Textbook

# Design and Analysis of Experiments, 9th Edition

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Design and Analysis of Experiments, 9th Edition

continues to help senior and graduate students in engineering, business, and statistics-as well as working practitioners-to design and analyze experiments for improving the quality, efficiency and performance of working systems.

This bestselling text maintains its comprehensive coverage by including: new examples, exercises, and problems (including in the areas of biochemistry and biotechnology); new topics and problems in the area of response surface; new topics in nested and split-plot design; and the residual maximum likelihood method is now emphasized throughout the book.

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Preface iii

1 Introduction 1

1.1 Strategy of Experimentation 1

1.2 Some Typical Applications of Experimental Design 8

1.3 Basic Principles 12

1.4 Guidelines for Designing Experiments 14

1.5 A Brief History of Statistical Design 21

1.6 Summary: Using Statistical Techniques in Experimentation 23

1.7 Problems 24

2 Simple Comparative Experiments 26

2.1 Introduction 27

2.2 Basic Statistical Concepts 27

2.3 Sampling and Sampling Distributions 31

2.4 Inferences About the Differences in Means, Randomized Designs 37

2.5 Inferences About the Differences in Means, Paired Comparison Designs 55

2.6 Inferences About the Variances of Normal Distributions 59

2.7 Problems 61

3 Experiments with a Single Factor: The Analysis of Variance 69

3.1 An Example 70

3.2 The Analysis of Variance 72

3.3 Analysis of the Fixed Effects Model 74

3.5 Practical Interpretation of Results 94

3.6 Sample Computer Output 106

3.7 Determining Sample Size 110

3.8 Other Examples of Single-Factor Experiments 113

3.9 The Random Effects Model 120

3.10 The Regression Approach to the Analysis of Variance 129

3.11 Nonparametric Methods in the Analysis of Variance 133

3.12 Problems 135

4 Randomized Blocks, Latin Squares, and Related Designs 145

4.1 The Randomized Complete Block Design 145

4.2 The Latin Square Design 164

4.3 The Graeco-Latin Square Design 172

4.4 Balanced Incomplete Block Designs 174

4.5 Problems 184

5 Introduction to Factorial Designs 192

5.1 Basic Definitions and Principles 192

5.2 The Advantage of Factorials 196

5.3 The Two-Factor Factorial Design 197

5.4 The General Factorial Design 215

5.5 Fitting Response Curves and Surfaces 220

5.6 Blocking in a Factorial Design 229

5.7 Problems 234

6 The 2k Factorial Design 244

6.1 Introduction 244

6.2 The 22 Design 245

6.3 The 23 Design 254

6.4 The General 2k Design 268

6.5 A Single Replicate of the 2k Design 270

6.6 Additional Examples of Unreplicated 2k Designs 285

6.7 2k Designs are Optimal Designs 297

6.8 The Addition of Center Points to the 2k Design 302

6.9 Why We Work with Coded Design Variables 308

6.10 Problems 310

7 Blocking and Confounding in the 2k Factorial Design 326

7.1 Introduction 326

7.2 Blocking a Replicated 2k Factorial Design 327

7.3 Confounding in the 2k Factorial Design 329

7.5 Another Illustration of Why Blocking Is Important 337

7.8 Partial Confounding 342

7.9 Problems 344

8 Two-Level Fractional Factorial Designs 347

8.1 Introduction 348

8.2 The One-Half Fraction of the 2k Design 348

8.3 The One-Quarter Fraction of the 2k Design 364

8.4 The General 2k−p Fractional Factorial Design 371

8.5 Alias Structures in Fractional Factorials and Other Designs 380

8.6 Resolution III Designs 382

8.7 Resolution IV and V Designs 397

8.8 Supersaturated Designs 405

8.9 Summary 406

8.10 Problems 407

9 Additional Design and Analysis Topics for Factorial and Fractional Factorial Designs 426

9.1 The 3k Factorial Design 427

9.2 Confounding in the 3k Factorial Design 435

9.3 Fractional Replication of the 3k Factorial Design 441

9.4 Factorials with Mixed Levels 445

9.5 Nonregular Fractional Factorial Designs 448

9.6 Constructing Factorial and Fractional Factorial Designs Using an Optimal Design Tool 467

9.7 Problems 480

10 Fitting Regression Models (online at www.wiley.com/college[BCS site]) 486

10.1 Introduction 487

10.2 Linear Regression Models 487

10.3 Estimation of the Parameters in Linear Regression Models 488

10.4 Hypothesis Testing in Multiple Regression 500

10.5 Confidence Intervals in Multiple Regression 505

10.6 Prediction of New Response Observations 506

10.7 Regression Model Diagnostics 507

10.8 Testing for Lack of Fit 511

10.9 Problems 513

11 Response Surface Methods and Designs 517

11.1 Introduction to Response Surface Methodology 518

11.2 The Method of Steepest Ascent 520

11.3 Analysis of a Second-Order Response Surface 525

11.4 Experimental Designs for Fitting Response Surfaces 539

11.5 Experiments with Computer Models 565

11.6 Mixture Experiments 573

11.7 Evolutionary Operation 585

11.8 Problems 590

12 Robust Parameter Design and Process Robustness Studies (online at www.wiley.com/college[BCS site]) 601

12.1 Introduction 601

12.2 Crossed Array Designs 603

12.3 Analysis of the Crossed Array Design 606

12.4 Combined Array Designs and the Response Model Approach 608

12.5 Choice of Designs 615

12.6 Problems 618

13 Experiments with Random Factors 622

13.1 Random Effects Models 622

13.2 The Two-Factor Factorial with Random Factors 623

13.3 The Two-Factor Mixed Model 630

13.4 Rules for Expected Mean Squares 635

13.5 Approximate F-Tests 639

13.6 Some Additional Topics on Estimation of Variance Components 643

13.7 Problems 648

14 Nested and Split-Plot Designs 652

14.1 The Two-Stage Nested Design 653

14.2 The General m-Stage Nested Design 663

14.3 Designs with Both Nested and Factorial Factors 665

14.4 The Split-Plot Design 669

14.5 Other Variations of the Split-Plot Design 676

14.6 Problems 686

15 Other Design and Analysis Topics (online at www.wiley.com/college[BCS site]) 692

15.1 Nonnormal Responses and Transformations 693

15.2 Unbalanced Data in a Factorial Design 702

15.3 The Analysis of Covariance 706

15.4 Repeated Measures 729

15.5 Problems 731

Appendix (online at www.wiley.com/college[BCS site]) 000

Table I. Cumulative Standard Normal Distribution 000

Table II. Percentage Points of the t Distribution 000

Table III. Percentage Points of the 𝜒

2 Distribution 000

Table IV. Percentage Points of the F Distribution 000

Table V. Percentage Points of the Studentized Range Statistic 000

Table VI. Critical Values for Dunnett’s Test for Comparing Treatments with a Control 000

Table VII. Coefficients of Orthogonal Polynomials 000

Table VIII. Alias Relationships for 2k−p Fractional Factorial Designs with k ≤ 15 and n ≤ 64 000

Bibliography (online at www.wiley.com/college[BCS site]) 000

Index 000

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## New To This Edition

• 83 new homework problems (including in the areas of biochemistry and biotechnology).
• Additional examples of single-factor experiments, such as a study involving chocolate consumption and cardiovascular health (Chapter 3)
• New section on the random effects model (Chapter 3)
• New material on nonregular fractions as alternatives to traditional abberation fractions in 16 runs and analysis methods for those designs discussed and illustrated.
• New material on constructing factorial and fractional factorial designs using an optimal design tool (Chapter 9).
• New topics and problems in the area of response surface, including designs that combine screening and optimization and use optimal designs (Chapter 11).
• New topics in nested and split-plot design
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• Includes software examples taken from the four most dominant programs in the field: Design-Expert, Minitab, JMP, and SAS.
• Focuses on the connection between the experiment and the model that the experimenter can develop from the results of the experiement.
• Stresses the importance of experimental design as a tool for engineers and scientists to use for product design and development as well as process development and improvement. The use of experiemental design in developing products that are robust to environmental factors and other sources of variability is illustrated. The use of experimental design early in the product cycle can subsatantially reduce development lead time and cost, leading to processes and products that perform better in the field and have higher reliability than those developed using other approaches.
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Design and Analysis of Experiments, 9th Edition
ISBN : 978-1-119-32093-7
752 pages