1 Introduction 1

1.1 Strategy of Experimentation 1

1.2 Some Typical Applications of Experimental Design 8

1.3 Basic Principles 11

1.4 Guidelines for Designing Experiments 14

1.5 A Brief History of Statistical Design 21

1.6 Summary: Using Statistical Techniques in Experimentation 22

1.7 Problems 23

2 Simple Comparative Experiments 25

2.1 Introduction 25

2.2 Basic Statistical Concepts 27

2.3 Sampling and Sampling Distributions 30

2.4 Inferences About the Differences in Means, Randomized Designs 36

2.5 Inferences About the Differences in Means, Paired Comparison Designs 53

2.6 Inferences About the Variances of Normal Distributions 57

2.7 Problems 59

3 Experiments with a Single Factor: The Analysis of Variance 65

3.1 An Example 66

3.2 The Analysis of Variance 68

3.3 Analysis of the Fixed Effects Model 70

3.4 Model Adequacy Checking 80

3.5 Practical Interpretation of Results 89

3.6 Sample Computer Output 102

3.7 Determining Sample Size 105

3.8 Other Examples of Single-Factor Experiments 110

3.9 The Random Effects Model 116

3.10 The Regression Approach to the Analysis of Variance 125

3.11 Nonparametric Methods in the Analysis of Variance 128

3.12 Problems 130

4 Randomized Blocks, Latin Squares, and Related Designs 139

4.1 The Randomized Complete Block Design 139

4.2 The Latin Square Design 158

4.3 The Graeco-Latin Square Design 165

4.4 Balanced Incomplete Block Designs 168

4.5 Problems 177

5 Introduction to Factorial Designs 183

5.1 Basic Definitions and Principles 183

5.2 The Advantage of Factorials 186

5.3 The Two-Factor Factorial Design 187

5.4 The General Factorial Design 206

5.5 Fitting Response Curves and Surfaces 211

5.6 Blocking in a Factorial Design 219

5.7 Problems 225

6 The 2k Factorial Design 233

6.1 Introduction 233

6.2 The 22 Design 234

6.3 The 23 Design 241

6.4 The General 2k Design 253

6.5 A Single Replicate of the 2k Design 255

6.6 Additional Examples of Unreplicated 2k Design 269

6.7 2k Designs are Optimal Designs 280

6.8 The Addition of Center Points to the 2k Design 285

6.9 Why We Work with Coded Design Variables 290

6.10 Problems 292

7 Blocking and Confounding in the 2k Factorial Design 304

7.1 Introduction 304

7.2 Blocking a Replicated 2k Factorial Design 305

7.3 Confounding in the 2k Factorial Design 306

7.4 Confounding the 2k Factorial Design in Two Blocks 306

7.5 Another Illustration of Why Blocking Is Important 312

7.6 Confounding the 2k Factorial Design in Four Blocks 313

7.7 Confounding the 2k Factorial Design in 2p Blocks 315

7.8 Partial Confounding 316

7.9 Problems 319

8 Two-Level Fractional Factorial Designs 320

8.1 Introduction 320

8.2 The One-Half Fraction of the 2k Design 321

8.3 The One-Quarter Fraction of the 2k Design 333

8.4 The General 2k_p Fractional Factorial Design 340

8.5 Alias Structures in Fractional Factorials and other Designs 349

8.6 Resolution III Designs 351

8.7 Resolution IV and V Designs 366

8.8 Supersaturated Designs 374

8.9 Summary 375

8.10 Problems 376

9 Additional Design and Analysis Topics for Factorial and Fractional Factorial Designs 394

9.1 The 3k Factorial Design 395

9.2 Confounding in the 3k Factorial Design 402

9.3 Fractional Replication of the 3k Factorial Design 408

9.4 Factorials with Mixed Levels 412

9.5 Nonregular Fractional Factorial Designs 415

9.6 Constructing Factorial and Fractional Factorial Designs Using an Optimal Design Tool 431

9.7 Problems 444

10 Fitting Regression Models 449

10.1 Introduction 449

10.2 Linear Regression Models 450

10.3 Estimation of the Parameters in Linear Regression Models 451

10.4 Hypothesis Testing in Multiple Regression 462

10.5 Confidence Intervals in Multiple Regression 467

10.6 Prediction of New Response Observations 468

10.7 Regression Model Diagnostics 470

10.8 Testing for Lack of Fit 473

10.9 Problems 475

11 Response Surface Methods and Designs 478

11.1 Introduction to Response Surface Methodology 478

11.2 The Method of Steepest Ascent 480

11.3 Analysis of a Second-Order Response Surface 486

11.4 Experimental Designs for Fitting Response Surfaces 500

11.5 Experiments with Computer Models 523

11.6 Mixture Experiments 530

11.7 Evolutionary Operation 540

11.8 Problems 544

12 Robust Parameter Design and Process Robustness Studies 554

12.1 Introduction 554

12.2 Crossed Array Designs 556

12.3 Analysis of the Crossed Array Design 558

12.4 Combined Array Designs and the Response Model Approach 561

12.5 Choice of Designs 567

12.6 Problems 570

13 Experiments with Random Factors 573

13.1 Random Effects Models 573

13.2 The Two-Factor Factorial with Random Factors 574

13.3 The Two-Factor Mixed Model 581

13.4 Sample Size Determination with Random Effects 587

13.5 Rules for Expected Mean Squares 588

13.6 Approximate F Tests 592

13.7 Some Additional Topics on Estimation of Variance Components 596

13.8 Problems 601

14 Nested and Split-Plot Designs 604

14.1 The Two-Stage Nested Design 604

14.2 The General m-Stage Nested Design 614

14.3 Designs with Both Nested and Factorial Factors 616

14.4 The Split-Plot Design 621

14.5 Other Variations of the Split-Plot Design 627

14.6 Problems 637

15 Other Design and Analysis Topics 642

15.1 Nonnormal Responses and Transformations 643

15.2 Unbalanced Data in a Factorial Design 652

15.3 The Analysis of Covariance 655

15.4 Repeated Measures 675

15.5 Problems 677

Appendix 681

Table I. Cumulative Standard Normal Distribution 682

Table II. Percentage Points of the t Distribution 684

Table III. Percentage Points of the _2 Distribution 685

Table IV. Percentage Points of the F Distribution 686

Table V. Operating Characteristic Curves for the Fixed Effects Model Analysis of Variance 691

Table VI. Operating Characteristic Curves for the Random Effects Model Analysis of Variance 695

Table VII. Percentage Points of the Studentized Range Statistic 699

Table VIII. Critical Values for Dunnett's Test for Comparing Treatments with a Control 701

Table IX. Coefficients of Orthogonal Polynomials 703

Table X. Alias Relationships for 2k_p Fractional Factorial Designs with k 15 and n 64 704

Bibliography 717

Index 723

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