Design for Six Sigma Statistics

Design for Six Sigma Statistics

Authors: Andrew Sleeper

Published: December 2005

eISBN: 9780071483025 0071483020 | ISBN: 9780071451628

Contents

Foreword

Preface

Chapter 1 Engineering in a Six Sigma Company

1.1 Understanding Six Sigma and DFSS Terminology

1.2 Laying the Foundation for DFSS

1.3 Choosing the Best Statistical Tool

1.4 Example of Statistical Tools in New Product Development

Chapter 2 Visualizing Data

2.1 Case Study: Data Graphed Out of Context Leads to Incorrect Conclusions

2.2 Visualizing Time Series Data

2.2.1 Concealing the Story with Art

2.2.2 Concealing Patterns by Aggregating Data

2.2.3 Choosing the Aspect Ratio to Reveal Patterns

2.2.4 Revealing Instability with the IX, MR Control Chart

2.3 Visualizing the Distribution of Data

2.3.1 Visualizing Distributions with Dot Graphs

2.3.2 Visualizing Distributions with Boxplots

2.3.3 Visualizing Distributions with Histograms

2.3.4 Visualizing Distributions with Stem-and-Leaf Displays

2.3.5 Revealing Patterns by Transforming Data

2.4 Visualizing Bivariate Data

2.4.1 Visualizing Bivariate Data with Scatter Plots

2.4.2 Visualizing Both Marginal and Joint Distributions

2.4.3 Visualizing Paired Data

2.5 Visualizing Multivariate Data

2.5.1 Visualizing Historical Data with Scatter Plot Matrices

2.5.2 Visualizing Experimental Data with Multi-Vari Charts

2.6 Summary: Guidelines for Visualizing Data with Integrity

Chapter 3 Describing Random Behavior

3.1 Measuring Probability of Events

3.1.1 Describing Collections of Events

3.1.2 Calculating the Probability of Events

3.1.3 Counting Possible Outcomes

3.1.4 Calculating Probabilities for Sampling Problems

3.2 Representing Random Processes by Random Variables

3.2.1 Describing Random Variables

3.2.2 Selecting the Appropriate Type of Random Variable

3.2.3 Specifying a Random Variable as a Member of a Parametric Family

3.2.4 Specifying the Cumulative Probability of a Random Variable

3.2.5 Specifying the Probability Values of a Discrete Random Variable

3.2.6 Specifying the Probability Density of a Continuous Random Variable

3.3 Calculating Properties of Random Variables

3.3.1 Calculating the Expected Value of a Random Variable

3.3.2 Calculating Measures of Variation of a Random Variable

3.3.3 Calculating Measures of Shape of a Random Variable

3.3.4 Calculating Quantiles of a Random Variable

Chapter 4 Estimating Population Properties

4.1 Communicating Estimation

4.1.1 Sampling for Accuracy and Precision

4.1.2 Selecting Good Estimators

4.2 Selecting Appropriate Distribution Models

4.3 Estimating Properties of a Normal Population

4.3.1 Estimating the Population Mean

4.3.2 Estimating the Population Standard Deviation

4.3.3 Estimating Short-Term and Long-Term Properties of a Normal Population

4.3.4 Estimating Statistical Tolerance Bounds and Intervals

4.4 Estimating Properties of Failure Time Distributions

4.4.1 Describing Failure Time Distributions

4.4.2 Estimating Reliability from Complete Life Data

4.4.3 Estimating Reliability from Censored Life Data

4.4.4 Estimating Reliability from Life Data with Zero Failures

4.5 Estimating the Probability of Defective Units by the Binomial Probability π

4.5.1 Estimating the Probability of Defective Units π

4.5.2 Testing a Process for Stability in the Proportion of Defective Units

4.6 Estimating the Rate of Defects by the Poisson Rate Parameter λ

4.6.1 Estimating the Poisson Rate Parameter λ

4.6.2 Testing a Process for Stability in the Rate of Defects

Chapter 5 Assessing Measurement Systems

5.1 Assessing Measurement System Repeatability Using a Control Chart

5.2 Assessing Measurement System Precision Using Gage R&R Studies

5.2.1 Conducting a Gage R&R Study

5.2.2 Assessing Sensory Evaluation with Gage R&R

5.2.3 Investigating a Broken Measurement System

5.3 Assessing Attribute Measurement Systems

5.3.1 Assessing Agreement of Attribute Measurement Systems

5.3.2 Assessing Bias and Repeatability of Attribute Measurement Systems

Chapter 6 Measuring Process Capability

6.1 Verifying Process Stability

6.1.1 Selecting the Most Appropriate Control Chart

6.1.2 Interpreting Control Charts for Signs of Instability

6.2 Calculating Measures of Process Capability

6.2.1 Measuring Potential Capability

6.2.2 Measuring Actual Capability

6.3 Predicting Process Defect Rates

6.4 Conducting a Process Capability Study

6.5 Applying Process Capability Methods in a Six Sigma Company

6.5.1 Dealing with Inconsistent Terminology

6.5.2 Understanding the Mean Shift

6.5.3 Converting between Long-Term and Short-Term

6.6 Applying the DFSS Scorecard

6.6.1 Building a Basic DFSS Scorecard

Chapter 7 Detecting Changes

7.1 Conducting a Hypothesis Test

7.1.1 Define Objective and State Hypothesis

7.1.2 Choose Risks α and β and Select Sample Size n

7.1.3 Collect Data and Test Assumptions

7.1.4 Calculate Statistics and Make Decision

7.2 Detecting Changes in Variation

7.2.1 Comparing Variation to a Specific Value

7.2.2 Comparing Variations of Two Processes

7.2.3 Comparing Variations of Three or More Processes

7.3 Detecting Changes in Process Average

7.3.1 Comparing Process Average to a Specific Value

7.3.2 Comparing Averages of Two Processes

7.3.3 Comparing Repeated Measures of Process Average

7.3.4 Comparing Averages of Three or More Processes

Chapter 8 Detecting Changes in Discrete Data

8.1 Detecting Changes in Proportions

8.1.1 Comparing a Proportion to a Specific Value

8.1.2 Comparing Two Proportions

8.2 Detecting Changes in Defect Rates

8.3 Detecting Associations in Categorical Data

Chapter 9 Detecting Changes in Nonnormal Data

9.1 Detecting Changes Without Assuming a Distribution

9.1.1 Comparing a Median to a Specific Value

9.1.2 Comparing Two Process Distributions

9.1.3 Comparing Two or More Process Medians

9.2 Testing for Goodness of Fit

9.3 Normalizing Data with Transformations

9.3.1 Normalizing Data with the Box-Cox Transformation

9.3.2 Normalizing Data with the Johnson Transformation

Chapter 10 Conducting Efficient Experiments

10.1 Conducting Simple Experiments

10.1.1 Changing Everything at Once

10.1.2 Analyzing a Simple Experiment

10.1.3 Insuring Against Experimental Risks

10.1.4 Conducting a Computer-Aided Experiment

10.1.5 Selecting a More Efficient Treatment Structure

10.2 Understanding the Terminology and Procedure for Efficient Experiments

10.2.1 Understanding Experimental Terminology

10.2.2 Following a Procedure for Efficient Experiments

10.3 Conducting Two-Level Experiments

10.3.1 Selecting the Most Efficient Treatment Structure

10.3.2 Calculating Sample Size

10.3.3 Analyzing Screening Experiments

10.3.4 Analyzing Modeling Experiments

10.3.5 Testing a System for Nonlinearity with a Center Point Run

10.4 Conducting Three-Level Experiments

10.5 Improving Robustness with Experiments

Chapter 11 Predicting the Variation Caused by Tolerances

11.1 Selecting Critical to Quality (CTQ) Characteristics

11.2 Implementing Consistent Tolerance Design

11.3 Predicting the Effects of Tolerances in Linear Systems

11.3.1 Developing Linear Transfer Functions

11.3.2 Calculating Worst-Case Limits

11.3.3 Predicting the Variation of Linear Systems

11.3.4 Applying the Root-Sum-Square Method to Tolerances

11.4 Predicting the Effects of Tolerances in Nonlinear Systems

11.5 Predicting Variation with Dependent Components

11.6 Predicting Variation with Geometric Dimensioning and Tolerancing

11.7 Optimizing System Variation

Appendix

References

Index