Design of Experiments: A Realistic Approach / Edition 1

by Virgil L. Anderson, Robert A. McLean

Overview

The book is written for anyone who wants to design experiments, carry them out, and analyze the results. The authors provide a clear-cut, practical approach to designing experiments in any discipline and explain the general principles upon which such design is based. The reader then can apply these theories to any specific problem in his own work.

No advanced mathematics is needed to utilize Design of Experiments – the necessary statistical concepts and briefly reviewed in the first two chapters. Subsequent chapters explain why and how the design of experiments in an intrinsic part of the scientific method, what problems will be encountered by the researcher in setting up his experiment and how to deal with them, and how to accurately analyze the result in terms of the sample taken and the method used. Each chapter includes problems encountered in specific fields so that the reader can test himself on his comprehension of the material. The diversity of the applications that these problems encompass also allows the reader to grasp the basic principles that unite the statistical approach to experiment design.

Researchers and students in engineering, agriculture, pharmacy, veterinary science, chemistry, biology, the social; sciences, statistics, mathematics, or any other field that requires the design, solution, and analysis of problems will find this book absolutely indispensable.

Product Details

ISBN-13:	9780367403454
Publisher:	Taylor & Francis
Publication date:	09/05/2019
Series:	Statistics: A Series of Textbooks and Monographs
Pages:	440
Product dimensions:	6.00(w) x 9.00(h) x (d)

About the Author

Dr. Vigor L. Anderson is a Professor of Statistics at Purdue University and is currently an University Associate with Bayer and McElrath Inc. Management Consultants, Detroit. He has been a statistical consultant to nearly every department at Purdue and to more than 25 industrial organizations, as well as to the Highway Research Board of the National Academy of Sciences. Dr. Anderson’s research interest concerns the application of statistics to various disciplines and he has published widely in diverse technical and scientific journals. He was Director of the NIH Biometry Trainee Program (1957-1971) and of the Statistics and Computing laboratory at Purdue (1956-1966). Dr. Anderson has also taught and organized courses on statistical methods and design of experiments in many industrial organizations. He is a Fellow of the American Statistical Association and a member of numerous professional and honorary societies.

Table of Contents

Problems xi

Preface xiii

1 Review of Some Basic Statistical Concepts 1

1.1 Testing Hypotheses and Sample Size 1

1.2 One Way Classification, Assumptions Met 6

1.2.1 ANOVA Notation and Rationale 12

1.3 Unequal Variances and Transformations in ANOVA 16

1.3.1 Bartlett Test (Equal Subclass Numbers) 20

1.3.2 Bartlett and Kendall log s² ANOVA 21

1.3.3 Burr-Foster Q-Test of Homogeneity 22

1.3.4 Transformation of y 23

1.3.5 Other Transformations 24

1.3.6 Test for Normality 25

1.4 Curve Fitting in One Way Classification 27

1.4.1 Orthogonal Polynomials 28

1.4.2 Lack of Fit Principle 34

1.5 References 38

2 Some Intermediate Data Analysis Concepts 40

2.1 Two Factor Experiments with One Observation Per Cell 41

2.1.1 Both Factors Qualitative 45

2.1.2 One Factor Qualitative and the Other Quantitative 47

2.1.3 Both Factors Quantitative 48

2.1.4 Summary of Section 2.1 51

2.2 Two Factor Experiments with More Than One Observation Per Cell 51

2.2.1 Expected Mean Square Algorithm 52

Example 2.1 Fixed Model 53

Example 2.2 Random Model 56

Example 2.3 Mixed Model 56

Example 2.4 Fixed Model 59

Example 2.5 Fixed Model (More than one observation per cell) 59

Example 2.6 Random Model 60

Example 2.7 Mixed Model (M fixed, T random) 60

2.2.2 ANOVA of Two Way Classification with More Than One Observation Per Cell 62

Example 2.8 Both Qualitative Factors 66

Example 2.9 One Factor Qualitative and One Quantitative 71

Example 2.10 Both Factors Quantitative 73

2.3 References

3 A Scientific Approach to Experimentation 79

3.1 Recognition That a Problem Exists 81

3.2 Formulation of the Problem 82

3.3 Agreeing on Factors and Levels to Be Used in the Experiment 83

3.4 Specifying the Variables to Be Measured 84

3.5 Definition of the Inference Space for the Problem 84

3.6 Random Selection of the Experimental Units 85

3.7 Assignment of Treatments to the Experimental Units 86

3.8 Outline of the Analysis Corresponding to the Design before the Data Are Taken 87

3.9 Collection of the Data 89

3.10 Analysis of the Data 90

3.11 Conclusions 90

3.12 Implementation 91

3.13 Summary 91

3.14 References 93

4 Completely Randomized Design (CRD) 94

4.1 One Factor 94

4.2 More Than One Factor 98

4.2.1 All Fixed Factors 98

Example 4.1 Engineering 105

4.2.2 Some Factors Fixed and Some Random 111

Example 4.2 Engineering 113

4.2.3 All Random Factors 116

4.2.4 Spacing Factor Levels 119

4.3 References 121

5 Randomized Complete Block Design (RCBD) 123

5.1 Blocks Fixed 125

5.1.1 A Medical-Engineering Example 131

5.1.2 RCBD More Than One Observation Per Cell (Example) 132

Example 5.1 Medical 135

5.1.3 RCBD When Interaction Is Present and One Observation Per Cell 137

5.2 Blocks Random 137

Example 5.2 Genetics 142

5.3 Allocation of Experimental Effort in RCBD 143

5.4 Relative Efficiency of Designs 151

5.5 References 153

6 Nested (Hierarchical) and Nested Factorial Designs 154

6.1 Nested (Hierarchical) 154

6.1.1 All Factors Random 154

Example 6.1 Economics 156

Example 6.2 Genetics 159

6.1.2 Fixed and Random Factors 160

6.2 Nested Factorial 162

6.2.1 Cardiac Valve Experiment 163

Example 6.3 Medical 167

6.2.2 Social Science Application 171

6.2.3 Nutrition Application 172

6.2.4 An Application in Ammunition Manufacturing 175

6.3 References 180

7 Split Plot Type Designs 181

7.1 Split Plot Designs 181

Example 7.1 Cardiac Valve 189

Example 7.2 Metallurgy 193

7.2 Split-Split Plot Designs 199

7.3 Regression Analyses from Split Plot Data 206

7.4 References 208

8 Latin Square Type Designs 210

8.1 Latin Square 210

Example 8.1 Engineering 216

8.2 Associated Designs 218

Example 8.2 Pharmacy 219

8.3 References 223

9 2ⁿ Factorial Experiments (Complete and Incomplete Blocks) 225

9.1 Complete Blocks 226

9.1.1 The 2² Factorial 227

9.1.2 The 2³ Factorial 229

9.1.3 The 2ⁿ Factorial 231

Example 9.1 Metallurgy 232

Example 9.2 Metallurgy 237

9.2 Incomplete Block 241

9.2.1 The 2² Factorial 241

9.2.2 The 2³ Factorial 243

9.2.3 General Approach 245

Example 9.3 Animal Science 248

9.3 References 251

10 Fractional Factorial Experiments for Two-Leveled Factors 252

10.1 The 1/2 Replication 253

Example 10.1 Highway Engineering 256

10.2 A More Complicated Design (1/4 Replication) 260

Example 10.2 General 261

10.3 Blocking within the Fractional Replication 268

10.4 Some Other Versions and Developments in Fractional Factorials 270

10.4.1 Parallel Fractional Replicates 270

10.4.2 The 2^n-p Fractional Designs 272

10.4.5 Symmetrical and Asymmetrical Fractional Factorial Plans 272

10.4.4 The 3/4 Fractional Factorial 273

10.4.5 Case When Some Three Factor Interactions Cannot Be Assumed Negligible 275

10.5 General 2ⁿ Problems 277

10.6 References 278

11 Three-Level Factorial Experiments 280

11.1 Confounding in a 3ⁿ System 281

11.1.1 The 3² Factorial 282

11.1.2 Other 3-Leveled Factorial Experiments 284

11.1.3 Method of Confounding 285

11.2 System of Confounding 289

11.2.1 A 3² Factorial Experiment in Blocks of 3 289

11.2.2 Two 3³ Factorial Experiments 291

11.2.3 Two 3⁴ Factorial Experiments 291

11.3 Fractional Replications 293

11.3.1 A 1/3 Replicate of 3⁵ Factorial 293

11.3.2 A General Approach 294

11.4 A Special Use of Fractional Factorials 295

11.5 Special Latin Square Designs as Fractional Factorials 298

11.6 Extension of 3ⁿ to pⁿ, Where p Is a Prime Number 300

11.7 References 301

12 Mixed Factorial Experiments and Other Incomplete Block Designs 302

12.1 Designs for Factorial Experiments with the Number of Levels the Same Prime Power 302

12.1.1 One Factor (To Demonstrate Pseudofactor) 303

12.1.2 Two Factors 304

12.2 Designs in Which the Number of Levels Are Different Prime Numbers 307

12.2.1 Design with 9 Blocks of 4 for the 2 x 2 x 3 x 3 309

12.2.2 Design with 6 Blocks of 6 for the 2 x 2 x 3 x 3 309

12.2.3 Design with 4 Blocks of 9 for the 2 x 2 x 3 x 3 309

12.2.4 Design with 3 Blocks of 12 for the 2 x 2 x 3 x 3 309

12.2.5 Design with 2 Blocks of 18 for the 2 x 2 x 3 x 3 310

12.2.6 A Partially Balanced Incomplete Block Design (Four Replications of 6 Blocks of 6) 310

12.3 Designs That Have the Number of Levels as Products of Prime Numbers 310

Example 12.1 Industrial Engineering 311

12.4 Designs in Which the Pseudofactors Have Different Powers on the Prime Number of Levels 316

12.5 Designs in Which the Number of Levels Are Products of Powers of Prime Numbers 317

12.6 Fractional Mixed Factorials 2^m3ⁿ 317

12.7 Lattice Designs (Pseudofactorial) 319

12.7.1 One-Restrictional Designs 320

12.7.2 Two-Restrictional Designs 323

12.7.3 Designs with More Than Two Restrictions 324

12.8 Additional Incomplete Block Designs 324

12.9 References 325

13 Response Surface Exploration 326

13.1 Fixed Designs 327

13.1.1 Random Balance 327

13.1.2 Systematic Supersaturated 330

13.1.3 Random Method 333

13.1.4 Mixture Designs 335

Example 13.1 Chemical Flare 343

13.1.5 Rotatable Designs 348

13.1.6 Fractional Factorials (Orthogonal) 350

13.1.7 Complete Factorials (Orthogonal) 352

13.1.8 Composite Design 353

13.2 Sequential Designs 361

13.2.1 Univariate Method or One-Factor-at-A-Time 361

13.2.2 Simplex (Sequential) 362

13.2.3 Computer Aided Designs 367

13.2.4 Steepest Ascent Method 370

13.2.5 Canonical Analysis 374

13.2.6 Evolutionary Operation (EVOP) 379

Example 13.2 Steel Manufacturing 380

13.3 References 386

Appendices 388

Author Index 413

Subject Index 415

Editorial Reviews

"Professors Anderson and McLean have done a noteworthy job of writing a text dealing with experiments. . . .a valuable contribution to the experimental design literature and it is strongly recommended for your statistical library. "
—-Journal of Qualtiy Technology
"The authors employ a wide range of examples to illustrate the theory and practice of experimental design. . .For the teacher, the examples analyzed fully and others outlined as problems for the student will prove useful source of ideas. . . .refreshingly different from other texts. "
—-Nature
"The material in this textbook has been thoroughly tested in the classroom by both of the authors. The reviews enthusiastically recommends it for use as a text. . .This book will also serve as valuable reference work for practitioners. "
—-Mathematical Review

From the Publisher