Statistics for Experimenters

GEORGE E. P. BOX, PhD, DSc, is Ronald Aylmer Fisher Professor Emeritus of Statistics and Industrial Engineering at the University of Wisconsin–Madison. He is a Fellow of the Royal Society, an Honorary Fellow and Shewhart and Deming Medalist of the American Society for Quality and was awarded the Guy Medal in Gold of the Royal Statistical Society. He is also the recipient of the Samuel S. Wilks Memorial Medal of the American Statistical Association. J. STUART HUNTER, PhD, DSc, is Professor Emeritus of Civil Engineering at Princeton University. Dr. Hunter is a member of the National Academy of Engineering and has served as consultant to many industries and government agencies. He has been a staff member of the National Academy of Sciences, Committee on National Statistics; statistician in residence at the University of Wisconsin; and is the founding editor of Technometrics.The late WILLIAM G. HUNTER, PhD, was Professor of Statistics and Engineering at the University of Wisconsin–Madison.

"This is a very well written book that every design engineering and design technician needs to own." (IEEE Electrical Insulation Magazine, May/June 2008) "…very few of our profession would fail to benefit from and enjoy reading it." (Journal of the American Statistical Association, December 2006)"...belongs on the shelf on every industrial statistician. There is much wisdom and depth here, and the improvements embodied in this new edition are substantial enough to recommend it even to those who already possess the first edition." (The American Statistician, November 2006)"...remains one of the essential books in experimental design and analysis...buying the second edition is absolutely worth the effort..." (MAA Reviews, August 18, 2006)"…the new edition is a significant improvement on what was already a classic." (AIChE Journal, July 2006)"Is it really possible to update a well-known, classic textbook and improve it? Yes, it is not only possible but it has been done." (Technometrics, May 2006)"...it often happens that there is no statistician around when you desperately need one - then it may be useful to pull this from your laboratory textbook shelf." (Canadian Journal of Medical Laboratory Science, February 2006)"A very useful and valuable statistics book…highly recommended." (CHOICE, February 2006)"This is an excellent book indeed. Like the first edition, this book will soon become a must for all experimenters and educators/trainers. I would strongly recommend this book to everyone." (Journal of Quality Technology, January 2006)"This text is, undoubtedly, an essential reference for all researchers and an invaluable course book for undergraduate and graduate students." (Mathematical Reviews, 20006b)"...this is a welcome second edition of a much loved book...valuable..." (International Statistical Institute, January 2006)

• Preface to the Second Edition xvChapter 1 Catalyzing the Generation of Knowledge 11.1. The Learning Process 11.2. Important Considerations 51.3. The Experimenter’s Problem and Statistical Methods 61.4. A Typical Investigation 91.5. How to Use Statistical Techniques 13References and Further Reading 14Chapter 2 Basics (Probability, Parameters, and Statistics) 172.1. Experimental Error 172.2. Distributions 182.3. Statistics and Parameters 232.4. Measures of Location and Spread 242.5. The Normal Distribution 272.6. Normal Probability Plots 332.7. Randomness and Random Variables 342.8. Covariance and Correlation as Measures of Linear Dependence 372.9. Student’s t Distribution 392.10. Estimates of Parameters 432.11. Random Sampling from a Normal Population 442.12. The Chi-Square and F Distributions 462.13. The Binomial Distribution 482.14. The Poisson Distribution 54Appendix 2A. Mean and Variance of Linear Combinations of Observations 57References and Further Reading 60Chapter 3 Comparing Two Entities: Reference Distributions, Tests, and Confidence Intervals 673.1. Relevant Reference Sets and Distributions 673.2. Randomized Paired Comparison Design: Boys’ Shoes Example 813.3. Blocking and Randomization 923.4. Reprise: Comparison, Replication, Randomization, and Blocking in Simple Experiments 943.5. More on Significance Tests 943.6. Inferences About Data that are Discrete: Binomial Distribution 1053.7. Inferences about Frequencies (Counts Per Unit): The Poisson Distribution 1103.8. Contingency Tables and Tests of Association 112Appendix 3A. Comparison of the Robustness of Tests to Compare Two Entities 117Appendix 3B. Calculation of reference distribution from past data 120References and Further Reading 123Chapter 4 Comparing a Number of Entities, Randomized Blocks, and Latin Squares 1334.1. Comparing k Treatments in a Fully Randomized Design 1334.2. Randomized Block Designs 1454.3. A Preliminary Note on Split-Plot Experiments and their Relationship to Randomized Blocks 1564.4. More than one blocking component: Latin Squares 1574.5. Balanced Incomplete Block Designs 162Appendix 4A. The Rationale for the Graphical Anova 166Appendix 4B. Some Useful Latin Square, Graeco–Latin Square, and Hyper-Graeco–Latin Square Designs 167References and Further Reading 168Chapter 5 Factorial Designs at Two Levels 1735.1. Introduction 1735.2. Example 1: The Effects of Three Factors (Variables) on Clarity of Film 1745.3. Example 2: The Effects of Three Factors on Three Physical Properties of a Polymer Solution 1755.4. A 23 Factorial Design: Pilot Plant Investigation 1775.5. Calculation of Main Effects 1785.6. Interaction Effects 1815.7. Genuine Replicate Runs 1835.8. Interpretation of Results 1855.9. The Table of Contrasts 1865.10. Misuse of the ANOVA for 2k Factorial Experiments 1885.11. Eyeing the Data 1905.12. Dealing with More Than One Response: A Pet Food Experiment 1935.13. A 24 Factorial Design: Process Development Study 1995.14. Analysis Using Normal and Lenth Plots 2035.15. Other Models for Factorial Data 2085.16. Blocking the 2k Factorial Designs 2115.17. Learning by Doing 2155.18. Summary 219Appendix 5A. Blocking Larger Factorial Designs 219Appendix 5B. Partial Confounding 221References and Further Reading 222Chapter 6 Fractional Factorial Designs 2356.1. Effects of Five Factors on Six Properties of Films in Eight Runs 2356.2. Stability of New Product, Four Factors in Eight Runs, a 24−1 Design 2366.3. A Half-Fraction Example: The Modification of a Bearing 2396.4. The Anatomy of the Half Fraction 2406.5. The 2III 7−4 Design: A Bicycle Example 2446.6. Eight-Run Designs 2466.7. Using Table 6.6: An Illustration 2476.8. Sign Switching, Foldover, and Sequential Assembly 2496.9. An Investigation Using Multiple-Column Foldover 2526.10. Increasing Design Resolution from III to IV by Foldover 2576.11. Sixteen-Run Designs 2586.12. The 25−1 Nodal Half Replicate of the 25 Factorial: Reactor Example 2596.13. The 2IV 8−4 Nodal Sixteenth Fraction of a 28 Factorial 2636.14. The 2 III 15−11 Nodal Design: the Sixty-fourth Fraction of the 215 Factorial 2666.15. Constructing Other Two-Level Fractions 2696.16. Elimination of Block Effects 271References and Further Reading 273Chapter 7 Additional Fractionals and Analysis 2817.1. Plackett and Burman Designs 2817.2. Choosing Follow-Up Runs 2947.3. Justifications for the Use of Fractionals 303Appendix 7A. Technical Details 305Appendix 7B. An Approximate Partial Analysis for PB Designs 308Appendix 7C. Hall’s Orthogonal Designs 310References and Further Reading 313Chapter 8 Factorial Designs and Data Transformation 3178.1. A Two-Way (Factorial) Design 3178.2. Simplification and Increased Sensitivity from Transformation 320Appendix 8A. Rationale for Data Transformation 329Appendix 8B. Bartlett’s χν2 for Testing Inhomogeneity of Variance 329References and Further Reading 329Chapter 9 Multiple Sources of Variation 3359.1. Split-Plot Designs, Variance Components, and Error Transmission 3359.2. Split-Plot Designs 3359.3. Estimating Variance Components 3459.4. Transmission of Error 353References and Further Reading 359Chapter 10 Least Squares and Why We Need Designed Experiments 36310.1. Estimation With Least Squares 36410.2. The Versatility of Least Squares 37810.3. The Origins of Experimental Design 39710.4. Nonlinear Models 407Appendix 10A. Vector Representation of Statistical Concepts 410Appendix 10B. Matrix Version of Least Squares 416Appendix 10C. Analysis of Factorials, Botched and Otherwise 418Appendix 10D. Unweighted and Weighted Least Squares 420References and Further Reading 424Chapter 11 Modeling, Geometry, and Experimental Design 43711.1. Some Empirical Models 44111.2. Some Experimental Designs and the Design Information Function 44711.3. Is the Surface Sufficiently Well Estimated? 45311.4. Sequential Design Strategy 45411.5. Canonical Analysis 46111.6. Box–Behnken Designs 475References and Further Reading 483Chapter 12 Some Applications of Response Surface Methods 48912.1. Iterative Experimentation To Improve a Product Design 48912.2. Simplification of a Response Function by Data Transformation 50312.3. Detecting and Exploiting Active and Inactive Factor Spaces for Multiple-Response Data 50912.4. Exploring Canonical Factor Spaces 51312.5. From Empiricism to Mechanism 51812.6. Uses of RSM 526Appendix 12A. Average Variance of ŷ 526Appendix 12B. 528References and Further Reading 530Chapter 13 Designing Robust Products and Processes: An Introduction 53913.1. Environmental Robustness 53913.2. Robustness To Component Variation 549Appendix 13A. A Mathematical Formulation for Environmental Robustness 556Appendix 13B. Choice of Criteria 558References and Further Reading 559Chapter 14 Process Control, Forecasting, and Time Series: An Introduction 56514.1. Process Monitoring 56514.2. The Exponentially Weighted Moving Average 56914.3. The CuSum Chart 57414.4. Process Adjustment 57614.5. A Brief Look At Some Time Series Models and Applications 58514.6. Using a Model to Make a Forecast 58814.7. Intervention Analysis: A Los Angeles Air Pollution Example 593References and Further Reading 595Chapter 15 Evolutionary Process Operation 59915.1. More than One Factor 60215.2. Multiple Responses 60615.3. The Evolutionary Process Operation Committee 607References and Further Reading 608Appendix Tables 611Author Index 625Subject Index 629