Modern Experimental Design

by Ryan, Thomas P.

• ISBN13: 9780471210771
• ISBN10: 0471210773
• Edition: 1st
• Format: Hardcover
• Copyright: 2007-02-02
• Publisher: Wiley-Interscience

Summary

This volume covers the first full year of experimental design topics at the beginning graduate level with a well balanced, down-to-earth, and complete presentation, covering both design and analysis equally. Mathematical rigor is kept to a minimum with up-to-date discussions on hard-to-change factors, the selection of factor levels in terms of physical units, designs with more than one response variable, and multi-response optimization are also included due to the intense applicability to the industrial sector.Suitable for use as either an undergraduate or graduate text, depending on the audience, this book covers a wide range of topics, including some that have received increased attention in recent years, such as hard-to-change factors, uniform designs, multiple response optimization, and Analysis of Means (ANOM). Conditional effects are emphasized and advocated for the first time as a routine and important method of analysis. There is a large number of cited references and extensive discussions of software capabilities, with considerable illustrative use of Design-Expert, in particular, JMP, and Minitab.

Author Biography

THOMAS P. RYAN, PhD, has served on the Editorial Review Board of the Journal of Quality Technology since 1990. He is the author of three other books published by Wiley, and is an elected Fellow of the American Statistical Association, the American Society for Quality, and the Royal Statistical Society. He is currently teaching advanced courses on design of experiments and engineering statistics at statistics.com, and serves as a consultant to Cytel Software Corporation.

Table of Contents

Preface	p. xv
Introduction	p. 1
Experiments All Around Us	p. 2
Objectives for Experimental Designs	p. 3
Planned Experimentation versus Use of Observational Data	p. 5
Basic Design Concepts	p. 6
Randomization	p. 6
Replication versus Repeated Measurements	p. 7
Example	p. 8
Size of an Effect That Can be Detected	p. 11
Terminology	p. 12
Steps for the Design of Experiments	p. 13
Recognition and Statement of the Problem	p. 14
Selection of Factors and Levels	p. 14
Choice of Factors	p. 14
Choice of Levels	p. 15
Processes Should Ideally be in a State of Statistical Control	p. 18
Types of Experimental Designs	p. 20
Analysis of Means	p. 20
Missing Data	p. 22
Experimental Designs and Six Sigma	p. 22
Quasi-Experimental Design	p. 23
Summary	p. 23
References	p. 23
Exercises	p. 26
Completely Randomized Design	p. 31
Completely Randomized Design	p. 31
Model	p. 32
Example: One Factor, Two Levels	p. 33
Assumptions	p. 33
Examples: One Factor, More Than Two Levels	p. 35
Multiple Comparisons	p. 36
Unbalanced and Missing Data	p. 39
Computations	p. 40
Example Showing the Effect of Unequal Variances	p. 41
Analysis of Means	p. 42
ANOM for a Completely Randomized Design	p. 43
Example	p. 44
ANOM with Unequal Variances	p. 45
Applications	p. 47
Nonparametric ANOM	p. 47
ANOM for Attributes Data	p. 47
Software for Experimental Design	p. 48
Missing Values	p. 48
Summary	p. 48
Appendix	p. 49
References	p. 49
Exercises	p. 51
Designs that Incorporate Extraneous (Blocking) Factors	p. 56
Randomized Block Design	p. 56
Assumption	p. 57
Blocking an Out-of-Control Process	p. 60
Efficiency of a Randomized Block Design	p. 61
Example	p. 61
Critique	p. 63
ANOM	p. 64
Incomplete Block Designs	p. 65
Balanced Incomplete Block Designs	p. 65
Analysis	p. 66
Recovery of Interblock Information	p. 68
ANOM	p. 68
Partially Balanced Incomplete Block Designs	p. 69
Lattice Design	p. 70
Nonparametric Analysis for Incomplete Block Designs	p. 70
Other Incomplete Block Designs	p. 70
Latin Square Design	p. 71
Assumptions	p. 72
Model	p. 74
Example	p. 74
Efficiency of a Latin Square Design	p. 77
Using Multiple Latin Squares	p. 77
ANOM	p. 79
Graeco-Latin Square Design	p. 80
Model	p. 80
Degrees of Freedom Limitations on the Design Construction	p. 81
Sets of Graeco-Latin Square Designs	p. 82
Application	p. 82
ANOM	p. 83
Youden Squares	p. 84
Model	p. 85
Lists of Youden Designs	p. 86
Using Replicated Youden Designs	p. 86
Analysis	p. 86
Missing Values	p. 86
Software	p. 89
Summary	p. 90
References	p. 91
Exercises	p. 93
Full Factorial Designs with Two Levels	p. 101
The Nature of Factorial Designs	p. 101
The Deleterious Effects of Interactions	p. 106
Conditional Effects	p. 107
Sample Sizes for Conditional Effects Estimation	p. 113
Can We "Transform Away" Interactions?	p. 114
Effect Estimates	p. 114
Why Not One-Factor-at-a-Time Designs?	p. 115
ANOVA Table for Unreplicated Two-Factor Design?	p. 116
The 2 3 Design	p. 119
Built-in Replication	p. 122
Multiple Readings versus Replicates	p. 123
Reality versus Textbook Examples	p. 124
Factorial Design but not "Factorial Model"	p. 124
Bad Data in Factorial Designs	p. 127
ANOM Display	p. 134
Normal Probability Plot Methods	p. 136
Missing Data in Factorial Designs	p. 138
Resulting from Bad Data	p. 139
Proposed Solutions	p. 140
Inaccurate Levels in Factorial Designs	p. 140
Checking for Statistical Control	p. 141
Blocking 2k Designs	p. 142
The Role of Expected Mean Squares in Experimental Design	p. 144
Hypothesis Tests with Only Random Factors in 2k Designs? Avoid Them!	p. 146
Hierarchical versus Nonhierarchical Models	p. 147
Hard-to-Change Factors	p. 148
Software for Designs with Hard-to-Change Factors	p. 150
Factors Not Reset	p. 150
Detecting Dispersion Effects	p. 150
Software	p. 151
Summary	p. 151
Derivation of Conditional Main Effects	p. 152
Relationship Between Effect Estimates and Regression Coefficients	p. 153
Precision of the Effect Estimates	p. 153
Expected Mean Squares for the Replicated 22 Design	p. 153
Expected Mean Squares, in General	p. 155
References	p. 157
Exercises	p. 162
Fractional Factorial Designs with Two Levels	p. 169
2k-1 Designs	p. 170
Which Fraction?	p. 176
Effect Estimates and Regression Coefficients	p. 177
Alias Structure	p. 177
What if I Had Used the Other Fraction?	p. 179
2k-1 Designs	p. 181
Basic Concepts	p. 185
Designs with k - p = 16	p. 187
Normal Probability Plot Methods when k - p = 16	p. 187
Other Graphical Methods	p. 188
Utility of Small Fractional Factorials vis-a-vis Normal Probability Plots	p. 188
Design Efficiency	p. 190
Retrieving a Lost Defining Relation	p. 190
Minimum Aberration Designs and Minimum Confounded Effects Designs	p. 192
Blocking Factorial Designs	p. 194
Blocking Fractional Factorial Designs	p. 195
Blocks of Size 2	p. 200
Foldover Designs	p. 201
Semifolding	p. 203
Conditional Effects	p. 208
Semifolding a 2k-1 Design	p. 210
General Strategy?	p. 215
Semifolding with Software	p. 215
John's 3/4 Designs	p. 216
Projective Properties of 2k-p Designs	p. 219
Small Fractions and Irregular Designs	p. 220
An Example of Sequential Experimentation	p. 222
Critique of Example	p. 224
Inadvertent Nonorthogonality-Case Study	p. 225
Fractional Factorial Designs for Natural Subsets of Factors	p. 226
Relationship Between Fractional Factorials and Latin Squares	p. 228
Alternatives to Fractional Factorials	p. 229
Designs Attributed to Genichi Taguchi	p. 229
Missing and Bad Data	p. 230
Plackett-Burman Designs	p. 230
Software	p. 230
Summary	p. 233
References	p. 234
Exercises	p. 238
Designs With More Than Two Levels	p. 248
3k Designs	p. 248
Decomposing the A*B Interaction	p. 251
Inference with Unreplicated 3k Designs	p. 252
Conditional Effects	p. 255
3k-p Designs	p. 257
Understanding 3k-p Designs	p. 259
Constructing 3k-p Designs	p. 260
Alias Structure	p. 262
Constructing a 3 3-1 Design	p. 262
Need for Mixed Number of Levels	p. 263
Replication of 3k-1 Designs?	p. 264
Mixed Factorials	p. 264
Constructing Mixed Factorials	p. 265
Additional Examples	p. 266
Mixed Fractional Factorials	p. 274
Orthogonal Arrays with Mixed Levels	p. 275
Minimum Aberration Designs and Minimum Confounded Effects Designs	p. 277
Four or More Levels	p. 278
Software	p. 280
Catalog of Designs	p. 284
Summary	p. 284
References	p. 284
Exercises	p. 286
Nested Designs	p. 291
Various Examples	p. 294
Software Shortcomings	p. 295
A Workaround	p. 295
Staggered Nested Designs	p. 298
Nested and Staggered Nested Designs with Factorial Structure	p. 300
Estimating Variance Components	p. 300
ANOM for Nested Designs?	p. 302
Summary	p. 302
References	p. 302
Exercises	p. 304
Robust Designs	p. 311
"Taguchi Designs?"	p. 312
Identification of Dispersion Effects	p. 314
Designs with Noise Factors	p. 316
Product Array, Combined Array, or Compound Array?	p. 318
Software	p. 320
Further Reading	p. 322
Summary	p. 322
References	p. 323
Exercises	p. 326
Split-Unit, Split-Lot, and Related Designs	p. 330
Split-Unit Design	p. 331
Split-Plot Mirror Image Pairs Designs	p. 336
Split-Unit Designs in Industry	p. 336
Split-Unit Designs with Fractional Factorials	p. 340
Blocking Split-Plot Designs	p. 342
Split-Unit Plackett-Burman Designs	p. 343
Examples of Split-Plot Designs for Hard-to-Change Factors	p. 343
Split-Split-Plot Designs	p. 345
Split-Lot Design	p. 345
Strip-Plot Design	p. 346
Applications of Strip-Block (Strip-Plot) Designs	p. 347
Commonalities and Differences Between these Designs	p. 349
Software	p. 350
Summary	p. 351
References	p. 351
Exercises	p. 354
Response Surface Designs	p. 360
Response Surface Experimentation: One Design or More Than One?	p. 362
Which Designs?	p. 364
Classical Response Surface Designs versus Alternatives	p. 364
Effect Estimates?	p. 369
Method of Steepest Ascent (Descent)	p. 370
Central Composite Designs	p. 373
CCD Variations	p. 377
Small Composite Designs	p. 377
Draper-Lin Designs	p. 378
Additional Applications	p. 383
Properties of Space-Filling Designs	p. 384
Applications of Uniform Designs	p. 386
Box-Behnken Designs	p. 386
Application	p. 388
Conditional Effects?	p. 389
Other Response Surface Designs	p. 390
Hybrid Designs	p. 390
Uniform Shell Designs	p. 393
Koshal Designs	p. 393
Hoke Designs	p. 394
Blocking Response Surface Designs	p. 394
Blocking Central Composite Designs	p. 394
Blocking Box-Behnken Designs	p. 396
Blocking Other Response Surface Designs	p. 396
Comparison of Designs	p. 397
Analyzing the Fitted Surface	p. 398
Characterization of Stationary Points	p. 401
Confidence Regions on Stationary Points	p. 402
Ridge Analysis	p. 403
Ridge Analysis with Noise Factors	p. 404
Optimum Conditions and Regions of Operability	p. 404
Response Surface Designs for Computer Simulations	p. 404
ANOM with Response Surface Designs?	p. 405
Further Reading	p. 405
The Present and Future Direction of Response Surface Designs	p. 406
Software	p. 406
Catalogs of Designs	p. 408
Summary	p. 408
References	p. 409
Exercises	p. 414
Repeated Measures Designs	p. 425
One Factor	p. 426
The Example in Section 2.1.2	p. 428
More Than One Factor	p. 428
Crossover Designs	p. 429
Designs for Carryover Effects	p. 432
How Many Repeated Measures?	p. 437
Further Reading	p. 438
Software	p. 438
Summary	p. 439
References	p. 439
Exercises	p. 444
Multiple Responses	p. 447
Overlaying Contour Plots	p. 448
Seeking Multiple Response Optimization with Desirability Functions	p. 449
Weight and Importance	p. 451
Dual Response Optimization	p. 452
Designs Used with Multiple Responses	p. 452
Applications	p. 453
Multiple Response Optimization Variations	p. 463
The Importance of Analysis	p. 469
Software	p. 469
Summary	p. 471
References	p. 472
Exercises	p. 474
Miscellaneous Design Topics	p. 483
One-Factor-at-a-Time Designs	p. 483
Cotter Designs	p. 487
Rotation Designs	p. 488
Screening Designs	p. 489
Plackett-Burman Designs	p. 489
Projection Properties of Plackett-Burman Designs	p. 493
Applications	p. 494
Supersaturated Designs	p. 498
Applications	p. 499
Lesser-Known Screening Designs	p. 500
Design of Experiments for Analytic Studies	p. 500
Equileverage Designs	p. 501
One Factor, Two Levels	p. 502
Are Commonly Used Designs Equileverage?	p. 502
Optimal Designs	p. 503
Alphabetic Optimality	p. 504
Applications of Optimal Designs	p. 507
Designs for Restricted Regions of Operability	p. 508
Space-Filling Designs	p. 514
Uniform Designs	p. 515
From Raw Form to Coded Form	p. 518
Sphere-Packing Designs	p. 518
Latin Hypercube Design	p. 519
Trend-Free Designs	p. 521
Cost-Minimizing Designs	p. 522
Mixture Designs	p. 522
Optimal Mixture Designs or Not?	p. 523
ANOM	p. 523
Design of Measurement Capability Studies	p. 523
Design of Computer Experiments	p. 523
Design of Experiments for Categorical Response Variables	p. 524
Weighing Designs and Calibration Designs	p. 524
Calibration Designs	p. 525
Weighing Designs	p. 526
Designs for Assessing the Capability of a System	p. 528
Designs for Nonlinear Models	p. 528
Model-Robust Designs	p. 528
Designs and Analyses for Non-normal Responses	p. 529
Design of Microarray Experiments	p. 529
Multi-Vari Plot	p. 530
Evolutionary Operation	p. 531
Software	p. 531
Summary	p. 532
References	p. 533
Exercises	p. 542
Tying It All Together	p. 544
Training for Experimental Design Use	p. 544
References	p. 545
Exercises	p. 546
Answers to Selected Exercises	p. 551
Statistical Tables	p. 565
Author Index	p. 575
Subject Index	p. 587
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