Modern Experimental Design (Wiley Series in Probability and Statistics)

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Modern Experimental Design (Wiley Series in Probability and Statistics)

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  • 製本 Hardcover:ハードカバー版/ページ数 593 p.
  • 言語 ENG
  • 商品コード 9780471210771
  • DDC分類 519.57

基本説明

Covers a wide range of topics, including some that have received increased attention in recent years, such as hard-to-change factors, uniform designs, and more.

Full Description


A complete and well-balanced introduction to modern experimental design Using current research and discussion of the topic along with clear applications, Modern Experimental Design highlights the guiding role of statistical principles in experimental design construction. This text can serve as both an applied introduction as well as a concise review of the essential types of experimental designs and their applications. Topical coverage includes designs containing one or multiple factors, designs with at least one blocking factor, split-unit designs and their variations as well as supersaturated and Plackett-Burman designs. In addition, the text contains extensive treatment of:* Conditional effects analysis as a proposed general method of analysis* Multiresponse optimization* Space-filling designs, including Latin hypercube and uniform designs* Restricted regions of operability and debarred observations* Analysis of Means (ANOM) used to analyze data from various types of designs* The application of available software, including Design-Expert, JMP, and MINITAB This text provides thorough coverage of the topic while also introducing the reader to new approaches.Using a large number of references with detailed analyses of datasets, Modern Experimental Design works as a well-rounded learning tool for beginners as well as a valuable resource for practitioners.

Table of Contents

Preface                                            xv
1 Introduction 1
1.1 Experiments All Around Us 2
1.2 Objectives for Experimental Designs 3
1.3 Planned Experimentation versus Use of 5
Observational Data
1.4 Basic Design Concepts 6
1.4.1 Randomization 6
1.4.2 Replication versus Repealed 7
Measurements
1.4.3 Example 8
1.4.4 Size of an Effect That Can be 11
Detected
1.5 Terminology 12
1.6 Steps for the Design of Experiments 13
1.6.1 Recognition and Statement of the 14
Problem
1.6.2 Selection of Factors and Levels 14
1.6.2.1 Choice of Factors 14
1.6.2.2 Choice of Levels 15
1.7 Processes Should Ideally be in a State 18
of Statistical Control
1.8 Types of Experimental Designs 20
1.9 Analysis of Means 20
1.10 Missing Data 22
1.11 Experimental Designs and Six Sigma 22
1.12 Quasi-Experimental Design 23
1.13 Summary 23
References 23
Exercises 26
2 Completely Randomized Design 31
2.1 Completely Randomized Design 31
2.1.1 Model 32
2.1.2 Example: One Factor, Two Levels 33
2.1.2.1 Assumptions 33
2.1.3 Examples: One Factor, More Than Two 35
Levels
2.1.3.1 Multiple Comparisons 36
2.1.3.2 Unbalanced and Missing Data 39
2.1.3.3 Computations 40
2.1.4 Example Showing the Effect of 41
Unequal Variances
2.2 Analysis of Means 42
2.2.1 ANOM for a Completely Randomized 43
Design
2.2.1.1 Example 44
2.2.2 ANOM with Unequal Variances 45
2.2.2.1 Applications 47
2.2.3 Nonparametric ANOM 47
2.2.4 ANOM for Attributes Data 47
2.3 Software for Experimental Design 48
2.4 Missing Values 48
2.5 Summary 48
Appendix 49
References 49
Exercises 51
3 Designs that Incorporate Extraneous 56
(Blocking) Factors
3.1 Randomized Block Design 56
3.1.1 Assumption 57
3.1.2 Blocking an Out-of-Control Process 60
3.1.3 Efficiency of a Randomized Block 61
Design
3.1.4 Example 61
3.1.4.1 Critique 63
3.1.5 ANOM 64
3.2 Incomplete Block Designs 65
3.2.1 Balanced Incomplete Block Designs 65
3.2.1.1 Analysis - 66
3.2.1.2 Recovery of Interblock 68
Information
3.2.1.3 ANOM 68
3.2.2 Partially Balanced Incomplete Block 69
Designs
3.2.2.1 Lattice Design 70
3.2.3 Nonparametric Analysis for 70
Incomplete Block Designs
3.2.4 Other Incomplete Block Designs 70
3.3 Latin Square Design 71
3.3.1 Assumptions 72
3.3.2 Model 74
3.3.3 Example 74
3.3.4 Efficiency of a Latin Square Design 77
3.3.5 Using Multiple Latin Squares 77
3.3.6 ANOM 79
3.4 Graeco豊atin Square Design 80
3.4.1 Model 80
3.4.2 Degrees of Freedom Limitations on 81
the Design Construction
3.4.3 Sets of Graeco豊atin Square Designs 82
3.4.4 Application 82
3.4.5 ANOM 83
3.5 Youden Squares 84
3.5.1 Model 85
3.5.2 Lists of Youden Designs 86
3.5.3 Using Replicated Youden Designs 86
3.5.4 Analysis 86
3.6 Missing Values 86
3.7 Software 89
3.8 Summary 90
References 91
Exercises 93
4 Full Factorial Designs with Two Levels 101
4.1 The Nature of Factorial Designs 101
4.2 The Deleterious Effects of Interactions 106
4.2.1 Conditional Effects 107
4.2.1.1 Sample Sizes for Conditional 113
Effects Estimation
4.2.2 Can We "Transform Away" 114
Interactions?
4.3 Effect Estimates 114
4.4 Why Not One-Factor-at-a-Time Designs? 115
4.5 ANOVA Table for Unreplicated 116
Two-Factor Design?
4.6 The 2ウ Design 119
4.7 Built-in Replication 122
4.8 Multiple Readings versus Replicates 123
4.9 Reality versus Textbook Examples 124
4.9.1 Factorial Design but not "Factorial 124
Model"
4.10 Bad Data in Factorial Designs 127
4.10.1 ANOM Display 134
4.11 Normal Probability Plot Methods 136
4.12 Missing Data in Factorial Designs 138
4.12.1 Resulting from Bad Data 139
4.12.2 Proposed Solutions 140
4.13 Inaccurate Levels in Factorial Designs 140
4.14 Checking for Statistical Control 141
4.15 Blocking 2k Designs 142
4.16 The Role of Expected Mean Squares in 144
Experimental Design
4.17 Hypothesis Tests with Only Random 146
Factors in 2k Designs? Avoid Them!
4.18 Hierarchical versus Nonhierarchical 147
Models
4.19 Hard-to-Change Factors 148
4.19.1 Software for Designs with 150
Hard-to-Change Factors
4.20 Factors Not Reset 150
4.21 Detecting Dispersion Effects 150
4.22 Software 151
4.23 Summary 151
Appendix A Derivation of Conditional Main 152
Effects
Appendix B Relationship Between Effect 153
Estimates and Regression Coefficients:
Appendix C Precision of the Effect Estimates 153
Appendix D Expected Mean Squares for the 153
Replicated 2イ Design
Appendix E Expected Mean Squares, in General 155
References 157
Exercises 162
5 Fractional Factorial Designs with Two Levels 169
5.1 24-1 Designs 170
5.1.1 Which Fraction? 176
5.1.2 Effect Estimates and Regression 177
Coefficients
5.1.3 Alias Structure 177
5.1.4 What if I Had Used the Other 179
Fraction?
5.2 2k-2 Designs 181
5.2.1 Basic Concepts 185
5.3 Designs with k  p = 16 187
5.3.1 Normal Probability Plot Methods 187
when k  p = 16
5.3.2 Other Graphical Methods 188
5.4 Utility of Small Fractional Factorials 188
vis- vis Normal Probability Plots
5.5 Design Efficiency 190
5.6 Retrieving a Lost Defining Relation 190
5.7 Minimum Aberration Designs and Minimum 192
Confounded Effects Designs
5.8 Blocking Factorial Designs 194
5.8.1 Blocking Fractional Factorial 195
Designs
5.8.1.1 Blocks of Size 2 200
5.9 Foldover Designs 201
5.9.1 Semifolding 203
5.9.1.1 Conditional Effects 208
5.9.1.2 Semifolding a 2k-1 Design 210
5.9.1.3 General Strategy? 215
5.9.1.4 Semifolding with Software 215
5.10 John's 3/4 Designs 216
5.11 Projective Properties of 2k-p Designs 219
5.12 Small Fractions and Irregular Designs 220
5.13 An Example of Sequential 222
Experimentation
5.13.1 Critique of Example 224
5.14 Inadvertent Nonorthogonality佑ase Study 225
5.15 Fractional Factorial Designs for 226
Natural Subsets of Factors
5.16 Relationship Between Fractional 228
Factorials and Latin Squares
5.17 Alternatives to Fractional Factorials 229
5.17.1 Designs Attributed to Genichi 229
Taguchi
5.18 Missing and Bad Data 230
5.19 Plackett-Burman Designs 230
5.20 Software 230
5.21 Summary 233
References 234
Exercises 238
6 Designs With More Than Two Levels 248
6.1 3k Designs 248
6.1.1 Decomposing the A*B Interaction 251
6.1.2 Inference with Unreplicated 3k 252
Designs
6.2 Conditional Effects 255
6.3 34-P Designs 257
6.3.1 Understanding 3k-p Designs 259
6.3.2 Constructing 3k-p Designs 260
6.3.3 Alias Structure 262
6.3.4 Constructing a 3ウ-ケ Design 262
6.3.5 Need for Mixed Number of Levels 263
6.3.6 Replication of 3k-p Designs? 264
6.4 Mixed Factorials 264
6.4.1 Constructing Mixed Factorials 265
6.4.2 Additional Examples 266
6.5 Mixed Fractional Factorials 274
6.6 Orthogonal Arrays with Mixed Levels 275
6.7 Minimum Aberration Designs and Minimum 277
Confounded Effects Designs
6.8 Four or More Levels 278
6.9 Software 280
6.10 Catalog of Designs 284
6.11 Summary 284
References 284
Exercises 286
7 Nested Designs 291
7.1 Various Examples 294
7.2 Software Shortcomings 295
7.2.1 A Workaround 295
7.3 Staggered Nested Designs 298
7.4 Nested and Staggered Nested Designs 300
with Factorial Structure
7.5 Estimating Variance Components 300
7.6 ANOM for Nested Designs? 302
7.7 Summary 302
References 302
Exercises 304
8 Robust Designs 311
8.1 "Taguchi Designs?" 312
8.2 Identification of Dispersion Effects 314
8.3 Designs with Noise Factors 316
8.4 Product Array, Combined Array, or 318
Compound Array?
8.5 Software 320
8.6 Further Reading 322
8.7 Summary 322
References 323
Exercises 326
9 Split-Unit, Split-Lot, and Related Designs 330
9.1 Split-Unit Design 331
9.1.1 Split-Plot Mirror Image Pairs 336
Designs
9.1.2 Split-Unit Designs in Industry 336
9.1.3 Split-Unit Designs with Fractional 340
Factorials
9.1.4 Blocking Split-Plot Designs 342
9.1.5 Split-Unit Plackett-Burman Designs 343
9.1.6 Examples of Split-Plot Designs for 343
Hard-to-Change Factors
9.1.7 Split-Split-Plot Designs 345
9.2 Split-Lot Design 345
9.2.1 Strip-Plot Design 346
9.2.1.1 Applications of Strip-Block 347
(Strip-Plot) Designs
9.3 Commonalities and Differences Between 349
these Designs
9.4 Software 350
9.5 Summary 351
References 351
Exercises 354
10 Response Surface Designs 360
10.1 Response Surface Experimentation: One 362
Design or More Than One?
10.2 Which Designs? 364
10.3 Classical Response Surface Designs 364
versus Alternatives
10.3.1 Effect Estimates? 369
10.4 Method of Steepest Ascent (Descent) 370
10.5 Central Composite Designs 373
10.5.1 CCD Variations 377
10.5.2 Small Composite Designs 377
10.5.2.1 Draper豊in Designs 378
10.5.3 Additional Applications 383
10.6 Properties of Space-Filling Designs 384
10.7 Applications of Uniform Designs 386
10.8 Box烹ehnken Designs 386
10.8.1 Application 388
10.9 Conditional Effects? 389
10.10 Other Response Surface Designs 390
10.10.1 Hybrid Designs 390
10.10.2 Uniform Shell Designs 393
10.10.3 Koshal Designs 393
10.10.4 Hoke Designs 394
10.11 Blocking Response Surface Designs 394
10.11.1 Blocking Central Composite Designs 394
10.11.2 Blocking Box烹ehnken Designs 396
10.11.3 Blocking Other Response Surface 396
Designs
10.12 Comparison of Designs 397
10.13 Analyzing the Fitted Surface 398
10.13.1 Characterization of Stationary 401
Points
10.13.2 Confidence Regions on Stationary 402
Points
10.13.3 Ridge Analysis 403
10.13.3.1 Ridge Analysis with Noise 404
Factors
10.13.4 Optimum Conditions and Regions of 404
Operability
10.14 Response Surface Designs for Computer 404
Simulations
10.15 ANOM with Response Surface Designs? 405
10.16 Further Reading 405
10.17 The Present and Future Direction of 406
Response Surface Designs
10.18 Software 406
10.19 Catalogs of Designs 408
10.20 Summary 408
References 409
Exercises 414
11 Repeated Measures Designs 425
11.1 One Factor 426
11.1.1 The Example in Section 2.1.2 428
11.2 More Than One Factor 428
11.3 Crossover Designs 429
11.4 Designs for Carryover Effects 432
11.5 How Many Repeated Measures? 437
11.6 Further Reading 438
11.7 Software 438
11.8 Summary 439
References 439
Exercises 444
12 Multiple Responses 447
12.1 Overlaying Contour Plots 448
12.2 Seeking Multiple Response Optimization 449
with Desirability Functions
12.2.1 Weight and Importance 451
12.3 Dual Response Optimization 452
12.4 Designs Used with Multiple Responses 452
12.5 Applications 453
12.6 Multiple Response Optimization 463
Variations
12.7 The Importance of Analysis 469
12.8 Software 469
12.9 Summary 471
References 472
Exercises 474
13 Miscellaneous Design Topics 483
13.1 One-Factor-at-a-Time Designs 483
13.2 Cotter Designs 487
13.3 Rotation Designs 488
13.4 Screening Designs 489
13.4.1 Plackett烹urman Designs 489
13.4.1.1 Projection Properties of 493
Plackett烹urman Designs
13.4.1.2 Applications 494
13.4.2 Supersaturated Designs 498
13.4.2.1 Applications 499
13.4.3 Lesser-Known Screening Designs 500
13.5 Design of Experiments for Analytic 500
Studies
13.6 Equileverage Designs 501
13.6.1 One Factor, Two Levels 502
13.6.2 Are Commonly Used Designs 502
Equileverage?
13.7 Optimal Designs 503
13.7.1 Alphabetic Optimality 504
13.7.2 Applications of Optimal Designs 507
13.8 Designs for Restricted Regions of 508
Operability
13.9 Space-Filling Designs 514
13.9.1 Uniform Designs 515
13.9.1.1 From Raw Form to Coded Form 518
13.9.2 Sphere-Packing Designs 518
13.9.3 Latin Hypercube Design 519
13.10 Trend-Free Designs 521
13.11 Cost-Minimizing Designs 522
13.12 Mixture Designs 522
13.12.1 Optimal Mixture Designs or Not? 523
13.12.2 ANOM 523
13.13 Design of Measurement Capability 523
Studies
13.14 Design of Computer Experiments 523
13.15 Design of Experiments for Categorical 524
Response Variables
13.16 Weighing Designs and Calibration 524
Designs
13.16.1 Calibration Designs 525
13.16.2 Weighing Designs 526
13.17 Designs for Assessing the Capability 528
of a System
13.18 Designs for Nonlinear Models 528
13.19 Model-Robust Designs 528
13.20 Designs and Analyses for Non-normal 529
Responses
13.21 Design of Microarray Experiments 529
13.22 Multi-Vari Plot 530
13.23 Evolutionary Operation 531
13.24 Software 531
13.25 Summary 532
References 533
Exercises 542
14 Tying It All Together 544
14.1 Training for Experimental Design Use 544
References 545
Exercises 546
Answers to Selected Exercises 551
Appendix: Statistical Tables 565
Author Index 575
Subject Index 587