Modern Experimental Design

Modern Experimental Design......Page 4
Contents......Page 8
Preface......Page 18
1 Introduction......Page 20
1.1 Experiments All Around Us......Page 21
1.2 Objectives for Experimental Designs......Page 22
1.3 Planned Experimentation versus Use of Observational Data......Page 24
1.4.1 Randomization......Page 25
1.4.2 Replication versus Repeated Measurements......Page 26
1.4.3 Example......Page 27
1.4.4 Size of an Effect That Can be Detected......Page 30
1.5 Terminology......Page 31
1.6 Steps for the Design of Experiments......Page 32
1.6.2.1 Choice of Factors......Page 33
1.6.2.2 Choice of Levels......Page 34
1.7 Processes Should Ideally be in a State of Statistical Control......Page 37
1.9 Analysis of Means......Page 39
1.11 Experimental Designs and Six Sigma......Page 41
References......Page 42
Exercises......Page 45
2.1 Completely Randomized Design......Page 50
2.1.1 Model......Page 51
2.1.2.1 Assumptions......Page 52
2.1.3 Examples: One Factor, More Than Two Levels......Page 54
2.1.3.1 Multiple Comparisons......Page 55
2.1.3.2 Unbalanced and Missing Data......Page 58
2.1.3.3 Computations......Page 59
2.1.4 Example Showing the Effect of Unequal Variances......Page 60
2.2 Analysis of Means......Page 61
2.2.1 ANOM for a Completely Randomized Design......Page 62
2.2.1.1 Example......Page 63
2.2.2 ANOM with Unequal Variances......Page 64
2.2.4 ANOM for Attributes Data......Page 66
2.5 Summary......Page 67
References......Page 68
Exercises......Page 70
3.1 Randomized Block Design......Page 75
3.1.1 Assumption......Page 76
3.1.2 Blocking an Out-of-Control Process......Page 79
3.1.4 Example......Page 80
3.1.4.1 Critique......Page 82
3.1.5 ANOM......Page 83
3.2.1 Balanced Incomplete Block Designs......Page 84
3.2.1.1 Analysis......Page 85
3.2.1.3 ANOM......Page 87
3.2.2 Partially Balanced Incomplete Block Designs......Page 88
3.2.4 Other Incomplete Block Designs......Page 89
3.3 Latin Square Design......Page 90
3.3.1 Assumptions......Page 91
3.3.3 Example......Page 93
3.3.5 Using Multiple Latin Squares......Page 96
3.3.6 ANOM......Page 98
3.4.1 Model......Page 99
3.4.2 Degrees of Freedom Limitations on the Design Construction......Page 100
3.4.4 Application......Page 101
3.4.5 ANOM......Page 102
3.5 Youden Squares......Page 103
3.5.1 Model......Page 104
3.6 Missing Values......Page 105
3.7 Software......Page 108
3.8 Summary......Page 109
References......Page 110
Exercises......Page 112
4.1 The Nature of Factorial Designs......Page 120
4.2 The Deleterious Effects of Interactions......Page 125
4.2.1 Conditional Effects......Page 126
4.2.1.1 Sample Sizes for Conditional Effects Estimation......Page 132
4.3 Effect Estimates......Page 133
4.4 Why Not One-Factor-at-a-Time Designs?......Page 134
4.5 ANOVA Table for Unreplicated Two-Factor Design?......Page 135
4.6 The 2(3) Design......Page 138
4.7 Built-in Replication......Page 141
4.8 Multiple Readings versus Replicates......Page 142
4.9.1 Factorial Design but not “Factorial Model”......Page 143
4.10 Bad Data in Factorial Designs......Page 146
4.10.1 ANOM Display......Page 153
4.11 Normal Probability Plot Methods......Page 155
4.12 Missing Data in Factorial Designs......Page 157
4.12.1 Resulting from Bad Data......Page 158
4.13 Inaccurate Levels in Factorial Designs......Page 159
4.14 Checking for Statistical Control......Page 160
4.15 Blocking 2(k) Designs......Page 161
4.16 The Role of Expected Mean Squares in Experimental Design......Page 163
4.17 Hypothesis Tests with Only Random Factors in 2(k) Designs? Avoid Them!......Page 165
4.18 Hierarchical versus Nonhierarchical Models......Page 166
4.19 Hard-to-Change Factors......Page 167
4.21 Detecting Dispersion Effects......Page 169
4.23 Summary......Page 170
Appendix A Derivation of Conditional Main Effects......Page 171
Appendix D Expected Mean Squares for the Replicated 2(2) Design......Page 172
Appendix E Expected Mean Squares, in General......Page 174
References......Page 176
Exercises......Page 181
5 Fractional Factorial Designs with Two Levels......Page 188
5.1 2(k–1) Designs......Page 189
5.1.1 Which Fraction?......Page 195
5.1.3 Alias Structure......Page 196
5.1.4 What if I Had Used the Other Fraction?......Page 198
5.2 2(k–2) Designs......Page 200
5.2.1 Basic Concepts......Page 204
5.3.1 Normal Probability Plot Methods when k – p = 16......Page 206
5.4 Utility of Small Fractional Factorials vis-à-vis Normal Probability Plots......Page 207
5.6 Retrieving a Lost Defining Relation......Page 209
5.7 Minimum Aberration Designs and Minimum Confounded Effects Designs......Page 211
5.8 Blocking Factorial Designs......Page 213
5.8.1 Blocking Fractional Factorial Designs......Page 214
5.8.1.1 Blocks of Size 2......Page 219
5.9 Foldover Designs......Page 220
5.9.1 Semifolding......Page 222
5.9.1.1 Conditional Effects......Page 227
5.9.1.2 Semifolding a 2(k–1) Design......Page 229
5.9.1.4 Semifolding with Software......Page 234
5.10 John’s 3/4 Designs......Page 235
5.11 Projective Properties of 2(k–p) Designs......Page 238
5.12 Small Fractions and Irregular Designs......Page 239
5.13 An Example of Sequential Experimentation......Page 241
5.13.1 Critique of Example......Page 243
5.14 Inadvertent Nonorthogonality—Case Study......Page 244
5.15 Fractional Factorial Designs for Natural Subsets of Factors......Page 245
5.16 Relationship Between Fractional Factorials and Latin Squares......Page 247
5.17.1 Designs Attributed to Genichi Taguchi......Page 248
5.20 Software......Page 249
5.21 Summary......Page 252
References......Page 253
Exercises......Page 257
6.1 3(k) Designs......Page 267
6.1.1 Decomposing the A*B Interaction......Page 270
6.1.2 Inference with Unreplicated 3(k) Designs......Page 271
6.2 Conditional Effects......Page 274
6.3 3(k–p) Designs......Page 276
6.3.1 Understanding 3(k–p) Designs......Page 278
6.3.2 Constructing 3(k–p) Designs......Page 279
6.3.4 Constructing a 3(3–1) Design......Page 281
6.3.5 Need for Mixed Number of Levels......Page 282
6.4 Mixed Factorials......Page 283
6.4.1 Constructing Mixed Factorials......Page 284
6.4.2 Additional Examples......Page 285
6.5 Mixed Fractional Factorials......Page 293
6.6 Orthogonal Arrays with Mixed Levels......Page 294
6.7 Minimum Aberration Designs and Minimum Confounded Effects Designs......Page 296
6.8 Four or More Levels......Page 297
6.9 Software......Page 299
References......Page 303
Exercises......Page 305
7 Nested Designs......Page 310
7.1 Various Examples......Page 313
7.2.1 A Workaround......Page 314
7.3 Staggered Nested Designs......Page 317
7.5 Estimating Variance Components......Page 319
References......Page 321
Exercises......Page 323
8 Robust Designs......Page 330
8.1 “Taguchi Designs?”......Page 331
8.2 Identification of Dispersion Effects......Page 333
8.3 Designs with Noise Factors......Page 335
8.4 Product Array, Combined Array, or Compound Array?......Page 337
8.5 Software......Page 339
8.7 Summary......Page 341
References......Page 342
Exercises......Page 345
9 Split-Unit, Split-Lot, and Related Designs......Page 349
9.1 Split-Unit Design......Page 350
9.1.2 Split-Unit Designs in Industry......Page 355
9.1.3 Split-Unit Designs with Fractional Factorials......Page 359
9.1.4 Blocking Split-Plot Designs......Page 361
9.1.6 Examples of Split-Plot Designs for Hard-to-Change Factors......Page 362
9.2 Split-Lot Design......Page 364
9.2.1 Strip-Plot Design......Page 365
9.2.1.1 Applications of Strip-Block (Strip-Plot) Designs......Page 366
9.3 Commonalities and Differences Between these Designs......Page 368
9.4 Software......Page 369
References......Page 370
Exercises......Page 373
10 Response Surface Designs......Page 379
10.1 Response Surface Experimentation: One Design or More Than One?......Page 381
10.3 Classical Response Surface Designs versus Alternatives......Page 383
10.3.1 Effect Estimates?......Page 388
10.4 Method of Steepest Ascent (Descent)......Page 389
10.5 Central Composite Designs......Page 392
10.5.2 Small Composite Designs......Page 396
10.5.2.1 Draper–Lin Designs......Page 397
10.5.3 Additional Applications......Page 402
10.6 Properties of Space-Filling Designs......Page 403
10.8 Box–Behnken Designs......Page 405
10.8.1 Application......Page 407
10.9 Conditional Effects?......Page 408
10.10.1 Hybrid Designs......Page 409
10.10.3 Koshal Designs......Page 412
10.11.1 Blocking Central Composite Designs......Page 413
10.11.3 Blocking Other Response Surface Designs......Page 415
10.12 Comparison of Designs......Page 416
10.13 Analyzing the Fitted Surface......Page 417
10.13.1 Characterization of Stationary Points......Page 420
10.13.2 Confidence Regions on Stationary Points......Page 421
10.13.3 Ridge Analysis......Page 422
10.14 Response Surface Designs for Computer Simulations......Page 423
10.16 Further Reading......Page 424
10.18 Software......Page 425
10.20 Summary......Page 427
References......Page 428
Exercises......Page 433
11 Repeated Measures Designs......Page 444
11.1 One Factor......Page 445
11.2 More Than One Factor......Page 447
11.3 Crossover Designs......Page 448
11.4 Designs for Carryover Effects......Page 451
11.5 How Many Repeated Measures?......Page 456
11.7 Software......Page 457
References......Page 458
Exercises......Page 463
12 Multiple Responses......Page 466
12.1 Overlaying Contour Plots......Page 467
12.2 Seeking Multiple Response Optimization with Desirability Functions......Page 469
12.2.1 Weight and Importance......Page 470
12.4 Designs Used with Multiple Responses......Page 471
12.5 Applications......Page 472
12.6 Multiple Response Optimization Variations......Page 482
12.8 Software......Page 488
12.9 Summary......Page 490
References......Page 491
Exercises......Page 493
13.1 One-Factor-at-a-Time Designs......Page 502
13.2 Cotter Designs......Page 506
13.3 Rotation Designs......Page 507
13.4.1 Plackett–Burman Designs......Page 508
13.4.1.1 Projection Properties of Plackett–Burman Designs......Page 512
13.4.1.2 Applications......Page 513
13.4.2 Supersaturated Designs......Page 517
13.4.2.1 Applications......Page 518
13.5 Design of Experiments for Analytic Studies......Page 519
13.6 Equileverage Designs......Page 520
13.6.2 Are Commonly Used Designs Equileverage?......Page 521
13.7 Optimal Designs......Page 522
13.7.1 Alphabetic Optimality......Page 523
13.7.2 Applications of Optimal Designs......Page 526
13.8 Designs for Restricted Regions of Operability......Page 527
13.9 Space-Filling Designs......Page 533
13.9.1 Uniform Designs......Page 534
13.9.2 Sphere-Packing Designs......Page 537
13.9.3 Latin Hypercube Design......Page 538
13.10 Trend-Free Designs......Page 540
13.12 Mixture Designs......Page 541
13.14 Design of Computer Experiments......Page 542
13.16 Weighing Designs and Calibration Designs......Page 543
13.16.1 Calibration Designs......Page 544
13.16.2 Weighing Designs......Page 545
13.19 Model-Robust Designs......Page 547
13.21 Design of Microarray Experiments......Page 548
13.22 Multi-Vari Plot......Page 549
13.24 Software......Page 550
13.25 Summary......Page 551
References......Page 552
Exercises......Page 561
14.1 Training for Experimental Design Use......Page 563
References......Page 564
Exercises......Page 565
Answers to Selected Exercises......Page 570
Appendix: Statistical Tables......Page 584
Author Index......Page 594
Subject Index......Page 606