1. Basic Principles and Experiments with a Single Factor 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 The General Linear Model, 11
1.5 Variable selection in Regression Analysis, 17
1.6 One-Way Layout, 19
1.7 Multiple Comparisons, 26
1.8 Quantitative Factors and Orthogonal Polynomials, 30
1.9 Residual Analysis: Assessment of Model Assumptions, 35
1.10 Practical Summary, 40
Exercises, 41

2. Experiments With More Than One Factor 48
2.1 Paired Comparison Design, 48
2.2 Randomized Block Design, 51
2.3 Two-Way Layout, 55
2.4 Multi-Way Layout, 63
2.5 Transformation of the Response, 66
2.6 Latin Square Design: Two Blocking Variables, 70
2.7 Graeco-Latin Square Design, 74
2.8 Balanced Incomplete Block Design, 76
2.9 Analysis of Covariance: Incorporating Auxiliary Information, 80
2.10 Practical Summary, 83
Exercises, 84
Appendix 2A: Table of Latin Squares, Graeco-Latin Squares, and Hyper-Graeco-Latin Squares, 93

3. Full Factorial Experiments at Two Levels 96
3.1 An Epitaxial Layer Growth Experiment, 96
3.2 Nominal-the-Best Problem and Quadratic Loss Function, 98
3.3 Full Factorial Designs at Two Levels: A General Discussion, 99
3.4 Factorial Effects and Plots, 103
3.5 Fundamental Principles for Factorial Effects: Hierarchical Ordering, Effect Sparsity, and Effect Heredity, 111
3.6 Using Regression and the Model Matrix to Compute Factorial Effects, 113
3.7 Comparisons with the "One-Factor-at-a-Time" Approach, 114
3.8 Log Transformation of the Sample Variances, 117
3.9 Effect of Simultaneous Testing, 118
3.10 Normal and Half-Normal Plots, 120
3.11 Analysis of Location and Dispersion: Revisiting the Epitaxial Layer Growth Experiment, 123
3.12 Blocking and Optimal Arrangement of 2^k Factorial Designs in 2^q Blocks, 126
3.13 A Formal Test of Effect Significance for Unreplicated Experiments: Without s², 131
3.14 Testing Variance Homogeneity, 135
3.15 A Formal Test of Effect Significance for y_i : With s², 136
3.16 A Formal Test of Effect Significance for ln s_i² , 139
3.17 A Summary of Analysis Strategies, 140
3.18 Practical Summary, 141
Exercises, 143
Appendix 3A: Table of 2^k Factorial Designs in 2^q Blocks, 150

4. Fractional Factorial Experiments at Two Levels 153
4.1 A Leaf Spring Experiment, 153
4.2 Fractional Factorial Designs: Effect Aliasing and the Criteria of Resolution and Minimum Aberration, 154
4.3 Analysis, 161
4.4 Techniques for Resolving the Ambiguities in Aliased Effects, 167
4.5 Selection of 2^k-p Designs Using Minimum Aberration and Related Criteria, 175
4.6 Blocking in Fractional Factorial Designs, 179
4.7 Practical Summary, 181
Exercises, 183
Appendix 4A: Tables of 2^k-p Fractional Factorial Designs, 193
Appendix 4B: Tables of 2^k-p Fractional Factorial Designs in 2^q Blocks, 199

5. Full Factorial and Fractional Factorial Experiments at Three Levels 205
5.1 A Seat-Belt Experiment, 205
5.2 Larger-the-Better and Smaller-the-Better Problems, 207
5.3 3^k Full Factorial Designs, 208
5.4 3^k-p Fractional Factorial Designs, 214
5.5 Simple Analysis Methods: Plots and Analysis of Variance, 218
5.6 An Alternative Analysis Method, 226
5.7 Analysis Strategies for Multiple Responses I: Out-of-Spec Probabilities, 232
5.8 Blocking in 3^k and 3^k-p Designs, 240
5.9 Practical Summary, 242
Exercises, 244
Appendix 5A: Tables of 3^k-p Fractional Factorial Designs, 250
Appendix 5B: Tables of 3^k-p Fractional Factorial Designs in 3^q Blocks, 251

6. Other Design and Analysis Techniques for Experiments at More Than Two Levels 256
6.1 A Router Bit Experiment Based on a Mixed Two-Level and Four-Level Design, 256
6.2 Method of Replacement and Construction of 2^m4ⁿ Designs, 258
6.3 Minimum Aberration 2^m4ⁿ Designs with n=1,2, 262
6.4 An Analysis Strategy For 2^m4ⁿ Experiments, 265
6.5 Analysis of the Router Bit Experiment, 267
6.6 A Paint Experiment Based on a Mixed Two-Level and Three-Level Design, 271
6.7 Design and Analysis of 36-Run Experiments at Two and Three Levels, 273
6.8 r^k-p Fractional Factorial Designs for Any Prime Number r, 278
6.9 Related Factors: Method of Sliding Levels and Nested Effects Analysis, 283
6.10 Practical Summary, 290
Exercises, 291
Appendix 6A: Tables of 2^m4¹ Minimum Aberration Designs, 298
Appendix 6B: Tables of 2^m4² Minimum Aberration Designs, 300
Appendix 6C: OA(25,5⁶), 302
Appendix 6D: OA(49, 7⁸), 302

7. Nonregular Designs: Construction and Properties 305
7.1 Two Experiments: Weld-Repaired Castings and Blood Glucose Testing, 305
7.2 Some Advantages of Nonregular Designs over the 2^k-p and 3^k-p Series of Designs, 307
7.3 A Lemma on Orthogonal Arrays, 308
7.4 Plackett-Burman Designs and Hall?s Designs, 309
7.5 A Collection of Useful Mixed-Level Orthogonal Arrays, 313
7.6 Construction of Mixed-Level Orthogonal Arrays Based on Difference Matrices, 315
7.7 Construction of Mixed-Level Orthogonal Arrays through the Method of Replacement, 318
7.8 Orthogonal Main-Effect Plans through Collapsing Factors, 320
7.9 Practical Summary, 324
Exercises, 326
Appendix 7A: Plackett-Burman Designs OA(N,2^N-1) with N=4k, 330
Appendix 7B: Hall?s 16-Run Orthogonal Arrays of Types II to V, 333
Appendix 7C: Some Useful Mixed-Level Orthogonal Arrays, 335
Appendix 7D: Some Useful Difference Matrices, 345
Appendix 7E: Some Useful Orthogonal Main-Effect Plans, 347

8. Experiments with Complex Aliasing 350
8.1 Partial Aliasing of Effects and the Alias Matrix, 350
8.2 Traditional Analysis Strategy: Screening Design and Main Effect Analysis, 353
8.3 Simplification of Complex Aliasing via Effect Sparsity, 354
8.4 An Analysis Strategy for Designs with Complex Aliasing, 356
8.5 A Bayesian Variable Selection Strategy for Designs with Complex Aliasing, 363
8.6 Supersaturated Designs: Design Construction and Analysis, 371
8.7 Practical Summary, 375
Exercises, 376
Appendix 8A: Further Details for the Full Conditional Distributions, 382

9. Response Surface Methodology 387
9.1 A Ranitidine Separation Experiment, 387
9.2 Sequential Nature of Response Surface Methodology, 389
9.3 From First-Order Experiments to Second-Order Experiments: Steepest Ascent Search and Rectangular Grid Search, 392
9.4 Analysis of Second-Order Response Surfaces, 401
9.5 Analysis of the Ranitidine Experiment, 405
9.6 Analysis Strategies for Multiple Responses II: Contour Plots and the Use of Desirability Functions, 409
9.7 Central Composite Designs, 412
9.8 Box-Behnken Designs and Uniform Shell Designs, 417
9.9 Practical Summary, 420
Exercises, 422
Appendix 9A: Table of Central Composite Designs, 431
Appendix 9B: Table of Box-Behnken Designs, 433
Appendix 9C: Table of Uniform Shell Designs, 434

10. Introduction to Robust Parameter Design 436
10.1 A Robust Parameter Design Perspective of the Layer Growth and Leaf Spring Experiments, 436
10.2 Strategies for Reducing Variation, 439
10.3 Noise (Hard-to-Control) Factors, 440
10.4 Variation Reduction through Robust Parameter Design, 442
10.5 Experimentation and Modeling Strategies I: Cross Array, 444
10.6 Experimentation and Modeling Strategies II: Single Array and Response Modeling, 456
10.7 Cross Arrays: Estimation Capacity and Optimal Selection, 459
10.8 Choosing Between Cross Arrays and Single Arrays, 461
10.9 Optimal Selection of Single Arrays, 466
10.10 Signal-to-Noise Ratio and Its Limitations for Parameter Design Optimization, 468
10.11 Further Topics, 472
10.12 Practical Summary, 473
Exercises, 474
Appendix 10A: Tables of Single Arrays Based on 2^k-p Designs, 484

11. Robust Parameter Design for Signal-Response Systems 495
11.1 An Injection Molding Experiment, 495
11.2 Signal-Response Systems and Their Classification, 499
11.3 Performance Measures for Parameter Design Optimization, 503
11.4 Modeling and Analysis Strategies, 507
11.5 Analysis of the Injection Molding Experiment, 510
11.6 Choice of Experimental Plans, 516
11.7 Practical Summary, 519
Exercises, 520

12. Experiments for Improving Reliability 529
12.1 Experiments with Failure Time Data, 529
12.2 Regression Model for Failure Time Data, 533
12.3 A Likelihood Approach for Handling Failure Time Data with Censoring, 535
12.4 Design-Dependent Model Selection Strategies, 539
12.5 A Bayesian Approach to Estimation and Model Selection for Failure Time Data, 540
12.6 Analysis of Reliability Experiments with Failure Time Data, 543
12.7 Reliability Experiments with Degradation Data, 548
12.8 A Simple Analysis for Degradation Data, 552
12.9 Practical Summary, 555
Exercises, 556

13. Experiments with Nonnormal Data 563
13.1 A Wave Soldering Experiment with Count Data, 563
13.2 Generalized Linear Models, 564
13.3 Analysis of Generalized Linear Models, 569
13.4 Analysis of the Wave Soldering Experiment, 572
13.5 Other Uses and Extensions of Generalized Linear Models, 574
13.6 A Foam Molding Experiment with Ordinal Data, 575
13.7 Modeling and Analysis for Ordinal Data, 576
13.8 Analysis of Foam Molding Experiment, 580
13.9 Scoring: A Simple Method for Analyzing Ordinal Data, 583
13.10 Practical Summary, 584
Exercises, 585

Appendices. Statistical Tables 596-620