Statistical Methods for Quality Improvement

Preface to the Second Edition xxi

Preface to the First Edition xxiii

PART I FUNDAMENTAL QUALITY IMPROVEMENT AND STATISTICAL CONCEPTS

1 Introduction 3

1.1 Quality and Productivity, 4

1.2 Quality Costs (or Does It?), 5

1.3 The Need for Statistical Methods, 5

1.4 Early Use of Statistical Methods for Improving Quality, 6

1.5 Influential Quality Experts, 7

1.6 Summary, 9

2 Basic Tools for Improving Quality 13

2.1 Histogram, 13

2.2 Pareto Charts, 17

2.3 Scatter Plots, 21

2.4 Control Chart, 24

2.5 Check Sheet, 26

2.6 Cause-and-Effect Diagram, 26

2.7 Defect Concentration Diagram, 28

2.8 The Seven Newer Tools, 28

2.9 Software, 30

2.10 Summary, 31

3 Basic Concepts in Statistics and Probability 33

3.1 Probability, 33

3.2 Sample Versus Population, 35

3.3 Location, 36

3.4 Variation, 38

3.5 Discrete Distributions, 41

3.6 Continuous Distributions, 55

3.7 Choice of Statistical Distribution, 69

3.8 Statistical Inference, 69

3.9 Enumerative Studies Versus Analytic Studies, 81

PARTII CONTROL CHARTS AND PROCESS CAPABILITY

4 Control Charts for Measurements With Subgrouping (for One Variable) 89

4.1 Basic Control Chart Principles, 89

4.2 Real-Time Control Charting Versus Analysis of Past Data, 92

4.3 Control Charts: When to Use, Where to Use, How Many to Use, 94

4.4 Benefits from the Use of Control Charts, 94

4.5 Rational Subgroups, 95

4.6 Basic Statistical Aspects of Control Charts, 95

4.7 Illustrative Example, 96

4.8 Illustrative Example with Real Data, 114

4.9 Determining the Point of a Parameter Change, 116

4.10 Acceptance Sampling and Acceptance Control Chart, 117

4.11 Modified Limits, 124

4.12 Difference Control Charts, 124

4.13 Other Charts, 126

4.14 Average Run Length (ARL), 127

4.15 Determining the Subgroup Size, 129

4.16 Out-of-Control Action Plans, 131

4.17 Assumptions for the Charts in This Chapter, 132

4.18 Measurement Error, 140

4.19 Software, 142

4.20 Summary, 143

5 Control Charts for Measurements Without Subgrouping (for One Variable) 157

5.2 Transform the Data or Fit a Distribution?, 170

5.3 Moving Average Chart, 171

5.4 Controlling Variability with Individual Observations, 173

5.5 Summary, 175

6 Control Charts for Attributes 181

6.1 Charts for Nonconforming Units, 182

6.2 Charts for Nonconformities, 202

6.3 Summary, 218

7 Process Capability 225

7.1 Data Acquisition for Capability Indices, 225

7.2 Process Capability Indices, 227

7.3 Estimating the Parameters in Process Capability Indices, 232

7.4 Distributional Assumption for Capability Indices, 235

7.5 Confidence Intervals for Process Capability Indices, 236

7.6 Asymmetric Bilateral Tolerances, 243

7.7 Capability Indices That Are a Function of Percent Nonconforming, 245

7.8 Modified k Index, 250

7.9 Other Approaches, 251

7.10 Process Capability Plots, 251

7.11 Process Capability Indices Versus Process Performance Indices, 252

7.12 Process Capability Indices with Autocorrelated Data, 253

7.13 Software for Process Capability Indices, 253

7.14 Summary, 253

8 Alternatives to Shewhart Charts 261

8.1 Introduction, 261

8.2 Cumulative Sum Procedures: Principles and Historical Development, 263

8.3 CUSUM Procedures for Controlling Process Variability, 283

8.4 Applications of CUSUM Procedures, 286

8.5 Generalized Likelihood Ratio Charts: Competitive Alternative to CUSUM Charts, 286

8.6 CUSUM Procedures for Nonconforming Units, 286

8.7 CUSUM Procedures for Nonconformity Data, 290

8.8 Exponentially Weighted Moving Average Charts, 294

8.9 Software, 301

8.10 Summary, 301

9 Multivariate Control Charts for Measurement and Attribute Data 309

9.1 Hotelling's T2 Distribution, 312

9.2 A T2 Control Chart, 313

9.3 Multivariate Chart Versus Individual X-Charts, 326

9.4 Charts for Detecting Variability and Correlation Shifts, 327

9.5 Charts Constructed Using Individual Observations, 330

9.6 When to Use Each Chart, 335

9.7 Actual Alpha Levels for Multiple Points, 336

9.8 Requisite Assumptions, 336

9.9 Effects of Parameter Estimation on ARLs, 337

9.10 Dimension-Reduction and Variable Selection Techniques, 337

9.11 Multivariate CUSUM Charts, 338

9.12 Multivariate EWMA Charts, 339

9.13 Effect of Measurement Error, 343

9.14 Applications of Multivariate Charts, 344

9.15 Multivariate Process Capability Indices, 344

9.16 Summary, 344

10 Miscellaneous Control Chart Topics 353

10.1 Pre-control, 353

10.2 Short-Run SPC, 356

10.3 Charts for Autocorrelated Data, 359

10.4 Charts for Batch Processes, 364

10.5 Charts for Multiple-Stream Processes, 364

10.6 Nonparametric Control Charts, 365

10.7 Bayesian Control Chart Methods, 366

10.8 Control Charts for Variance Components, 367

10.9 Control Charts for Highly Censored Data, 367

10.10 Neural Networks, 367

10.11 Economic Design of Control Charts, 368

10.12 Charts with Variable Sample Size and/or Variable Sampling Interval, 370

10.13 Users of Control Charts, 371

10.14 Software for Control Charting, 374

PART III BEYOND CONTROL CHARTS: GRAPHICAL AND STATISTICAL METHODS

11 Graphical Methods 387

11.1 Histogram, 388

11.2 Stem-and-Leaf Display, 389

11.3 Dot Diagrams, 390

11.4 Boxplot, 392

11.5 Normal Probability Plot, 396

11.6 Plotting Three Variables, 398

11.7 Displaying More Than Three Variables, 399

11.8 Plots to Aid in Transforming Data, 399

11.9 Summary, 401

12 Linear Regression 407

12.1 Simple Linear Regression, 407

12.2 Worth of the Prediction Equation, 411

12.3 Assumptions, 413

12.4 Checking Assumptions Through Residual Plots, 414

12.5 Confidence Intervals and Hypothesis Test, 415

12.6 Prediction Interval for Y, 416

12.7 Regression Control Chart, 417

12.8 Cause-Selecting Control Charts, 419

12.9 Linear, Nonlinear, and Nonparametric Profiles, 421

12.10 Inverse Regression, 423

12.11 Multiple Linear Regression, 426

12.12 Issues in Multiple Regression, 426

12.13 Software For Regression, 429

12.14 Summary, 429

13 Design of Experiments 435

13.1 A Simple Example of Experimental Design Principles, 435

13.2 Principles of Experimental Design, 437

13.3 Statistical Concepts in Experimental Design, 439

13.4 t-Tests, 441

13.5 Analysis of Variance for One Factor, 445

13.6 Regression Analysis of Data from Designed Experiments, 455

13.7 ANOVA for Two Factors, 460

13.8 The 23 Design, 469

13.9 Assessment of Effects Without a Residual Term, 474

13.10 Residual Plot, 477

13.11 Separate Analyses Using Design Units and Uncoded Units, 479

13.12 Two-Level Designs with More Than Three Factors, 480

13.13 Three-Level Factorial Designs, 482

13.14 Mixed Factorials, 483

13.15 Fractional Factorials, 483

13.16 Other Topics in Experimental Design and Their Applications, 493

13.17 Summary, 500

14 Contributions of Genichi Taguchi and Alternative Approaches 513

14.1 "Taguchi Methods", 513

14.2 Quality Engineering, 514

14.3 Loss Functions, 514

14.4 Distribution Not Centered at the Target, 518

14.5 Loss Functions and Specification Limits, 518

14.6 Asymmetric Loss Functions, 518

14.7 Signal-to-Noise Ratios and Alternatives, 522

14.8 Experimental Designs for Stage One, 524

14.9 Taguchi Methods of Design, 525

14.10 Determining Optimum Conditions, 553

14.11 Summary, 558

15 Evolutionary Operation 565

15.1 EVOP Illustrations, 566

15.2 Three Variables, 576

15.3 Simplex EVOP, 578

15.4 Other EVOP Procedures, 581

15.5 Miscellaneous Uses of EVOP, 581

15.6 Summary, 582

16 Analysis of Means 587

16.1 ANOM for One-Way Classifications, 588

16.2 ANOM for Attribute Data, 591

16.3 ANOM When Standards Are Given, 594

16.4 ANOM for Factorial Designs, 596

16.5 ANOM When at Least One Factor Has More Than Two Levels, 601

16.6 Use of ANOM with Other Designs, 610

16.7 Nonparametric ANOM, 610

16.8 Summary, 611

17 Using Combinations of Quality Improvement Tools 615

17.1 Control Charts and Design of Experiments, 616

17.2 Control Charts and Calibration Experiments, 616

17.3 Six Sigma Programs, 616

17.4 Statistical Process Control and Engineering Process Control, 624

Answers to Selected Exercises 629

Appendix: Statistical Tables 633

Author Index 645

Subject Index 657