اسم المؤلف
John Lawson
التاريخ
11 يناير 2022
المشاهدات
348
التقييم
(لا توجد تقييمات)

Design and Analysis of Experiments with SAS
Texts in Statistical Science
John Lawson
Brigham Young University
Provo, Utah, U.S.A.
Contents
Preface xi
1 Introduction 1
1.1 Statistics and Data Collection 1
1.2 Beginnings of Statistically Planned Experiments 2
1.3 Definitions and Preliminaries 2
1.4 Purposes of Experimental Design 5
1.5 Types of Experimental Designs 6
1.6 Planning Experiments 7
1.7 Performing the Experiments 9
1.8 Use of SAS Software 11
1.9 Review of Important Concepts 12
1.10 Exercises 14
2 Completely Randomized Designs with One Factor 15
2.1 Introduction 15
2.2 Replication and Randomization 15
2.3 A Historical Example 18
2.4 Linear Model for CRD 19
2.5 Verifying Assumptions of the Linear Model 27
2.6 Analysis Strategies When Assumptions Are Violated 30
2.7 Determining the Number of Replicates 37
2.8 Comparison of Treatments after the F -Test 41
2.9 Review of Important Concepts 48
2.10 Exercises 50
3 Factorial Designs 53
3.1 Introduction 53
3.2 Classical One at a Time versus Factorial Plans 53
3.3 Interpreting Interactions 55
3.4 Creating a Two-Factor Factorial Plan in SAS 58
3.5 Analysis of a Two-Factor Factorial in SAS 60
3.6 Factorial Designs with Multiple Factors – CRFD 80
3.7 Two-Level Factorials 86
3.8 Verifying Assumptions of the Model 102
3.9 Review of Important Concepts 106
viiviii CONTENTS
3.10 Exercises 108
3.11 Appendix{SAS Macro for Tukey’s Single df Test 112
4 Randomized Block Designs 115
4.1 Introduction 115
4.2 Creating an RCB in SAS 116
4.3 Model for RCB 119
4.4 An Example of an RCB 121
4.5 Determining the Number of Blocks 124
4.6 Factorial Designs in Blocks 125
4.7 Generalized Complete Block Design 128
4.8 Two Block Factors LSD 131
4.9 Review of Important Concepts 138
4.10 Exercises 140
4.11 Appendix{Data from Golf Experiment 145
5 Designs to Study Variances 147
5.1 Introduction 147
5.2 Random Factors and Random Sampling Experiments 148
5.3 One-Factor Sampling Designs 150
5.4 Estimating Variance Components 151
5.5 Two-Factor Sampling Designs 161
5.6 Nested Sampling Experiments (NSE) 170
5.7 Staggered Nested Designs 173
5.8 Designs with Fixed and Random Factors 179
5.9 Graphical Methods to Check Model Assumptions 186
5.10 Review of Important Concepts 194
5.11 Exercises 196
5.12 Appendix 198
6 Fractional Factorial Designs 199
6.1 Introduction 199
6.2 Half-Fractions of 2k Designs 200
6.3 Quarter and Higher Fractions of 2k Designs 209
6.4 Criteria for Choosing Generators for 2k−p Designs 211
6.5 Augmenting Fractional Factorials 222
6.6 Plackett-Burman (PB) Screening Designs 232
6.7 Mixed Level Factorials and Orthogonal Arrays (OA) 238
6.8 Review of Important Concepts 246
6.9 Exercises 248
7 Incomplete and Confounded Block Designs 255
7.1 Introduction 255
7.2 Balanced Incomplete Block (BIB) Designs 256
7.3 Analysis of Incomplete Block Designs 25
CONTENTS ix
7.4 PBIB-BTIB Designs 261
7.5 Youden Square Designs (YSD) 265
7.6 Confounded 2k and 2k−p Designs 266
7.7 Confounding 3 Level and p Level Factorial Designs 280
7.8 Blocking Mixed-Level Factorials and OAs 283
7.9 Partially Confounded Blocked Factorial (PCBF) 290
7.10 Review of Important Concepts 295
7.11 Exercises 298
8 Split-Plot Designs 301
8.1 Introduction 301
8.2 Split-Plot Experiments with CRD in Whole Plots CRSP 302
8.3 RCB in Whole Plots RBSP 309
8.4 Analysis Unreplicated 2k Split-Plot Designs 318
8.5 2k−p Fractional Factorials in Split Plots (FFSP) 324
8.6 Sample Size and Power Issues for Split-Plot Designs 338
8.7 Review of Important Concepts 339
8.8 Exercises 341
9 Crossover and Repeated Measures Designs 347
9.1 Introduction 347
9.2 Crossover Designs (COD) 347
9.3 Simple AB, BA Crossover Designs for Two Treatments 348
9.4 Crossover Designs for Multiple Treatments 358
9.5 Repeated Measures Designs 364
9.6 Univariate Analysis of Repeated Measures Design 365
9.7 Review of Important Concepts 374
9.8 Exercises 376
10 Response Surface Designs 381
10.1 Introduction 381
10.2 Fundamentals of Response Surface Methodology 381
10.3 Standard Designs for Second Order Models 385
10.4 Creating Standard Designs in SAS 392
10.5 Non-Standard Response Surface Designs 395
10.6 Fitting the Response Surface Model with SAS 403
10.7 Determining Optimum Operating Conditions 410
10.8 Blocked Response Surface (BRS) Designs 421
10.9 Response Surface Split-Plot (RSSP) Designs 424
10.10 Review of Important Concepts 435
10.11 Exercises 437
11 Mixture Experiments 443
11.1 Introduction 443
11.2 Models and Designs for Mixture Experiments 445
11.3 Creating Mixture Designs in SAS 452
11.4 Analysis of Mixture Experiment 454
11.5 Constrained Mixture Experiments 461
11.6 Blocking Mixture Experiments 470
11.7 Mixture Experiments with Process Variables 475
11.8 Mixture Experiments in Split-Plot Arrangements 484
11.9 Review of Important Concepts 487
11.10 Exercises 489
11.11 Appendix{Example of Fitting Independent Factors 498
12 Robust Parameter Design Experiments 501
12.1 Introduction 501
12.2 Noise-Sources of Functional Variation 502
12.3 Product Array Parameter Design Experiments 504
12.4 Analysis of Product Array Experiments 512
12.5 Single Array Parameter Design Experiments 529
12.6 Joint Modeling of Mean and Dispersion Effects 538
12.7 Review of Important Concepts 545
12.8 Exercises 547
13 Experimental Strategies for Increasing Knowledge 555
13.1 Introduction 555
13.2 Sequential Experimentation 555
13.3 One Step Screening and Optimization 559
13.4 Evolutionary Operation 560
13.5 Concluding Remarks 562
Bibliography 565
Index 57

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