Chapter 1 Introduction. 1
1-1 Strategy of Experimentation
1-2 Some Typical Applications of Experimental Design 8
1-3 Basi Principles 12
1-4 Guidelines for Designing Experiments 1
1-5 A Brief History of Statistical Design 19
1-6 Summary: Using Statistical Techniques in Experimentation 21
1- Problems 22
Chapter 2 Simple Comparative Experiments 23
2-1 Introduction 23
2-2 Basi Statistical Concepts 24
2-3 Sampling and Sampling Distributions 28
2-4 Inferences about the Differences in Means, Randomized Designs 34
2-4.1 Hypothesis Testing 34
2-4.2 Choice of Sample Size 41
2-4.3 Confidence Intervals 43
2-4.4 The Case Where 45
2-4.5 The Case Where and Are Known 45
2-4.6 Comparing a Single Mean to a Specified Value 46
2-4.7 Summary 47
2-5 Inferences about the Differences in Means, Paired Comparison Designs 48
2-5.1 The Paired Comparison Problem 48
2-5.2 Advantages of the Paired Comparison Design 51
2-6 Inferences about the Variances of Normal Distributions 52
2-7 Problems 54
Chapter 3 Experiments with a Single Factor: The Analysis of Variance 60
3-1 An Example 61
3-2 The Analysis of Variance 63
3-3 Analysis of the Fixed Effects Model 65
3-3.1 Decomposition of the Total Sum of Squares 66
3-3.2 Statistical Analysis 68
3-3.3 Estimation of the Model Parameters 73
3-3.4 Unbalanced Data 75
3-4 Model Adequacy Che king 75
3-4.1 The Normality Assumption 76
3-4.2 Plot of Residuals in Time Sequence 78
3-4.3 Plot of Residuals Versus Fitted Values 79
3-4.4 Plots of Residuals Versus Other Variables 84
3-5 Practical Interpretation of Results 85
3-5.1 A Regression Model 85
3-5.2 Comparisons Among Treatment Means 87
3-5.3 Graphical Comparisons of Means 87
3-5.4 Contrasts 88
3-5.5 Orthogonal Contrasts 91
3-5.6 Scheff??s Method for Comparing All Contrasts 93
3-5.7 Comparing Pairs of Treatment Means 94
3-5.8 Comparing Treatment Means withca Control 97
3-6 Sample Computer Output 98
3-7 Determining Sample Size 101
3-7.1 Operating Characteristi Curves 101
3-7.2 Specifying a Standard Deviation In rease 104
3-7.3 Confidence Interval Estimation Method 104
3-8 Dis overing Dispersion Effects 105
3-9 The Regression Approach to the Analysis of Variance 107
3-9.1 Least Squares Estimation of the Model Parameters 107
3-9.2 The General Regression Significance Test 108
3-10 Nonparametri Methods in the Analysis of Variance 110
3-10.1 The KruskalDWallis Test 110
3-10.2 General Comments on the Rank Transformation 112
3-11 Problems 112
Chapter 4 Randomized Blo ks, Latin Squares, and Related Designs 119
4-1 The Randomized Complete Block Design 119
4-1.1 Statistical Analysis of the RCBD 121
4-1.2 Model Adequacy Checking 128
4-1.3 Some Other Aspeccts of the Randomized Complete Block Design 130
4-1.4 Estimating Model Parameters and the General Regression Significance Test 133
4-2 The Latin Square Design 136
4-3 The Graeco-Latin Square Design 142
4-4 Balanced In omplete Block Designs 145
4-4.1 Statistical Analysis of the BIBD 146
4-4.2 Least Squares Estimation of the Parameters 150
4-4.3 Recovery of Interblock Information in the BIBD 152
4-5 Problems 154
Chapter 5 Introduction to Factorial Designs 160
5-1 Basi Definitions and Principles 160
5-2 The Advantage of Factorials 163
5-3 The Two-Factor Factorial Design 164
5-3.1 An Example 164
5-3.2 Statistical Analysis of the Fixed Effects Model 167
5-3.3 Model Adequacy Checking 172
5-3.4 Estimating the Model Parameters 175
5-3.5 Choice of Sample Size 177
5-3.6 The Assumption of No Interaction in a Two-Factor Model 178
5-3.7 One Observation per Cell 179
5-4 The General Factorial Design 182
5-5 Fitting Response Curves and Surfaces 188
5-6 Blocking in a Factorial Design 193
5-7 Problems 197
Chapter 6 The 2k Factorial Design 203
6-1 Introduction 203
6-2 The 22 Design 204
6-3 The 23 Design 211
6-4 The General 2k Design 224
6-5 A Single Replicate of the 2k Design 226
6-6 The Addition of Center Points to the 2k Design 247
6-7 Why We Work with Coded Design Variables 251
6-8 Problems 254
Chapter 7 Blocking and Confounding in the 2k Factorial Design 265
7-1 Introduction 265
7-2 Blocking a Replicated 2k Factorial Design 266
7-3 Confounding in the 2k Factorial Design 266
7-4 Confounding the 2k Factorial Design in Two Blocks 267
7-5 Another Illustration of Why Blocking Is Important 273
7-6 Confounding the 2k Factorial Design in Four Blocks 275
7-7 Confounding the 2k Factorial Design in 2p Blocks 276
7-8 Partial Confounding 278
7-9 Problems 280
Chapter 8 Two-Level Fractional Factorial Designs 282
8-1 Introduction 282
8-2 The One-Half Fraction of the 2k Design 283
8-2.1 Definitions and Basic Principles 283
8-2.2 Design Resolution 285
8-2.3 Construction and Analysis of the One-Half Fraction 286
8-3 The One-Quarter Fraction of the 2k Design 296
8-4 The General 2k2p Fractional Factorial Design 303
8-4.1 Choosing a Design 303
8-4.2 Analysis of 2k2p Fractional Factorials 306
8-4.3 Blocking Fractional Factorials 307
8-5 Resolution III Designs 312
8-5.1 Constructing Resolution III Designs 312
8-5.2 Fold Over of Resolution III Fractions to Separate Aliased Effects 314
8-5.3 PlackettDBurman Designs 319
8-6 Resolution IV and V Designs 322
8-6.1 Resolution IV Designs 322
8-6.2 Sequential Experimentation with Resolution IV Designs 325
8-6.3 Resolution V Designs 331
8-7 Supersaturated Designs 333
8-8 Summary 335
8-9 Problems.. 335
Chapter 9 Three-Level and Mixed-Level Factorial and Fractional Factorial Designs 347
9-1 The 3k Factorial Design 347
9-1.1 Notation and Motivation for the 3k Design 347
9-1.2 The 32 Design 349
9-1.3 The 33 Design 351
9-1.4 The General 3k Design 355
9-2 Confounding in the 3k Factorial Design 356
9-2.1 The 3k Factorial Design in Three Blocks 356
9-2.2 The 3k Factorial Design in Nine Blocks 360
9-2.3 The 3k Fa torial Design in 3p Blocks 360
9-3 Fractional Replication of the 3k Factorial Design 361
9-3.1 The One-Third Fraction of the 3k Factorial Design 361
9-3.2 Other 3k2p Fractional Factorial Designs 364
9-4 Factorials with Mixed Levels 365
9-4.1 Factors at Two and Three Levels 366
9-4.2 Factors at Two and Four Levels 367
9-5 Problems 369
Chapter 10 Fitting Regression Models 373
10-1 Introduction 373
10-2 Linear Regression Models 374
10-3 Estimation of the Parameters in Linear Regression Models 375
10-4 Hypothesis Testing in Multiple Regression 388
10-4.1 Test for Signifi ance of Regression 388
10-4.2 Tests on Individual Regression Coefficients and Groups of Coefficients 390
10-5 Confidence Intervals in Multiple Regression 393
10-5.1 Confidence Intervalscon the Individual Regression Coeffi ients 393
10-5.2 Confidence Interval on the Mean Response 394
10-6 Prediction of New Response Observations 394
10-7 Regression Model Diagnostics 396
10-7.1 Scaled Residuals and PRESS 396
10-7.2 Influence Diagnostics 399
10-8 Testing for Lack of Fit 400
10-9 Problems 401
Chapter 11 Response Surface Methods and Designs 405
11-1 Introduction to Response Surface Methodology 405
11-2 The Method of Steepest Ascent 407
11-3 Analysis of a Second-Order Response Surface 413
11-3.1 Location of the Stationary Point 413
11-3.2 Chara terizing the Response Surface 415
11-3.3 Ridge Systems 422
11-3.4 Multiple Responses 423
11-4 Experimental Designs for Fitting Response Surfaces 427
11-4.1 Designs for Fitting the First-Order Model 428
11-4.2 Designs for Fitting the Second-Order Model 428
11-4.3 Blocking in Response Surface Designs 436
11-4.4 Computer-Generated (Optimal) Designs 439
11-5 Mixture Experiments 444
11-6 Evolutionary Operation 452
11-7 Problems 458
Chapter 12 Robust Parameter Design and Process Robustness Studies 464
12-1 Introduction 464
12-2 Crossed Array Designs 466
12-3 Analysis of the Crossed Array Design 468
12-4 Combined Array Designs and the Response Model Approach 471
12-5 Choice of Designs 477
12-6 Problems 480
Chapter 13 Experiments with Random Factors 484
13-1 The Random Effects Model 485
13-2 The Two-Factor Factorial with Random Factors 490
13-3 The Two-Factor Mixed Model 495
13-4 Sample Size Determination with Random Effects 500
13-5 Rules for Expected Mean Squares 501
13-6 Approximate FcTests 505
13-7 Some Additional Topics on Estimation of Variance Components 511
13-7.1 Approximate Confidence Intervals on Variance Components 511
13-7.2 The Modified Large-Sample Method 514
13-7.3 Maximum Likelihood Estimation of Variance Components 516
13-8 Problems 521
Chapter 14 Nested and Split-Plot Designs 525
14-1 The Two-Stage Nested Design 525
14-1.1 Statistical Analysis 526
14-1.2 Diagnosti Checking 531
14-1.3 Variance Components 532
14-1.4 Staggered Nested Designs 533
14-2 The Generalcm-Stage Nested Design 534
14-3 Designs with Both Nested and Factorial Factors 536
14-4 The Split-Plot Design 540
14-5 Other Variations of the Split-Plot Design 545
14-5.1 Split-Plot Designs with More Than Two Factors 545
14-5.2 The Split-Split-Plot Design 550
14-5.3 The Strip-Split-Plot Design 552
14-6 Problems 554
Chapter 15 Other Design and Analysis Topics 559
15-1 Nonnormal Responses and Transformations 560
15-1.1 Selecting a Transformation: The BoxDCox Method 560
15-1.2 The Generalized Linear Model 563
15-2 Unbalanced Data in a Factorial Design 570
15-2.1 Proportional Data: An Easy Case 571
15-2.2 Approximate Methods 572
15-2.3 The Exa t Method 574
15-3 The Analysis of Covariance 574
15-3.1 Description of the Procedure 576
15-3.2 Computer Solution 583
15-3.3 Development by the General Regression Significance Test 584
15-3.4 Factorial Experiments with Covariates 586
15D4 Repeated Measures 590
15-5 Problems 592
Bibliography 595
Appendix 603
Table I. Cumulative Standard Normal Distribution 604
Table II. Percentage Points of the t Distribution 606
Table III. Percentage Points of the x2 Distribution 607
Table IV. Percentage Points of the F Distribution 608
Table V. Operating Characteristi Curves for the Fixed Effects Model Analysis of Variance 613
Table VI. Operating Characteristi Curves for the Random Effects Model Analysis of Variance 617
Table VII. Percentage Points of the Studentized Range Statisti 621
Table VIII. Critical Values for Dunnett's Test for Comparing Treatments with a Control 623
Table IX. Coefficients of Orthogonal Polynomials 625
Table X. Alias Relationships for 2k-p Fractional Factorial Designs withck≤15 and n≤64 626
Index ...638
鄂公网安备 42010302001612号 