................................35 Rational Subgrouping ....................................................................38 Process Capability Using Non-normal Data Learning Objectives .......................................................................54 How Do You Perform a Process Capability Study? .......................55 Best Fit Distribution ........................................................................57 Johnson Transformation ................................................................60 Box-Cox Transformation ................................................................63
Learning Objectives .........................................................................1 Project Xs ........................................................................................2 Tool: Brainstorming ..........................................................................7 Cause-Effect Diagram Learning Objectives .........................................................................9 How to Construct ...........................................................................15 How to Interpret .............................................................................17 Failure Mode Effect Analysis Learning Objectives .......................................................................23 How Does an FMEA Work? ...........................................................25 How to Construct ...........................................................................28 When Is an FMEA Complete? .......................................................33 Measure Checkpoints for Completion ............................................36
Define
Measure
Develop Project Charter Determine Customers & CTQs Map High-Level Process
Measure Ys Plan for Data Collection Validate Measurement System Measure Baseline Sigma Identify Possible Xs
Analyze
Test Hypotheses List Vital Few Xs
Improve
Select the Solution Design Solution, Controls, & Design for Culture Prove Effectiveness
Control
Identify Control Subjects Develop Feedback Loops Develop Process Control Plan to Hold the Gains Document Implement, Replicate
List below the questions you would like to have answered by the workshop and the capabilities you would like to acquire: 1.
2.
3.
Learning Map Phases/Steps
Deliverables
Measure
Tools
When the two dimensions of quality are placed side by side they impact your organization and customers. To meet customer requirements, you must address both dimensions by identifying the right features and provide them without failure. Having the right mix of customer features that are free from failures increases customer satisfaction and decreases their dissatisfaction. This not only elevates the salability of the product or service, but it also reduces the likelihood that customers will move to competitors.
1. Breakthroughs achieve substantially higher levels of performance quickly. Breakthroughs do not just happen. They require a systematic change process, one that can be achieved with the â&#x20AC;&#x2022;project-by-projectâ&#x20AC;&#x2013; approach. 2. Costs of Poor Quality (COPQ) are those costs that would disappear if every task were done perfectly the first time, every time. It can also be defined as the difference between the theoretical minimum cost and the actual cost. 3. Improving products, processes, and services is a never-ending pursuit. Achieving breakthroughs may require a tenfold improvement, or even better than 3.4 ppm, which is a Six Sigma level. 4. Lean and Six Sigma are methodologies and toolsets that can enable an organization to improve performance systematically. 5. For an organization to continue making breakthroughs and meet the needs of their stakeholders, they must master the skills to plan, control, and improve quality.
The costs of poor quality are those that would disappear if every task were continuously performed without deficiency every time.
Actual cost – minimum cost = COPQ.
Caution: Minimum cost is not necessarily equal to standard cost. Standard costs often include allowances for defects, spoilage, or loss. The American Society for Quality uses four categories to stratify COPQ:
Prevention
Appraisal
Internal Failure
External Failure
The ratio of the individual category costs to total costs varies widely. Many companies exhibit ratios which look like the following: Quality Cost Category
Percent of Total Cost of Quality
Internal Failure
25 to 40%
External Failure
25 to 40%
Appraisal
10 to 50%
Prevention
.05 to 5%
Organizations are forced to improve the quality of their services and products in order to maintain their competitiveness. These services and products, which were created to respond to customer needs, may no longer be good enough for todayâ&#x20AC;&#x2122;s challenging competition. Customers have multiple sources available to fulfill most of their needs and will switch suppliers when their needs are no longer being met, or when another supplier offers superior products or services for less cost. Too much variation in your processes creates deficiencies in the goods and services you deliver. It erodes financial margins, and reduces customer loyalty. Reducing variation can lead to superior performance. Merely improving average performance is not enough. Customers, costs, and profits are adversely affected by the range as well. Lean Six Sigma focuses on identifying variation in your processes and products, and identifying the causes for that variation by reducing the average and the range.
1. It is a disciplined and rigorous process to solve complex problems by ―getting the facts‖ before solutions are carried out. 2. It uses projects to solve the most critical problems. 3. It involves a multi-functional team led by a Black Belt or Green Belt, trained in proven methods and tools. 4. It begins by understanding the problem from the customer point of view, this is referred to as the ―voice of the customer (VOC).‖ 5. It uses rigorous analysis to prove theories about root causes of the problem before it implements a change. 6. It uses systematic planning, control, and understanding of human issues to make the improvement a success.
1. It is a methodology used to design or redesign processes, services, and products with Six Sigma levels of performance. 2. It designs in quality up frontâ&#x20AC;&#x201D;fewer defects. 3. It is a top-down set of customer-driven requirements synchronized to system capability. 4. It uses multi-functional design teams to meet the changing needs of customers. 5. It assures predictability of process performance early in design. 6. It utilizes systematic tools to make final design decisions. 7. It evaluates process variation to verify that customer requirements are met by the design.
8. It represents an improved service or product development process.
Lean Value Stream Management or just â&#x20AC;&#x2022;Lean:â&#x20AC;&#x2013; 1. Is a methodology used to improve cycle time, throughput, and eliminate waste 2. Provides more value to customers 3. Creates greater profitability 4. Reduces lead time 5. Improves delivery time
All the activities required to bring a product from conception to commercialization
Includes detailed design, order taking, scheduling, processing, and delivery
Understanding the value stream allows one to see value-added steps, nonvalue added steps, and non-value added but needed steps
An activity that transforms or shapes material or information to meet customer requirements.
Those activities that require time or resources, but do not add value to the customerâ&#x20AC;&#x2122;s requirement (but may meet company requirements).
In this section probability, probability curves and standard distributions will be explored.
Value
Combinations
2
1
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2
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3
5
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6
5
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5
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4
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3
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2
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1
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. The shape of a dataset can be determined by examining a histogram or, if testing the distribution for normality, using a â&#x20AC;&#x153;Normal Probability Plot.â&#x20AC;? There are many different shapes a dataset may assume.
The Normal distribution is an example of a continuous random variable distribution. There are many different Normal distributions. A Normal distribution can be identified by specifying two numbers: the mean and the variance or standard deviation. If X is a normal random variable with mean ď and variance ď ł2, then the density function y is given by a normal distribution which is sometimes called a bell curve. It is symmetric. The total area underneath a distribution curve equals a probability of one. The area between two different values is the probability that the observed value will fall between those two values.
Standard Normal Distribution: Mean = 0 Standard Deviation = 1 Z = Number of standard deviations Determine Z value from Z-table: Other options: use Excel or MINITAB速 Be aware of the different Z-tables
N! is called “N factorial” N!=N(N-1)(N-2)...1 0!=1
N The expression is the combination of N items taken n at a time. n Its value is:
N! [n!( N n)!]
N! is called “N factorial” N!=N(N-1)(N-2). . . 1
0!=1
Construct a histogram of each of the data sets and compare them with a normal curve: MINITAB® : Graph > Histogram
Select “With Fit”
Select A, B, C, and D to plot
The plot shows the actual distribution with a histogram and a normal distribution line graph with the same mean and standard deviation. First ask, “Could it be a Normal distribution?” You will learn how to do a formal statistical test for that later. Two of the distributions are close enough to being normal that the formal statistical test would not reject their normality. Which ones do you think those are? Second, if not normal, what else might it be? Look at the distributions you just studied and see which ones are more likely to fit the data than a normal distribution. This is not a formal analysis, just a way to start thinking about distributions.
Use the following session commands to create 9 columns of numbers from a normal distribution with a Mean=70 and a Standard Deviation=9: MINITAB® : Calc > Random Data > Normal
Generate 250 Rows
Store in C1-C9
Mean = 70
Standard Deviation = 9
Use the following session commands to create column C10: MINITAB® : Calc > Row Statistics
Select columns C1-C9 Select Mean Store Result in C10 This exercise generates random data. So each person’s data will differ. The result will be a table.
MINITAB®: Stat > Basic Statistics > Display Descriptive Statistics
Select all 10 columns
MINITAB®: Graph > Dotplot > Multiple Ys
Select Columns 1 and 10 (C1 and C10)
Notice the differences in the range.
MINITAB®: Calc > Random Data > Chi-Square
Generate 250 Rows
Store in C1 - C9
Degrees of Freedom = 2
MINITAB®: Calc > Row Statistics > Mean C1-C9
This will replace your normal data unless you add a new worksheet to your MINITAB® session, or store the data in open columns. You should not have to change any other settings.
Store results into C10
MINITAB®: Stat > Basic Stats > Display Descriptive Stats > C1-C10 MINITAB®: Graph > Dotplot > Multiple Ys Simple (C9,C10)
Same scale for all variables
MINITAB®: Graph > Dotplot (C9, C10)
Same scale for all variables
To produce these charts: MINITAB®: Stat > Basic Statistics > Normality Test
Repeat for variable C10
ď&#x20AC; Use this checklist to help you prepare for your gate review. CHECKPOINTS 1.
You have defined the input, process, and output measures that are critical to understanding the performance of this process.
2.
You have defined defect, unit, and opportunity that you will use to calculate process sigma levels.
3.
You have developed your data-collection plan, including how much data will be collected and whether or not you will use sampling.
4.
The steps that will be taken to minimize the bias and assure the reliability and validity of the measurement process have been clearly documented.
5.
The collected data has been graphically displayed.
6.
The current process sigma and the sigma goal have been calculated for the project.
7.
Potential causes have been identified.
COMPLETE
15 Minutes