Design for Six Sigma Statistics 59 Tools for Diagnosing and Solving Problems in DFFS Initiatives

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ISBN: 9780071451628 | 0071451625
Cover: Hardcover
Copyright: 12/26/2005

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Design for Six Sigma Statistics meticulously details 59 mathematical procedures for executing DFSS programs, isolating and identifying problems, and solving them before the actual product launch. More than an introduction to statistical concepts and methods, this comprehensive resource offers real-world case studies and step-by-step MINTAB and Crystal Ball instruction for performing: DFSS Design of Experiments, Measuring Process Capability, Statistical Tolerancing in DFSS, DFSS Techniques within the supply chain. Book jacket.

Foreword

xiii

Preface

xix

Chapter 1 Engineering in a Six Sigma Company

(30)

1.1 Understanding Six Sigma and DFSS Terminology

(9)

1.2 Laying the Foundation for DFSS

(3)

1.3 Choosing the Best Statistical Tool

(7)

1.4 Example of Statistical Tools in New Product Development

(10)

Chapter 2 Visualizing Data

(114)

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

(4)

2.2 Visualizing Time Series Data

(12)

2.2.1 Concealing the Story with Art

(2)

2.2.2 Concealing Patterns by Aggregating Data

(3)

2.2.3 Choosing the Aspect Ratio to Reveal Patterns

(3)

2.2.4 Revealing Instability with the IX, MR Control Chart

(4)

2.3 Visualizing the Distribution of Data

(24)

2.3.1 Visualizing Distributions with Dot Graphs

(4)

2.3.2 Visualizing Distributions with Boxplots

(6)

2.3.3 Visualizing Distributions with Histograms

(8)

2.3.4 Visualizing Distributions with Stem-and-Leaf Displays

(2)

2.3.5 Revealing Patterns by Transforming Data

(3)

2.4 Visualizing Bivariate Data

(11)

2.4.1 Visualizing Bivariate Data with Scatter Plots

(2)

2.4.2 Visualizing Both Marginal and Joint Distributions

(3)

2.4.3 Visualizing Paired Data

(6)

2.5 Visualizing Multivariate Data

(8)

2.5.1 Visualizing Historical Data with Scatter Plot Matrices

(2)

2.5.2 Visualizing Experimental Data with Multi-Vari Charts

(5)

2.6 Summary: Guidelines for Visualizing Data with Integrity

(4)

Chapter 3 Describing Random Behavior

(48)

3.1 Measuring Probability of Events

(18)

3.1.1 Describing Collections of Events

(3)

3.1.2 Calculating the Probability of Events

101

(5)

3.1.2.1 Calculating Probability of Combinations of Events

102

(1)

3.1.2.2 Calculating Probability of Conditional Chains of Events

103

(1)

3.1.2.3 Calculating the Joint Probability of Independent Events

104

(2)

3.1.3 Counting Possible Outcomes

106

(1)

3.1.3.1 Counting Samples with Replacement

106

(1)

3.1.3.2 Counting Ordered Samples without Replacement

107

(1)

3.1.3.3 Counting Unordered Samples without Replacement

108

(1)

3.1.4 Calculating Probabilities for Sampling Problems

109

(7)

3.1.4.1 Calculating Probability Based on a Sample Space of Equally Likely Outcomes

109

(1)

3.1.4.2 Calculating Sampling Probabilities from a Finite Population

110

(3)

3.1.4.3 Calculating Sampling Probabilities from Populations with a Constant Probability of Defects

113

(2)

3.1.4.4 Calculating Sampling Probabilities from a Continuous Medium

115

(1)

3.2 Representing Random Processes by Random Variables

116

(13)

3.2.1 Describing Random Variables

117

(1)

3.2.2 Selecting the Appropriate Type of Random Variable

118

(1)

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

118

(2)

3.2.4 Specifying the Cumulative Probability of a Random Variable

120

(4)

3.2.5 Specifying the Probability Values of a Discrete Random Variable

124

(1)

3.2.6 Specifying the Probability Density of a Continuous Random Variable

125

(4)

3.3 Calculating Properties of Random Variables

129

(17)

3.3.1 Calculating the Expected Value of a Random Variable

129

(6)

3.3.2 Calculating Measures of Variation of a Random Variable

135

(3)

3.3.3 Calculating Measures of Shape of a Random Variable

138

(1)

3.3.4 Calculating Quantiles of a Random Variable

139

(6)

Chapter 4 Estimating Population Properties

145

(116)

4.1 Communicating Estimation

146

(10)

4.1.1 Sampling for Accuracy and Precision

147

(6)

4.1.2 Selecting Good Estimators

153

(3)

4.2 Selecting Appropriate Distribution Models

156

(2)

4.3 Estimating Properties of a Normal Population

158

(58)

4.3.1 Estimating the Population Mean

160

(13)

4.3.2 Estimating the Population Standard Deviation

173

(11)

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

184

(27)

4.3.3.1 Planning Samples to Identify Short-Term and Long-Term Properties

185

(4)

4.3.3.2 Estimating Short-Term and Long-Term Properties from Subgrouped Data

189

(14)

4.3.3.3 Estimating Short-Term and Long-Term Properties from Individual Data

203

(8)

4.3.4 Estimating Statistical Tolerance Bounds and Intervals

211

(5)

4.4 Estimating Properties of Failure Time Distributions

216

(22)

4.4.1 Describing Failure Time Distributions

217

(6)

4.4.2 Estimating Reliability from Complete Life Data

223

(7)

4.4.3 Estimating Reliability from Censored Life Data

230

(4)

4.4.4 Estimating Reliability from Life Data with Zero Failures

234

(4)

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

238

(10)

4.5.1 Estimating the Probability of Defective Units IT

239

(5)

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

244

(4)

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

248

(73)

4.6.1 Estimating the Poisson Rate Parameter X

249

(6)

4.6.2 Testing a Process for Stability in the Rate of Defects

255

(6)

Chapter 5 Assessing Measurement Systems

261

(4)

5.1 Assessing Measurement System Repeatability Using a Control Chart

265

(6)

5.2 Assessing Measurement System Precision Using Gage R&R Studies

271

(1)

5.2.1 Conducting a Gage R&R Study

272

(1)

5.2.1.1 Step 1: Define Measurement System and Objective for MSA

272

(2)

5.2.1.2 Step 2: Select n Parts for Measurement

274

(1)

5.2.1.3 Step 3: Select k Appraisers

275

(1)

5.2.1.4 Step 4: Select r, the Number of Replications

276

(3)

5.2.1.5 Step 5: Randomize Measurement Order

279

(1)

5.2.1.6 Step 6: Perform nkr Measurements

280

(1)

5.2.1.7 Step 7: Analyze Data

281

(6)

5.2.1.8 Step 8: Compute MSA Metrics

287

(6)

5.2.1.9 Step 9: Reach Conclusions

293

(3)

5.2.2 Assessing Sensory Evaluation with Gage R&R

296

(5)

5.2.3 Investigating a Broken Measurement System

301

(6)

5.3 Assessing Attribute Measurement Systems

307

(1)

5.3.1 Assessing Agreement of Attribute Measurement Systems

308

(5)

5.3.2 Assessing Bias and Repeatability of Attribute Measurement Systems

313

(6)

Chapter 6 Measuring Process Capability

319

(66)

6.1 Verifying Process Stability

321

(12)

6.1.1 Selecting the Most Appropriate Control Chart

324

(2)

6.1.1.1 Continuous Measurement Data

324

(2)

6.1.1.2 Count Data

326

(1)

6.1.2 Interpreting Control Charts for Signs of Instability

326

(7)

6.2 Calculating Measures of Process Capability

333

(28)

6.2.1 Measuring Potential Capability

336

(10)

6.2.1.1 Measuring Potential Capability with Bilateral Tolerances

336

(6)

6.2.1.2 Measuring Potential Capability with Unilateral Tolerances

342

(4)

6.2.2 Measuring Actual Capability

346

(25)

6.2.2.1 Measuring Actual Capability with Bilateral Tolerances

346

(13)

6.2.2.2 Measuring Actual Capability with Unilateral Tolerances

359

(2)

6.3 Predicting Process Defect Rates

361

(8)

6.4 Conducting a Process Capability Study

369

(2)

6.5 Applying Process Capability Methods in a Six Sigma Company

371

(5)

6.5.1 Dealing with Inconsistent Terminology

371

(1)

6.5.2 Understanding the Mean Shift

372

(2)

6.5.3 Converting between Long-Term and Short-Term

374

(2)

6.6 Applying the DFSS Scorecard

376

(1)

6.6.1 Building a Basic DFSS Scorecard

379

(6)

Chapter 7 Detecting Changes

385

(92)

7.1 Conducting a Hypothesis Test

387

(23)

7.1.1 Define Objective and State Hypothesis

388

(4)

7.1.2 Choose Risks a and f3 and Select Sample Size n

392

(8)

7.1.3 Collect Data and Test Assumptions

400

(5)

7.1.4 Calculate Statistics and Make Decision

405

(5)

7.2 Detecting Changes in Variation

410

(30)

7.2.1 Comparing Variation to a Specific Value

410

(10)

7.2.2 Comparing Variations of Two Processes

420

(13)

7.2.3 Comparing Variations of Three or More Processes

433

(7)

7.3 Detecting Changes in Process Average

440

(38)

7.3.1 Comparing Process Average to a Specific Value

441

(9)

7.3.2 Comparing Averages of Two Processes

450

(9)

7.3.3 Comparing Repeated Measures of Process Average

459

(8)

7.3.4 Comparing Averages of Three or More Processes

467

(10)

Chapter 8 Detecting Changes in Discrete Data

477

(40)

8.1 Detecting Changes in Proportions

478

(18)

8.1.1 Comparing a Proportion to a Specific Value

480

(10)

8.1.2 Comparing Two Proportions

490

(6)

8.2 Detecting Changes in Defect Rates

496

(9)

8.3 Detecting Associations in Categorical Data

505

(12)

Chapter 9 Detecting Changes in Nonnormal Data

517

(58)

9.1 Detecting Changes Without Assuming a Distribution

518

(25)

9.1.1 Comparing a Median to a Specific Value

521

(14)

9.1.2 Comparing Two Process Distributions

535

(4)

9.1.3 Comparing Two or More Process Medians

539

(4)

9.2 Testing for Goodness of Fit

543

(17)

9.3 Normalizing Data with Transformations

560

(18)

9.3.1 Normalizing Data with the Box-Cox Transformation

561

(9)

9.3.2 Normalizing Data with the Johnson Transformation

570

(5)

Chapter 10 Conducting Efficient Experiments

575

(110)

10.1 Conducting Simple Experiments

578

(41)

10.1.1 Changing Everything at Once

578

(4)

10.1.2 Analyzing a Simple Experiment

582

(8)

10.1.3 Insuring Against Experimental Risks

590

(9)

10.1.4 Conducting a Computer-Aided Experiment

599

(14)

10.1.5 Selecting a More Efficient Treatment Structure

613

(6)

10.2 Understanding the Terminology and Procedure for Efficient Experiments

619

(14)

10.2.1 Understanding Experimental Terminology

619

(3)

10.2.2 Following a Procedure for Efficient Experiments

622

(11)

10.2.2.1 Step 1: Define the Objective

623

(1)

10.2.2.2 Step 2: Define the !PO Structure

624

(2)

10.2.2.3 Step 3: Select Treatment Structure

626

(1)

10.2.2.4 Step 4: Select Design Structure

627

(1)

10.2.2.5 Step 5: Select Sample Size

628

(1)

10.2.2.6 Step 6: Prepare to Collect Data

629

(1)

10.2.2.7 Step 7: Collect Data

630

(1)

10.2.2.8 Step 8: Determine Significant Effects

631

(1)

10.2.2.9 Step 9: Reach Conclusions

632

(1)

10.2.2.10 Step 10: Verify Conclusions

632

(1)

10.3 Conducting Two-Level Experiments

633

(36)

10.3.1 Selecting the Most Efficient Treatment Structure

635

(8)

10.3.2 Calculating Sample Size

643

(5)

10.3.3 Analyzing Screening Experiments

648

(7)

10.3.4 Analyzing Modeling Experiments

655

(8)

10.3.5 Testing a System for Nonlinearity with a Center Point Run

663

(6)

10.4 Conducting Three-Level Experiments

669

(11)

10.5 Improving Robustness with Experiments

680

(5)

Chapter 11 Predicting the Variation Caused by Tolerances

685

(106)

11.1 Selecting Critical to Quality (CTQ) Characteristics

692

(6)

11.2 Implementing Consistent Tolerance Design

698

(6)

11.3 Predicting the Effects of Tolerances in Linear Systems

704

(27)

11.3.1 Developing Linear Transfer Functions

704

(7)

11.3.2 Calculating Worst-Case Limits

711

(5)

11.3.3 Predicting the Variation of Linear Systems

716

(8)

11.3.4 Applying the Root-Sum-Square Method to Tolerances

724

(7)

11.4 Predicting the Effects of Tolerances in Nonlinear Systems

731

(23)

11.5 Predicting Variation with Dependent Components

754

(11)

11.6 Predicting Variation with Geometric Dimensioning and Tolerancing

765

(6)

11.7 Optimizing System Variation

771

(20)

Appendix

791

(42)

References

833

(4)

Index

837

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Design for Six Sigma Statistics 59 Tools for Diagnosing and Solving Problems in DFFS Initiatives

Summary

Author Biography

Table of Contents

Supplemental Materials