Preface iii

1 Introduction 1

1.1 Strategy of Experimentation 1

1.2 Some Typical Applications of Experimental Design 7

1.3 Basic Principles 11

1.4 Guidelines for Designing Experiments 13

1.5 A Brief History of Statistical Design 19

1.6 Summary: Using Statistical Techniques in Experimentation 20

2 Simple Comparative Experiments 22

2.1 Introduction 22

2.2 Basic Statistical Concepts 23

2.3 Sampling and Sampling Distributions 27

2.4 Inferences About the Differences in Means, Randomized Designs 32

2.5 Inferences About the Differences in Means, Paired Comparison Designs 47

2.6 Inferences About the Variances of Normal Distributions 52

3 Experiments with a Single Factor: The Analysis of Variance 55

3.1 An Example 55

3.2 The Analysis of Variance 58

3.3 Analysis of the Fixed Effects Model 59

3.4 Model Adequacy Checking 68

3.5 Practical Interpretation of Results 76

3.6 Sample Computer Output 89

3.7 Determining Sample Size 93

3.8 Other Examples of Single-Factor Experiments 95

3.9 The Random Effects Model 101

3.10 The Regression Approach to the Analysis of Variance 109

3.11 Nonparametric Methods in the Analysis of Variance 113

4 Randomized Blocks, Latin Squares, and Related Designs 115

4.1 The Randomized Complete Block Design 115

4.2 The Latin Square Design 133

4.3 The Graeco-Latin Square Design 140

4.4 Balanced Incomplete Block Designs 142

5 Introduction to Factorial Designs 152

5.1 Basic Definitions and Principles 152

5.2 The Advantage of Factorials 155

5.3 The Two-Factor Factorial Design 156

5.4 The General Factorial Design 174

5.5 Fitting Response Curves and Surfaces 179

5.6 Blocking in a Factorial Design 188

6 The 2k Factorial Design 194

6.1 Introduction 194

6.2 The 22 Design 195

6.3 The 23 Design 203

6.4 The General 2k Design 215

6.5 A Single Replicate of the 2k Design 218

6.6 Additional Examples of Unreplicated 2k Designs 231

6.7 2k Designs are Optimal Designs 243

6.8 The Addition of Center Points to the 2k Design 248

6.9 Why We Work with Coded Design Variables 253

7 Blocking and Confounding in the 2k Factorial Design 256

7.1 Introduction 256

7.2 Blocking a Replicated 2k Factorial Design 256

7.3 Confounding in the 2k Factorial Design 259

7.4 Confounding the 2k Factorial Design in Two Blocks 259

7.5 Another Illustration of Why Blocking is Important 267

7.6 Confounding the 2k Factorial Design in Four Blocks 268

7.7 Confounding the 2k Factorial Design in 2p Blocks 270

7.8 Partial Confounding 271

8 Two-Level Fractional Factorial Designs 274

8.1 Introduction 274

8.2 The One-Half Fraction of the 2k Design 275

8.3 The One-Quarter Fraction of the 2k Design 290

8.4 The General 2k--pFractional Factorial Design 297

8.5 Alias Structures in Fractional Factorials and Other Designs 306

8.6 Resolution III Designs 308

8.7 Resolution IV and V Designs 322

8.8 Supersaturated Designs 329

8.9 Summary 331

9 Additional Design and Analysis Topics for Factorial and Fractional Factorial Designs 332

9.1 The 3k Factorial Design 333

9.2 Confounding in the 3k Factorial Design 340

9.3 Fractional Replication of the 3k Factorial Design 345

9.4 Factorials with Mixed Levels 349

9.5 Nonregular Fractional Factorial Designs 352

9.6 Constructing Factorial and Fractional Factorial Designs Using an Optimal Design Tool 369

10 Fitting Regression Models 382

10.1 Introduction 382

10.2 Linear Regression Models 383

10.3 Estimation of the Parameters in Linear Regression Models 384

10.4 Hypothesis Testing in Multiple Regression 395

10.5 Confidence Intervals in Multiple Regression 399

10.6 Prediction of New Response Observations 401

10.7 Regression Model Diagnostics 402

10.8 Testing for Lack of Fit 405

11 Response Surface Methods and Designs 408

11.1 Introduction to Response Surface Methodology 408

11.2 The Method of Steepest Ascent 411

11.3 Analysis of a Second-Order Response Surface 416

11.4 Experimental Designs for Fitting Response Surfaces 430

11.5 Experiments with Computer Models 454

11.6 Mixture Experiments 461

11.7 Evolutionary Operation 472

12 Robust Parameter Design and Process Robustness Studies 477

12.1 Introduction 477

12.2 Crossed Array Designs 479

12.3 Analysis of the Crossed Array Design 481

12.4 Combined Array Designs and the Response Model Approach 484

12.5 Choice of Designs 490

13 Experiments with Random Factors 493

13.1 Random Effects Models 493

13.2 The Two-Factor Factorial with Random Factors 494

13.3 The Two-Factor Mixed Model 500

13.4 Rules for Expected Mean Squares 505

13.5 Approximate F-Tests 508

13.6 Some Additional Topics on Estimation of Variance Components 512

14 Nested and Split-Plot Designs 518

14.1 The Two-Stage Nested Design 518

14.2 The General m-Stage Nested Design 528

14.3 Designs with Both Nested and Factorial Factors 530

14.4 The Split-Plot Design 534

14.5 Other Variations of the Split-Plot Design 540

15 Other Design and Analysis Topics (Available in e-text for students) W-1

Problems P-1

Appendix A-1

Table I. Cumulative Standard Normal Distribution A-2

Table II. Percentage Points of the t Distribution A-4

Table III. Percentage Points of the ¿ 2 Distribution A-5

Table IV. Percentage Points of the F Distribution A-6

Table V. Percentage Points of the Studentized Range Statistic A-11

Table VI. Critical Values for Dunnett's Test for Comparing Treatments with a Control A-13

Table VII. Coefficients of Orthogonal Polynomials A-15

Table VIII. Alias Relationships for 2k--pFractional Factorial Designs with k ¿ 15 and n ¿ 64 A-16

OC Bibliography (Available in e-text for students) B-1

Index I-1