# Experiments

## Planning, Analysis, and Optimization

Wiley Series in Probability and Statistics

3. Auflage Mai 2021

736 Seiten, Hardcover*Handbuch/Nachschlagewerk*

**978-1-119-47010-6**

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 Second Edition xvii

Preface to the First Edition xix

Suggestions of Topics for Instructors xxiii

List of Experiments and Data Sets xxv

1 Basic Concepts for Experimental Design and IntroductoryRegression Analysis

1.1 Introduction and Historical Perspective, 1

1.2 A Systematic Approach to the Planning and Implementationof 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, 29

1.9 Practical Summary, 34

Exercises, 36

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, 53

2.3 Quantitative Factors and Orthogonal Polynomials, 57

2.4 Expected Mean Squares and Sample Size Determination, 63

2.5 One-Way Random Effects Model, 70

2.6 Residual Analysis: Assessment of Model Assumptions, 74

2.7 Practical Summary, 79

Exercises, 80

References, 86

3 Experiments with More Than One Factor 87

3.1 Paired Comparison Designs, 87

3.2 Randomized Block Designs, 90

3.3 Two-Way Layout: Factors with Fixed Levels, 94

3.3.1 Two Qualitative Factors: A Regression ModelingApproach, 97

*3.4 Two-Way Layout: Factors with Random Levels, 99

3.5 Multi-Way Layouts, 108

3.6 Latin Square Designs: Two Blocking Variables, 110

3.7 Graeco-Latin Square Designs, 114

*3.8 Balanced Incomplete Block Designs, 115

*3.9 Split-Plot Designs, 120

3.10 Analysis of Covariance: Incorporating AuxiliaryInformation, 128

*3.11 Transformation of the Response, 133

3.12 Practical Summary, 137

Exercises, 138

Appendix 3A: Table of Latin Squares, Graeco-Latin Squares, andHyper-Graeco-Latin Squares, 150

References, 152

4 Full Factorial Experiments at Two Levels155

4.1 An Epitaxial Layer Growth Experiment, 155

4.2 Full Factorial Designs at Two Levels: A General Discussion, 157

4.3 Factorial Effects and Plots, 161

4.3.1 Main Effects, 162

4.3.2 Interaction Effects, 164

4.4 Using Regression to Compute Factorial Effects, 169

*4.5 ANOVA Treatment of Factorial Effects, 171

4.6 Fundamental Principles for Factorial Effects: Effect Hierarchy,Effect Sparsity, and Effect Heredity, 172

4.7 Comparisons with the "One-Factor-at-a-Time" Approach, 173

4.8 Normal and Half-Normal Plots for Judging EffectSignificance, 177

4.9 Lenth's Method: Testing Effect Significance for Experimentswithout Variance Estimates, 180

4.10 Nominal-the-Best Problem and Quadratic LossFunction, 183

4.11 Use of Log Sample Variance for Dispersion Analysis, 184

4.12 Analysis of Location and Dispersion: Revisiting the EpitaxialLayer Growth Experiment, 185

*4.13 Test of Variance Homogeneity and Pooled Estimate ofVariance, 188* 4.14 Studentized Maximum Modulus Test: Testing Effect Significancefor Experiments with Variance Estimates, 190

4.1 5Blocking and Optimal Arrangement of 2kFactorial Designs in 2qBlocks, 193

4.16 Practical Summary, 198

Exercises, 200

Appendix 4A: Table of 2kFactorial Designs in 2qBlocks, 207

References, 208

5 Fractional Factorial Experiments at Two Levels 211

5.1 A Leaf Spring Experiment, 211

5.2 Fractional Factorial Designs: Effect Aliasing and the Criteria ofResolution and Minimum Aberration, 213

5.3 Analysis of Fractional Factorial Experiments, 219

5.4 Techniques for Resolving the Ambiguities in Aliased Effects, 225

5.4.1 Fold-Over Technique for Follow-Up Experiments, 225

5.4.2 Optimal Design Approach for Follow-UpExperiments, 229

5.5 CME

5.6 Selection of 2k.pDesigns Using Minimum Aberration and RelatedCriteria, 234

5.7Blocking in Fractional Factorial Designs, 238

5.8Practical Summary, 240

Exercises, 242

Appendix 5A: Tables of 2k.pFractional Factorial Designs, 252

Appendix 5B: Tables of 2k.pFractional Factorial Designs in 2qBlocks, 260

References, 264

6 Full Factorial and Fractional Factorial Experiments at ThreeLevels267

6.1A Seat-Belt Experiment, 267

6.2 Larger-the-Better and Smaller-the-Better Problems, 268

6.3 3kFull Factorial Designs, 270

6.4 3k.pFractional Factorial Designs, 275

6.5 Simple Analysis Methods: Plots and Analysis of Variance, 279

6.6 An Alternative Analysis Method, 287

6.7Analysis Strategies for Multiple Responses I: Out-of-SpecProbabilities, 293

6.8 Blocking in 3kand 3k.pDesigns, 302

6.9 Practical Summary, 303

Exercises, 305

Appendix 6A: Tables of 3k.pFractional Factorial Designs, 312

Appendix 6B: Tables of 3k.pFractional Factorial Designs in 3qBlocks, 313

References, 317

7 Other Design and Analysis Techniques for Experiments atMore Than Two Levels319

7.1A Router Bit Experiment Based on a Mixed Two-Level andFour-Level Design, 319

7.2Method of Replacement and Construction of 2m4nDesigns, 322

7.3Minimum Aberration 2m4nDesigns withn=1,2, 325

7.4An Analysis Strategy for 2m4nExperiments, 328

7.5Analysis of the Router Bit Experiment, 330

7.6A Paint Experiment Based on a Mixed Two-Level and Three-LevelDesign, 334

7.7Design and Analysis of 36-Run Experiments at Two and ThreeLevels, 334

7.8rk.pFractional Factorial Designs for any Prime Numberr, 341

7.8.125-Run Fractional Factorial Designs at Five Levels, 342

7.8.249-Run Fractional Factorial Designs at Seven Levels, 345

7.8.3General Construction, 345

7.9 DSD

*7.10Related Factors: Method of Sliding Levels, Nested EffectsAnalysis, and Response Surface Modeling, 346

7.10.1Nested Effects Modeling, 348

7.10.2Analysis of Light Bulb Experiment, 350

7.10.3Response Surface Modeling, 353

7.10.4Symmetric and Asymmetric Relationships BetweenRelated Factors, 355

7.11Practical Summary, 356

Exercises, 357

Appendix 7A: Tables of 2m41Minimum Aberration Designs, 364

Appendix 7B: Tables of 2m42Minimum Aberration Designs, 366

Appendix 7C: OA(25, 56), 368

Appendix 7D: OA(49, 78), 368

Appendix 7E: Conference Matrices

References, 370

8Nonregular Designs: Construction and Properties371

8.1Two Experiments: Weld-Repaired Castings and Blood GlucoseTesting, 371

8.2Some Advantages of Nonregular Designs Over the 2k.pand 3k.pSeries of Designs, 373

8.3A Lemma on Orthogonal Arrays, 374

8.4Plackett - Burman Designs and Hall's Designs, 375

8.5A Collection of Useful Mixed-Level Orthogonal Arrays, 379

*8.6Construction of Mixed-Level Orthogonal Arrays Based onDifference Matrices, 381

8.6.1General Method for Constructing AsymmetricalOrthogonal Arrays, 382* 8.7Construction of Mixed-Level Orthogonal Arrays Through theMethod of Replacement, 384

8.8Orthogonal Main-Effect Plans Through Collapsing Factors, 386

8.9Practical Summary, 390

Exercises, 391

Appendix 8A: Plackett - Burman Designs OA(N,2N.1)with 12<=N<=48andN=4kBut Not a Power of 2, 397

Appendix 8B: Hall's 16-Run Orthogonal Arrays of Types II to V, 401

Appendix 8C: Some Useful Mixed-Level Orthogonal Arrays, 405

Appendix 8D: Some Useful Difference Matrices, 416

Appendix 8E: Some Useful Orthogonal Main-Effect Plans, 418

References, 419

9Experiments with Complex Aliasing421

9.1Partial Aliasing of Effects and the Alias Matrix, 421

9.2Traditional Analysis Strategy:Screening Design and Main EffectAnalysis, 424

9.3Simplification of Complex Aliasing via Effect Sparsity, 424

9.4An Analysis Strategy for Designs with Complex Aliasing, 426

9.4.1Some Limitations, 432

*9.5A Bayesian Variable Selection Strategy for Designswith Complex Aliasing, 433

9.5.1Bayesian Model Priors, 435

9.5.2Gibbs Sampling, 437

9.5.3Choice of Prior Tuning Constants, 438

9.5.4Blood Glucose Experiment Revisited, 439

9.5.5Other Applications, 441

*9.6Supersaturated Designs: Design Constructionand Analysis, 442

9.7Practical Summary, 445

Exercises, 446

Appendix 9A: Further Details for the Full Conditional Distributions, 454

References, 456

10 Response Surface Methodology459

10.1A Ranitidine Separation Experiment, 459

10.2Sequential Nature of Response SurfaceMethodology, 461

10.3From First-Order Experiments to Second-Order Experiments:Steepest Ascent Search and Rectangular Grid Search, 464

10.3.1Curvature Check, 465

10.3.2Steepest Ascent Search, 466

10.3.3Rectangular Grid Search, 470

10.4Analysis of Second-Order Response Surfaces, 473

10.4.1Ridge Systems, 475

10.5Analysis of the Ranitidine Experiment, 477

10.6Analysis Strategies for Multiple Responses II: Contour Plotsand the Use of Desirability Functions, 481

10.7Central Composite Designs, 484

10.8Box - Behnken Designs and Uniform Shell Designs, 489

10.9Practical Summary, 492

Exercises, 494

Appendix 10A: Table of Central Composite Designs, 505

Appendix 10B: Table of Box - Behnken Designs, 507

Appendix 10C: Table of Uniform Shell Designs, 508

References, 509

11 Introduction to Robust Parameter Design511

11.1 A Robust Parameter Design Perspective of the Layer Growthand Leaf Spring Experiments, 511

11.1.1 Layer Growth Experiment Revisited, 511

11.1.2 Leaf Spring Experiment Revisited, 512

11.2 Strategies for Reducing Variation, 514

11.3 Noise (Hard-to-Control) Factors, 516

11.4 Variation Reduction Through Robust Parameter Design, 518

11.5 Experimentation and Modeling Strategies I:Cross Array, 520

11.5.1 Location and Dispersion Modeling, 52

111.5.2 Response Modeling, 526

11.6 Experimentation and Modeling Strategies II: Single Array andResponse Modeling, 532

11.7 Cross Arrays: Estimation Capacity and Optimal Selection, 535

11.8 Choosing Between Cross Arrays and Single Arrays, 538

*11.8.1 Compound Noise Factor, 542

11.9 Signal-to-Noise Ratio and Its Limitations for Parameter DesignOptimization, 543

11.9.1 SN Ratio Analysis of Layer Growth Experiment, 546* 11.10 Further Topics, 547

11.11 Practical Summary, 548

Exercises, 550

References, 560

12 Analysis of Experiments with Nonnormal Data625

12.1 A Wave Soldering Experiment with Count Data, 625

12.2 Generalized Linear Models, 627

12.2.1 The Distribution of the Response, 627

12.2.2 The Form of the Systematic Effects, 629

12.2.3 GLM versus Transforming the Response, 630

12.3 Likelihood-Based Analysis of Generalized Linear Models, 631 [New equations for Section 12.3 in Word file 'Add to Section 12.3]

12.4 Likelihood-Based Analysis of the Wave SolderingExperiment, 634

12.5 Bayesian Analysis of Generalized Linear Models, 635

12.6 Bayesian Analysis of the Wave Soldering Experiment, 637

12.7 Other Uses and Extensions of Generalized Linear Models andRegression Models for Nonnormal Data, 639

*12.8 Modeling and Analysis for Ordinal Data, 639

12.8.1The Gibbs Sampler for Ordinal Data, 642

*12.9 Analysis of Foam Molding Experiment, 644

12.10 Scoring: A Simple Method for Analyzing Ordinal Data, 647

12.11 Practical Summary, 649

Exercises, 649

References, 661

13. [Insert 'New Chapter_POD']

14. [Insert 'New Chapter 14_CE']

Appendix A Upper Tail Probabilities of the Standard NormalDistribution, integral infinity z1 square root 2pie.u2/2du663

Appendix B Upper Percentiles of thetDistribution665

Appendix C Upper Percentiles of thechi2Distribution667

Appendix D Upper Percentiles of theFDistribution669

Appendix E Upper Percentiles of the Studentized RangeDistribution677

Appendix F Upper Percentiles of the Studentized MaximumModulus Distribution685

Appendix G Coefficients of Orthogonal Contrast Vectors699

Appendix H Critical Values for Lenth's Method701

Author Index705

Subject Index 709

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.