Experiments
Planning, Analysis, and Optimization
Wiley Series in Probability and Statistics
3. Edition May 2021
736 Pages, Hardcover
Handbook/Reference Book
ISBN:
978-1-119-47010-6
John Wiley & Sons
Further versions
Praise for the First Edition:
"If you ... want an up-to-date, definitive reference written by authors who have contributed much to this field, then this book is an essential addition to your library."
--Journal of the American Statistical Association
A COMPREHENSIVE REVIEW OF MODERN EXPERIMENTAL DESIGN
Experiments: Planning, Analysis, and Optimization, Third Edition provides a complete discussion of modern experimental design for product and process improvement--the design and analysis of experiments and their applications for system optimization, robustness, and treatment comparison. While maintaining the same easy-to-follow style as the previous editions, this book continues to present an integrated system of experimental design and analysis that can be applied across various fields of research including engineering, medicine, and the physical sciences. New chapters provide modern updates on practical optimal design and computer experiments, an explanation of computer simulations as an alternative to physical experiments. Each chapter begins with a real-world example of an experiment followed by the methods required to design that type of experiment. The chapters conclude with an application of the methods to the experiment, bridging the gap between theory and practice.
The authors modernize accepted methodologies while refining many cutting-edge topics including robust parameter design, analysis of non-normal data, analysis of experiments with complex aliasing, multilevel designs, minimum aberration designs, and orthogonal arrays.
The third edition includes:
* Information on the design and analysis of computer experiments
* A discussion of practical optimal design of experiments
* An introduction to conditional main effect (CME) analysis and definitive screening designs (DSDs)
* New exercise problems
This book includes valuable exercises and problems, allowing the reader to gauge their progress and retention of the book's subject matter as they complete each chapter.
Drawing on examples from their combined years of working with industrial clients, the authors present many cutting-edge topics in a single, easily accessible source. Extensive case studies, including goals, data, and experimental designs, are also included, and the book's data sets can be found on a related FTP site, along with additional supplemental material. Chapter summaries provide a succinct outline of discussed methods, and extensive appendices direct readers to resources for further study.
Experiments: Planning, Analysis, and Optimization, Third Edition is an excellent book for design of experiments courses at the upper-undergraduate and graduate levels. It is also a valuable resource for practicing engineers and statisticians.
Preface to the Third Edition xvii
Preface to the Second Edition xix
Preface to the First Edition xxi
Suggestions of Topics for Instructors xxv
List of Experiments and Data Sets xxvii
About the Companion Website xxxiii
1 Basic Concepts for Experimental Design and Introductory Regression Analysis 1
1.1 Introduction and Historical Perspective 1
1.2 A Systematic Approach to the Planning and Implementation of Experiments 4
1.3 Fundamental Principles: Replication, Randomization, and Blocking 8
1.4 Simple Linear Regression 11
1.5 Testing of Hypothesis and Interval Estimation 14
1.6 Multiple Linear Regression 20
1.7 Variable Selection in Regression Analysis 26
1.8 Analysis of Air Pollution Data 28
1.9 Practical Summary 34
Exercises 35
References 43
2 Experiments with a Single Factor 45
2.1 One-Way Layout 45
*2.1.1 Constraint on the Parameters 50
2.2 Multiple Comparisons 52
2.3 Quantitative Factors and Orthogonal Polynomials 56
2.4 Expected Mean Squares and Sample Size Determination 61
2.5 One-Way Random Effects Model 68
2.6 Residual Analysis: Assessment of Model Assumptions 71
2.7 Practical Summary 76
Exercises 77
References 82
3 Experiments with More than One Factor 85
3.1 Paired Comparison Designs 85
3.2 Randomized Block Designs 88
3.3 Two-Way Layout: Factors with Fixed Levels 92
3.3.1 Two Qualitative Factors: A Regression Modeling Approach 95
*3.4 Two-Way Layout: Factors with Random Levels 98
3.5 Multi-Way Layouts 105
3.6 Latin Square Designs: Two Blocking Variables 108
3.7 Graeco-Latin Square Designs 112
*3.8 Balanced Incomplete Block Designs 113
*3.9 Split-Plot Designs 118
3.10 Analysis of Covariance: Incorporating Auxiliary Information 126
*3.11 Transformation of the Response 130
3.12 Practical Summary 134
Exercises 135
Appendix 3A: Table of Latin Squares, Graeco-Latin Squares, and Hyper-Graeco-Latin Squares 147
References 148
4 Full Factorial Experiments at Two Levels 151
4.1 An Epitaxial Layer Growth Experiment 151
4.2 Full Factorial Designs at Two Levels: A General Discussion 153
4.3 Factorial Effects and Plots 157
4.3.1 Main Effects 158
4.3.2 Interaction Effects 159
4.4 Using Regression to Compute Factorial Effects 165
*4.5 ANOVA Treatment of Factorial Effects 167
4.6 Fundamental Principles for Factorial Effects: Effect Hierarchy, Effect Sparsity, and Effect Heredity 168
4.7 Comparisons with the "One-Factor-at-a-Time" Approach 169
4.8 Normal and Half-Normal Plots for Judging Effect Significance 172
4.9 Lenth's Method: Testing Effect Significance for Experiments Without Variance Estimates 174
4.10 Nominal-the-Best Problem and Quadratic Loss Function 178
4.11 Use of Log Sample Variance for Dispersion Analysis 179
4.12 Analysis of Location and Dispersion: Revisiting the Epitaxial Layer Growth Experiment 181
*4.13 Test of Variance Homogeneity and Pooled Estimate of Variance 184
*4.14 Studentized Maximum Modulus Test: Testing Effect Significance for Experiments With Variance Estimates 185
4.15 Blocking and Optimal Arrangement of 2¯k Factorial Designs in 2¯q Blocks 188
4.16 Practical Summary 193
Exercises 195
Appendix 4A: Table of 2¯k Factorial Designs in 2¯q Blocks 201
References 203
5 Fractional Factorial Experiments at Two Levels 205
5.1 A Leaf Spring Experiment 205
5.2 Fractional Factorial Designs: Effect Aliasing and the Criteria of Resolution and Minimum Aberration 206
5.3 Analysis of Fractional Factorial Experiments 212
5.4 Techniques for Resolving the Ambiguities in Aliased Effects 217
5.4.1 Fold-Over Technique for Follow-Up Experiments 218
5.4.2 Optimal Design Approach for Follow-Up Experiments 222
5.5 Conditional Main Effect (CME) Analysis: A Method to Unravel Aliased Interactions 227
5.6 Selection of 2¯k¯.p Designs Using Minimum Aberration and Related Criteria 232
5.7 Blocking in Fractional Factorial Designs 236
5.8 Practical Summary 238
Exercises 240
Appendix 5A: Tables of 2¯k¯.p Fractional Factorial Designs 252
Appendix 5B: Tables of 2¯k¯.p Fractional Factorial Designs in 2q Blocks 258
References 262
6 Full Factorial and Fractional Factorial Experiments at Three Levels 265
6.1 A Seat-Belt Experiment 265
6.2 Larger-the-Better and Smaller-the-Better Problems 267
6.3 3¯k Full Factorial Designs 268
6.4 3¯k¯.pFractional Factorial Designs 273
6.5 Simple Analysis Methods: Plots and Analysis of Variance 277
6.6 An Alternative Analysis Method 282
6.7 Analysis Strategies for Multiple Responses I: Out-Of-Spec Probabilities 291
6.8 Blocking in 3¯k and 3¯k¯.p Designs 299
6.9 Practical Summary 301
Exercises 303
Appendix 6A: Tables of 3¯k¯.p Fractional Factorial Designs 309
Appendix 6B: Tables of 3¯k¯.p Fractional Factorial Designs in 3¯q Blocks 310
References 314
7 Other Design and Analysis Techniques for Experiments at More than Two Levels 315
7.1 A Router Bit Experiment Based on a Mixed Two-Level and Four-Level Design 315
7.2 Method of Replacement and Construction of 2¯m4¯n Designs 318
7.3 Minimum Aberration 2¯m4¯n Designs with n = 1, 2, 321
7.4 An Analysis Strategy for 2¯m4¯n Experiments 324
7.5 Analysis of the Router Bit Experiment 326
7.6 A Paint Experiment Based on a Mixed Two-Level and Three-Level Design 329
7.7 Design and Analysis of 36-Run Experiments at Two And Three Levels 332
7.8 r¯k¯.pFractional Factorial Designs for any Prime Number r 337
7.8.1 25-Run Fractional Factorial Designs at Five Levels 337
7.8.2 49-Run Fractional Factorial Designs at Seven Levels 340
7.8.3 General Construction 340
7.9 Definitive Screening Designs 341
*7.10 Related Factors: Method of Sliding Levels, Nested Effects Analysis, and Response Surface Modeling 343
7.10.1 Nested Effects Modeling 346
7.10.2 Analysis of Light Bulb Experiment 347
7.10.3 Response Surface Modeling 349
7.10.4 Symmetric and Asymmetric Relationships Between Related Factors 352
7.11 Practical Summary 352
Exercises 353
Appendix 7A: Tables of 2¯m4¹ Minimum Aberration Designs 361
Appendix 7B: Tables of 2¯m4² Minimum Aberration Designs 362
Appendix 7C: OA(25, 5¯6) 364
Appendix 7D: OA(49, 7¯8) 364
Appendix 7E: Conference Matrices C6 C8 C10 C12 C14 and C16 366
References 368
8 Nonregular Designs: Construction and Properties 369
8.1 Two Experiments: Weld-Repaired Castings and Blood Glucose Testing 369
8.2 Some Advantages of Nonregular Designs Over the 2¯k¯.p AND 3¯k¯.p Series of Designs 370
8.3 A Lemma on Orthogonal Arrays 372
8.4 Plackett-Burman Designs and Hall's Designs 373
8.5 A Collection of Useful Mixed-Level Orthogonal Arrays 377
*8.6 Construction of Mixed-Level Orthogonal Arrays Based on Difference Matrices 379
8.6.1 General Method for Constructing Asymmetrical Orthogonal Arrays 380
*8.7 Construction of Mixed-Level Orthogonal Arrays Through the Method of Replacement 382
8.8 Orthogonal Main-Effect Plans Through Collapsing Factors 384
8.9 Practical Summary 388
Exercises 389
Appendix 8A: Plackett-Burman Designs OA(N, 2¯N¯.1) with 12 <= N <= 48 and N = 4 k but not a Power of 2 394
Appendix 8B: Hall'S 16-Run Orthogonal Arrays of Types II to V 397
Appendix 8C: Some Useful Mixed-Level Orthogonal Arrays 399
Appendix 8D: Some Useful Difference Matrices 411
Appendix 8E: Some Useful Orthogonal Main-Effect Plans 413
References 414
9 Experiments with Complex Aliasing 417
9.1 Partial Aliasing of Effects and the Alias Matrix 417
9.2 Traditional Analysis Strategy: Screening Design and Main Effect Analysis 420
9.3 Simplification of Complex Aliasing via Effect Sparsity 421
9.4 An Analysis Strategy for Designs with Complex Aliasing 422
9.4.1 Some Limitations 428
*9.5 A Bayesian Variable Selection Strategy for Designs with Complex Aliasing 429
9.5.1 Bayesian Model Priors 431
9.5.2 Gibbs Sampling 432
9.5.3 Choice of Prior Tuning Constants 434
9.5.4 Blood Glucose Experiment Revisited 435
9.5.5 Other Applications 437
*9.6 Supersaturated Designs: Design Construction and Analysis 437
9.7 Practical Summary 441
Exercises 442
Appendix 9A: Further Details for the Full Conditional Distributions 451
References 453
10 Response Surface Methodology 455
10.1 A Ranitidine Separation Experiment 455
10.2 Sequential Nature of Response Surface Methodology 457
10.3 From First-Order Experiments to Second-Order Experiments: Steepest Ascent Search and Rectangular Grid Search 460
10.3.1 Curvature Check 460
10.3.2 Steepest Ascent Search 461
10.3.3 Rectangular Grid Search 466
10.4 Analysis of Second-Order Response Surfaces 469
10.4.1 Ridge Systems 470
10.5 Analysis of the Ranitidine Experiment 472
10.6 Analysis Strategies for Multiple Responses II: Contour Plots and the Use of Desirability Functions 475
10.7 Central Composite Designs 478
10.8 Box-Behnken Designs and Uniform Shell Designs 483
10.9 Practical Summary 486
Exercises 488
Appendix 10A: Table of Central Composite Designs 498
Appendix 10B: Table of Box-Behnken Designs 500
Appendix 10C: Table of Uniform Shell Designs 501
References 502
11 Introduction to Robust Parameter Design 503
11.1 A Robust Parameter Design Perspective of the Layer Growth and Leaf Spring Experiments 503
11.1.1 Layer Growth Experiment Revisited 503
11.1.2 Leaf Spring Experiment Revisited 504
11.2 Strategies for Reducing Variation 506
11.3 Noise (Hard-to-Control) Factors 508
11.4 Variation Reduction Through Robust Parameter Design 510
11.5 Experimentation and Modeling Strategies I: Cross Array 512
11.5.1 Location and Dispersion Modeling 513
11.5.2 Response Modeling 518
11.6 Experimentation and Modeling Strategies II: Single Array and Response Modeling 523
11.7 Cross Arrays: Estimation Capacity and Optimal Selection 526
11.8 Choosing Between Cross Arrays and Single Arrays 529
*11.8.1 Compound Noise Factor 533
11.9 Signal-to-Noise Ratio and Its Limitations for Parameter Design Optimization 534
11.9.1 SN Ratio Analysis of Layer Growth Experiment 536
*11.10 Further Topics 537
11.11 Practical Summary 539
Exercises 541
References 550
12 Analysis of Experiments with Nonnormal Data 553
12.1 A Wave Soldering Experiment with Count Data 553
12.2 Generalized Linear Models 554
12.2.1 The Distribution of the Response 555
12.2.2 The Form of the Systematic Effects 557
12.2.3 GLM versus Transforming the Response 558
12.3 Likelihood-Based Analysis of Generalized Linear Models 558
12.4 Likelihood-Based Analysis of theWave Soldering Experiment 562
12.5 Bayesian Analysis of Generalized Linear Models 564
12.6 Bayesian Analysis of the Wave Soldering Experiment 565
12.7 Other Uses and Extensions of Generalized Linear Models and Regression Models for Nonnormal Data 567
*12.8 Modeling and Analysis for Ordinal Data 567
12.8.1 The Gibbs Sampler for Ordinal Data 569
*12.9 Analysis of Foam Molding Experiment 572
12.10 Scoring: A Simple Method for Analyzing Ordinal Data 575
12.11 Practical Summary 576
Exercises 577
References 587
13 Practical Optimal Design 589
13.1 Introduction 589
13.2 A Design Criterion 590
13.3 Continuous and Exact Design 590
13.4 Some Design Criteria 592
13.4.1 Nonlinear Regression Model, Generalized Linear Model, and Bayesian Criteria 593
13.5 Design Algorithms 595
13.5.1 Point Exchange Algorithm 595
13.5.2 Coordinate Exchange Algorithm 596
13.5.3 Point and Coordinate Exchange Algorithms for Bayesian Designs 596
13.5.4 Some Design Software 597
13.5.5 Some Practical Considerations 597
13.6 Examples 598
13.6.1 A Quadratic Regression Model in One Factor 598
13.6.2 Handling a Constrained Design Region 598
13.6.3 Augmenting an Existing Design 598
13.6.4 Handling an Odd-Sized Run Size 600
13.6.5 Blocking from Initially Running a Subset of a Designed Experiment 601
13.6.6 A Nonlinear Regression Model 605
13.6.7 A Generalized Linear Model 605
13.7 Practical Summary 606
Exercises 607
References 608
14 Computer Experiments 611
14.1 An Airfoil Simulation Experiment 611
14.2 Latin Hypercube Designs (LHDs) 613
14.2.1 Orthogonal Array-Based Latin Hypercube Designs 617
14.3 Latin Hypercube Designs with Maximin Distance or Maximum Projection Properties 619
14.4 Kriging: The Gaussian Process Model 622
14.5 Kriging: Prediction and Uncertainty Quantification 625
14.5.1 Known Model Parameters 626
14.5.2 Unknown Model Parameters 627
14.5.3 Analysis of Airfoil Simulation Experiment 629
14.6 Expected Improvement 631
14.6.1 Optimization of Airfoil Simulation Experiment 633
14.7 Further Topics 634
14.8 Practical Summary 636
Exercises 637
Appendix 14A: Derivation of the Kriging Equations (14.10) and (14.11) 643
Appendix 14B: Derivation of the EI Criterion (14.22) 644 References 645
Appendix A Upper Tail Probabilities of the Standard Normal Distribution integral ¯ infinity z 1/ square root 2pie¯.u2/²du 647
Appendix B Upper Percentiles of the t Distribution 649
Appendix C Upper Percentiles of the Chi-square Distribution 651
Appendix D Upper Percentiles of the F Distribution 653
Appendix E Upper Percentiles of the Studentized Range Distribution 661
Appendix F Upper Percentiles of the Studentized Maximum Modulus Distribution 669
Appendix G Coefficients of Orthogonal Contrast Vectors 683
Appendix H Critical Values for Lenth's Method 685
Author Index 689
Subject Index 693
Preface to the Second Edition xix
Preface to the First Edition xxi
Suggestions of Topics for Instructors xxv
List of Experiments and Data Sets xxvii
About the Companion Website xxxiii
1 Basic Concepts for Experimental Design and Introductory Regression Analysis 1
1.1 Introduction and Historical Perspective 1
1.2 A Systematic Approach to the Planning and Implementation of Experiments 4
1.3 Fundamental Principles: Replication, Randomization, and Blocking 8
1.4 Simple Linear Regression 11
1.5 Testing of Hypothesis and Interval Estimation 14
1.6 Multiple Linear Regression 20
1.7 Variable Selection in Regression Analysis 26
1.8 Analysis of Air Pollution Data 28
1.9 Practical Summary 34
Exercises 35
References 43
2 Experiments with a Single Factor 45
2.1 One-Way Layout 45
*2.1.1 Constraint on the Parameters 50
2.2 Multiple Comparisons 52
2.3 Quantitative Factors and Orthogonal Polynomials 56
2.4 Expected Mean Squares and Sample Size Determination 61
2.5 One-Way Random Effects Model 68
2.6 Residual Analysis: Assessment of Model Assumptions 71
2.7 Practical Summary 76
Exercises 77
References 82
3 Experiments with More than One Factor 85
3.1 Paired Comparison Designs 85
3.2 Randomized Block Designs 88
3.3 Two-Way Layout: Factors with Fixed Levels 92
3.3.1 Two Qualitative Factors: A Regression Modeling Approach 95
*3.4 Two-Way Layout: Factors with Random Levels 98
3.5 Multi-Way Layouts 105
3.6 Latin Square Designs: Two Blocking Variables 108
3.7 Graeco-Latin Square Designs 112
*3.8 Balanced Incomplete Block Designs 113
*3.9 Split-Plot Designs 118
3.10 Analysis of Covariance: Incorporating Auxiliary Information 126
*3.11 Transformation of the Response 130
3.12 Practical Summary 134
Exercises 135
Appendix 3A: Table of Latin Squares, Graeco-Latin Squares, and Hyper-Graeco-Latin Squares 147
References 148
4 Full Factorial Experiments at Two Levels 151
4.1 An Epitaxial Layer Growth Experiment 151
4.2 Full Factorial Designs at Two Levels: A General Discussion 153
4.3 Factorial Effects and Plots 157
4.3.1 Main Effects 158
4.3.2 Interaction Effects 159
4.4 Using Regression to Compute Factorial Effects 165
*4.5 ANOVA Treatment of Factorial Effects 167
4.6 Fundamental Principles for Factorial Effects: Effect Hierarchy, Effect Sparsity, and Effect Heredity 168
4.7 Comparisons with the "One-Factor-at-a-Time" Approach 169
4.8 Normal and Half-Normal Plots for Judging Effect Significance 172
4.9 Lenth's Method: Testing Effect Significance for Experiments Without Variance Estimates 174
4.10 Nominal-the-Best Problem and Quadratic Loss Function 178
4.11 Use of Log Sample Variance for Dispersion Analysis 179
4.12 Analysis of Location and Dispersion: Revisiting the Epitaxial Layer Growth Experiment 181
*4.13 Test of Variance Homogeneity and Pooled Estimate of Variance 184
*4.14 Studentized Maximum Modulus Test: Testing Effect Significance for Experiments With Variance Estimates 185
4.15 Blocking and Optimal Arrangement of 2¯k Factorial Designs in 2¯q Blocks 188
4.16 Practical Summary 193
Exercises 195
Appendix 4A: Table of 2¯k Factorial Designs in 2¯q Blocks 201
References 203
5 Fractional Factorial Experiments at Two Levels 205
5.1 A Leaf Spring Experiment 205
5.2 Fractional Factorial Designs: Effect Aliasing and the Criteria of Resolution and Minimum Aberration 206
5.3 Analysis of Fractional Factorial Experiments 212
5.4 Techniques for Resolving the Ambiguities in Aliased Effects 217
5.4.1 Fold-Over Technique for Follow-Up Experiments 218
5.4.2 Optimal Design Approach for Follow-Up Experiments 222
5.5 Conditional Main Effect (CME) Analysis: A Method to Unravel Aliased Interactions 227
5.6 Selection of 2¯k¯.p Designs Using Minimum Aberration and Related Criteria 232
5.7 Blocking in Fractional Factorial Designs 236
5.8 Practical Summary 238
Exercises 240
Appendix 5A: Tables of 2¯k¯.p Fractional Factorial Designs 252
Appendix 5B: Tables of 2¯k¯.p Fractional Factorial Designs in 2q Blocks 258
References 262
6 Full Factorial and Fractional Factorial Experiments at Three Levels 265
6.1 A Seat-Belt Experiment 265
6.2 Larger-the-Better and Smaller-the-Better Problems 267
6.3 3¯k Full Factorial Designs 268
6.4 3¯k¯.pFractional Factorial Designs 273
6.5 Simple Analysis Methods: Plots and Analysis of Variance 277
6.6 An Alternative Analysis Method 282
6.7 Analysis Strategies for Multiple Responses I: Out-Of-Spec Probabilities 291
6.8 Blocking in 3¯k and 3¯k¯.p Designs 299
6.9 Practical Summary 301
Exercises 303
Appendix 6A: Tables of 3¯k¯.p Fractional Factorial Designs 309
Appendix 6B: Tables of 3¯k¯.p Fractional Factorial Designs in 3¯q Blocks 310
References 314
7 Other Design and Analysis Techniques for Experiments at More than Two Levels 315
7.1 A Router Bit Experiment Based on a Mixed Two-Level and Four-Level Design 315
7.2 Method of Replacement and Construction of 2¯m4¯n Designs 318
7.3 Minimum Aberration 2¯m4¯n Designs with n = 1, 2, 321
7.4 An Analysis Strategy for 2¯m4¯n Experiments 324
7.5 Analysis of the Router Bit Experiment 326
7.6 A Paint Experiment Based on a Mixed Two-Level and Three-Level Design 329
7.7 Design and Analysis of 36-Run Experiments at Two And Three Levels 332
7.8 r¯k¯.pFractional Factorial Designs for any Prime Number r 337
7.8.1 25-Run Fractional Factorial Designs at Five Levels 337
7.8.2 49-Run Fractional Factorial Designs at Seven Levels 340
7.8.3 General Construction 340
7.9 Definitive Screening Designs 341
*7.10 Related Factors: Method of Sliding Levels, Nested Effects Analysis, and Response Surface Modeling 343
7.10.1 Nested Effects Modeling 346
7.10.2 Analysis of Light Bulb Experiment 347
7.10.3 Response Surface Modeling 349
7.10.4 Symmetric and Asymmetric Relationships Between Related Factors 352
7.11 Practical Summary 352
Exercises 353
Appendix 7A: Tables of 2¯m4¹ Minimum Aberration Designs 361
Appendix 7B: Tables of 2¯m4² Minimum Aberration Designs 362
Appendix 7C: OA(25, 5¯6) 364
Appendix 7D: OA(49, 7¯8) 364
Appendix 7E: Conference Matrices C6 C8 C10 C12 C14 and C16 366
References 368
8 Nonregular Designs: Construction and Properties 369
8.1 Two Experiments: Weld-Repaired Castings and Blood Glucose Testing 369
8.2 Some Advantages of Nonregular Designs Over the 2¯k¯.p AND 3¯k¯.p Series of Designs 370
8.3 A Lemma on Orthogonal Arrays 372
8.4 Plackett-Burman Designs and Hall's Designs 373
8.5 A Collection of Useful Mixed-Level Orthogonal Arrays 377
*8.6 Construction of Mixed-Level Orthogonal Arrays Based on Difference Matrices 379
8.6.1 General Method for Constructing Asymmetrical Orthogonal Arrays 380
*8.7 Construction of Mixed-Level Orthogonal Arrays Through the Method of Replacement 382
8.8 Orthogonal Main-Effect Plans Through Collapsing Factors 384
8.9 Practical Summary 388
Exercises 389
Appendix 8A: Plackett-Burman Designs OA(N, 2¯N¯.1) with 12 <= N <= 48 and N = 4 k but not a Power of 2 394
Appendix 8B: Hall'S 16-Run Orthogonal Arrays of Types II to V 397
Appendix 8C: Some Useful Mixed-Level Orthogonal Arrays 399
Appendix 8D: Some Useful Difference Matrices 411
Appendix 8E: Some Useful Orthogonal Main-Effect Plans 413
References 414
9 Experiments with Complex Aliasing 417
9.1 Partial Aliasing of Effects and the Alias Matrix 417
9.2 Traditional Analysis Strategy: Screening Design and Main Effect Analysis 420
9.3 Simplification of Complex Aliasing via Effect Sparsity 421
9.4 An Analysis Strategy for Designs with Complex Aliasing 422
9.4.1 Some Limitations 428
*9.5 A Bayesian Variable Selection Strategy for Designs with Complex Aliasing 429
9.5.1 Bayesian Model Priors 431
9.5.2 Gibbs Sampling 432
9.5.3 Choice of Prior Tuning Constants 434
9.5.4 Blood Glucose Experiment Revisited 435
9.5.5 Other Applications 437
*9.6 Supersaturated Designs: Design Construction and Analysis 437
9.7 Practical Summary 441
Exercises 442
Appendix 9A: Further Details for the Full Conditional Distributions 451
References 453
10 Response Surface Methodology 455
10.1 A Ranitidine Separation Experiment 455
10.2 Sequential Nature of Response Surface Methodology 457
10.3 From First-Order Experiments to Second-Order Experiments: Steepest Ascent Search and Rectangular Grid Search 460
10.3.1 Curvature Check 460
10.3.2 Steepest Ascent Search 461
10.3.3 Rectangular Grid Search 466
10.4 Analysis of Second-Order Response Surfaces 469
10.4.1 Ridge Systems 470
10.5 Analysis of the Ranitidine Experiment 472
10.6 Analysis Strategies for Multiple Responses II: Contour Plots and the Use of Desirability Functions 475
10.7 Central Composite Designs 478
10.8 Box-Behnken Designs and Uniform Shell Designs 483
10.9 Practical Summary 486
Exercises 488
Appendix 10A: Table of Central Composite Designs 498
Appendix 10B: Table of Box-Behnken Designs 500
Appendix 10C: Table of Uniform Shell Designs 501
References 502
11 Introduction to Robust Parameter Design 503
11.1 A Robust Parameter Design Perspective of the Layer Growth and Leaf Spring Experiments 503
11.1.1 Layer Growth Experiment Revisited 503
11.1.2 Leaf Spring Experiment Revisited 504
11.2 Strategies for Reducing Variation 506
11.3 Noise (Hard-to-Control) Factors 508
11.4 Variation Reduction Through Robust Parameter Design 510
11.5 Experimentation and Modeling Strategies I: Cross Array 512
11.5.1 Location and Dispersion Modeling 513
11.5.2 Response Modeling 518
11.6 Experimentation and Modeling Strategies II: Single Array and Response Modeling 523
11.7 Cross Arrays: Estimation Capacity and Optimal Selection 526
11.8 Choosing Between Cross Arrays and Single Arrays 529
*11.8.1 Compound Noise Factor 533
11.9 Signal-to-Noise Ratio and Its Limitations for Parameter Design Optimization 534
11.9.1 SN Ratio Analysis of Layer Growth Experiment 536
*11.10 Further Topics 537
11.11 Practical Summary 539
Exercises 541
References 550
12 Analysis of Experiments with Nonnormal Data 553
12.1 A Wave Soldering Experiment with Count Data 553
12.2 Generalized Linear Models 554
12.2.1 The Distribution of the Response 555
12.2.2 The Form of the Systematic Effects 557
12.2.3 GLM versus Transforming the Response 558
12.3 Likelihood-Based Analysis of Generalized Linear Models 558
12.4 Likelihood-Based Analysis of theWave Soldering Experiment 562
12.5 Bayesian Analysis of Generalized Linear Models 564
12.6 Bayesian Analysis of the Wave Soldering Experiment 565
12.7 Other Uses and Extensions of Generalized Linear Models and Regression Models for Nonnormal Data 567
*12.8 Modeling and Analysis for Ordinal Data 567
12.8.1 The Gibbs Sampler for Ordinal Data 569
*12.9 Analysis of Foam Molding Experiment 572
12.10 Scoring: A Simple Method for Analyzing Ordinal Data 575
12.11 Practical Summary 576
Exercises 577
References 587
13 Practical Optimal Design 589
13.1 Introduction 589
13.2 A Design Criterion 590
13.3 Continuous and Exact Design 590
13.4 Some Design Criteria 592
13.4.1 Nonlinear Regression Model, Generalized Linear Model, and Bayesian Criteria 593
13.5 Design Algorithms 595
13.5.1 Point Exchange Algorithm 595
13.5.2 Coordinate Exchange Algorithm 596
13.5.3 Point and Coordinate Exchange Algorithms for Bayesian Designs 596
13.5.4 Some Design Software 597
13.5.5 Some Practical Considerations 597
13.6 Examples 598
13.6.1 A Quadratic Regression Model in One Factor 598
13.6.2 Handling a Constrained Design Region 598
13.6.3 Augmenting an Existing Design 598
13.6.4 Handling an Odd-Sized Run Size 600
13.6.5 Blocking from Initially Running a Subset of a Designed Experiment 601
13.6.6 A Nonlinear Regression Model 605
13.6.7 A Generalized Linear Model 605
13.7 Practical Summary 606
Exercises 607
References 608
14 Computer Experiments 611
14.1 An Airfoil Simulation Experiment 611
14.2 Latin Hypercube Designs (LHDs) 613
14.2.1 Orthogonal Array-Based Latin Hypercube Designs 617
14.3 Latin Hypercube Designs with Maximin Distance or Maximum Projection Properties 619
14.4 Kriging: The Gaussian Process Model 622
14.5 Kriging: Prediction and Uncertainty Quantification 625
14.5.1 Known Model Parameters 626
14.5.2 Unknown Model Parameters 627
14.5.3 Analysis of Airfoil Simulation Experiment 629
14.6 Expected Improvement 631
14.6.1 Optimization of Airfoil Simulation Experiment 633
14.7 Further Topics 634
14.8 Practical Summary 636
Exercises 637
Appendix 14A: Derivation of the Kriging Equations (14.10) and (14.11) 643
Appendix 14B: Derivation of the EI Criterion (14.22) 644 References 645
Appendix A Upper Tail Probabilities of the Standard Normal Distribution integral ¯ infinity z 1/ square root 2pie¯.u2/²du 647
Appendix B Upper Percentiles of the t Distribution 649
Appendix C Upper Percentiles of the Chi-square Distribution 651
Appendix D Upper Percentiles of the F Distribution 653
Appendix E Upper Percentiles of the Studentized Range Distribution 661
Appendix F Upper Percentiles of the Studentized Maximum Modulus Distribution 669
Appendix G Coefficients of Orthogonal Contrast Vectors 683
Appendix H Critical Values for Lenth's Method 685
Author Index 689
Subject Index 693
C. F. JEFF WU, PHD, is Coca-Cola Professor in Engineering Statistics at the Georgia Institute of Technology. Dr. Wu has published more than 180 papers and is the recipient of numerous accolades, including the National Academy of Engineering membership and the COPSS Presidents' Award.
MICHAEL S. HAMADA, PHD, is Senior Scientist at Los Alamos National Laboratory (LANL) in New Mexico. Dr. Hamada is a Fellow of the American Statistical Association, a LANL Fellow, and has published more than 160 papers.
MICHAEL S. HAMADA, PHD, is Senior Scientist at Los Alamos National Laboratory (LANL) in New Mexico. Dr. Hamada is a Fellow of the American Statistical Association, a LANL Fellow, and has published more than 160 papers.
