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Design and Analysis of Experiments, Volume 2, Advanced Experimental Design

ISBN: 978-0-471-55177-5
780 pages
April 2005, ©2005
Design and Analysis of Experiments, Volume 2, Advanced Experimental Design (0471551775) cover image
A comprehensive overview of experimental design at the advanced level

The development and introduction of new experimental designs in the last fifty years has been quite staggering and was brought about largely by an ever-widening field of applications. Design and Analysis of Experiments, Volume 2: Advanced Experimental Design is the second of a two-volume body of work that builds upon the philosophical foundations of experimental design set forth half a century ago by Oscar Kempthorne, and features the latest developments in the field.

Volume 1: An Introduction to Experimental Design introduced students at the MS level to the principles of experimental design, including the groundbreaking work of R. A. Fisher and Frank Yates, and Kempthorne's work in randomization theory with the development of derived linear models. Design and Analysis of Experiments, Volume 2 provides more detail about aspects of error control and treatment design, with emphasis on their historical development and practical significance, and the connections between them. Designed for advanced-level graduate students and industry professionals, this text includes coverage of:

  • Incomplete block and row-column designs
  • Symmetrical and asymmetrical factorial designs
  • Systems of confounding
  • Fractional factorial designs, including main effect plans
  • Supersaturated designs
  • Robust design or Taguchi experiments
  • Lattice designs
  • Crossover designs

In order to facilitate the application of text material to a broad range of fields, the authors take a general approach to their discussions. To aid in the construction and analysis of designs, many procedures are illustrated using Statistical Analysis System (SAS®) software.

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Preface.

1. General Incomplete Block Design.

1.1 Introduction and Examples.

1.2 General Remarks on the Analysis of Incomplete Block Designs.

1.3 The Intrablock Analysis.

1.4 Incomplete Designs with Variable Block Size.

1.5 Disconnected Incomplete Block Designs.

1.6 Randomization Analysis.

1.7 Interblock Information in an Incomplete Block Design.

1.8 Combined Intra- and Interblock Analysis.

1.9 Relationships Among Intrablock, Interblock, and Combined Estimation.

1.10 Estimation of Weights for the Combined Analysis.

1.11 Maximum-Likelihood Type Estimation.

1.12 Efficiency Factor of an Incomplete Block Design.

1.13 Optimal Designs.

1.14 Computational Procedures.

2. Balanced Incomplete Block Designs.

2.1 Introduction.

2.2 Definition of the BIB Design.

2.3 Properties of BIB Designs.

2.4 Analysis of BIB Designs.

2.5 Estimation of ρ.

2.6 Significance Tests.

2.7 Some Special Arrangements.

2.8 Resistant and Susceptible BIB Designs.

3. Construction of Balanced Incomplete Block Designs.

3.1 Introduction.

3.2 Difference Methods.

3.3 Other Methods.

3.4 Listing of Existing BIB Designs.

4. Partially Balanced Incomplete Block Designs.

4.1 Introduction.

4.2 Preliminaries.

4.3 Definition and Properties of PBIB Designs.

4.4 Association Schemes and Linear Associative Algebras.

4.5 Analysis of PBIB Designs.

4.6 Classification of PBIB Designs.

4.7 Estimation of ρ for PBIB(2) Designs.

5. Construction of Partially Balanced Incomplete Block Designs.

5.1 Group-Divisible PBIB(2) Designs.

5.2 Construction of Other PBIB(2) Designs.

5.3 Cyclic PBIB Designs.

5.4 Kronecker Product Designs.

5.5 Extended Group-Divisible PBIB Designs.

5.6 Hypercubic PBIB Designs.

6. More Block Designs and Blocking Structures.

6.1 Introduction.

6.2 Alpha Designs.

6.3 Generalized Cyclic Incomplete Block Designs.

6.4 Designs Based on the Successive Diagonalizing Method.

6.5 Comparing Treatments with a Control.

6.6 Row–Column Designs.

7. Two-Level Factorial Designs.

7.1 Introduction.

7.2 Case of Two Factors.

7.3 Case of Three Factors.

7.4 General Case.

7.5 Interpretation of Effects and Interactions.

7.6 Analysis of Factorial Experiments.

8. Confounding in 2n Factorial Designs.

8.1 Introduction.

8.2 Systems of Confounding.

8.3 Composition of Blocks for a Particular System of Confounding.

8.4 Detecting a System of Confounding.

8.5 Using SAS for Constructing Systems of Confounding.

8.6 Analysis of Experiments with Confounding.

8.7 Interblock Information in Confounded Experiments.

8.8 Numerical Example Using SAS.

9. Partial Confounding in 2n Factorial Designs.

9.1 Introduction.

9.2 Simple Case of Partial Confounding.

9.3 Partial Confounding as an Incomplete Block Design.

9.4 Efficiency of Partial Confounding.

9.5 Partial Confounding in a 23 Experiment.

9.6 Partial Confounding in a 24 Experiment.

9.7 General Case.

9.7.1 Intrablock Information.

9.8 Double Confounding.

9.9 Confounding in Squares.

9.10 Numerical Examples Using SAS.

10. Designs with Factors at Three Levels.

10.1 Introduction.

10.2 Definition of Main Effects and Interactions.

10.3 Parameterization in Terms of Main Effects and Interactions.

10.4 Analysis of 3n Experiments.

10.5 Confounding in a 3n Factorial.

10.6 Useful Systems of Confounding.

10.7 Analysis of Confounded 3n Factorials.

10.8 Numerical Example.

11. General Symmetrical Factorial Design.

11.1 Introduction.

11.2 Representation of Effects and Interactions.

11.3 Generalized Interactions.

11.4 Systems of Confounding.

11.5 Intrablock Subgroup.

11.6 Enumerating Systems of Confounding.

11.7 Fisher Plans.

11.8 Symmetrical Factorials and Finite Geometries.

11.9 Parameterization of Treatment Responses.

11.10 Analysis of pn Factorial Experiments.

11.11 Interblock Analysis.

11.12 Combined Intra- and Interblock Information.

11.13 The sn Factorial.

11.14 General Method of Confounding for the Symmetrical Factorial Experiment.

11.15 Choice of Initial Block.

12. Confounding in Asymmetrical Factorial Designs.

12.1 Introduction.

12.2 Combining Symmetrical Systems of Confounding.

12.3 The GC/n Method.

12.4 Method of Finite Rings.

12.5 Balanced Factorial Designs (BFD).

13. Fractional Factorial Designs.

13.1 Introduction.

13.2 Simple Example of Fractional Replication.

13.3 Fractional Replicates for 2n Factorial Designs.

13.4 Fractional Replicates for 3n Factorial Designs.

13.5 General Case of Fractional Replication.

13.6 Characterization of Fractional Factorial Designs of Resolution III, IV, and V.

13.7 Fractional Factorials and Combinatorial Arrays.

13.8 Blocking in Fractional Factorials.

13.9 Analysis of Unreplicated Factorials.

14. Main Effect Plans.

14.1 Introduction.

14.2 Orthogonal Resolution III Designs for Symmetrical Factorials.

14.3 Orthogonal Resolution III Designs for Asymmetrical Factorials.

14.4 Nonorthogonal Resolution III Designs.

15. Supersaturated Designs.

15.1 Introduction and Rationale.

15.2 Random Balance Designs.

15.3 Definition and Properties of Supersaturated Designs.

15.4 Construction of Two-Level Supersaturated Designs.

15.5 Three-Level Supersaturated Designs.

15.6 Analysis of Supersaturated Experiments.

16. Search Designs.

16.1 Introduction and Rationale.

16.2 Definition of Search Design.

16.3 Properties of Search Designs.

16.4 Listing of Search Designs.

16.5 Analysis of Search Experiments.

16.6 Search Probabilities.

17. Robust-Design Experiments.

17.1 Off-Line Quality Control.

17.2 Design and Noise Factors.

17.3 Measuring Loss.

17.4 Robust-Design Experiments.

17.5 Modeling of Data.

18. Lattice Designs.

18.1 Definition of Quasi-Factorial Designs.

18.2 Types of Lattice Designs.

18.3 Construction of One-Restrictional Lattice Designs.

18.4 General Method of Analysis for One-Restrictional Lattice Designs.

18.5 Effects of Inaccuracies in the Weights.

18.6 Analysis of Lattice Designs as Randomized Complete Block Designs.

18.7 Lattice Designs as Partially Balanced Incomplete Block Designs.

18.8 Lattice Designs with Blocks of Size Kl.

18.9 Two-Restrictional Lattices.

18.10 Lattice Rectangles.

18.11 Rectangular Lattices.

18.12 Efficiency Factors.

19. Crossover Designs.

19.1 Introduction.

19.2 Residual Effects.

19.3 The Model.

19.4 Properties of Crossover Designs.

19.5 Construction of Crossover Designs.

19.6 Optimal Designs.

19.7 Analysis of Crossover Designs.

19.8 Comments on Other Models.

Appendix A: Fields and Galois Fields.

Appendix B: Finite Geometries.

Appendix C: Orthogonal and Balanced Arrays.

Appendix D: Selected Asymmetrical Balanced Factorial Designs.

Appendix E: Exercises.

References.

Author Index.

Subject Index.

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KLAUS HINKELMANN, PHD, is Emeritus Professor of Statistics at Virginia Polytechnic Institute and State University Department of Statistics, where he also served as both graduate administrator and department head. In addition to being a Fellow of both the American Statistical Association and the American Association for the Advancement of Science, Professor Hinkelmann is a member of the International Statistical Institute, and has served as a council member of the International Biometric Society. He was editor of Biometrics and the Current Index to Statistics.

OSCAR KEMPTHORNE, SCD, was Emeritus Professor of Statistics and Emeritus Distinguished Professor of Liberal Arts and Sciences at Iowa State University. He was a Fellow of the American Statistical Association, the Institute of Mathematical Statistics, and the American Association for the Advancement of Science, as well as an Honorary Fellow of the Royal Statistical Society and a member of the International Statistical Institute. In addition, Dr. Kempthorne was a past president of the Eastern North American Region (ENAR) of the International Biometric Society, a former chairman of statistics within the American Association for the Advancement of Science, and a past president of the Institute of Mathematical Statistics.

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"…a massively impressive work of scholarship…" (Short Book Reviews, December 2006)

"...a broad and in-depth book...covers not only classic but also up-to-date results and references, making it convenient for researchers. It is one of the very few advanced textbooks on experimental design..." (Technometrics, November 2006)

"I suspect this excellent book will be used most often by specialists in design...the book's importance is largely as a reference for experts...or as an independent learning tool…" (Journal of the American Statistical Association, June 2006)

"I would expect HK to attain essentially the same stature and appeal to virtually the same markets as the 1952 edition." (Journal of Quality Technology, January 2006)

"…the authors have done a commendable job in putting together the vast amount of literature that is available on the topics…of great value to students, and also to teachers and researchers." (Mathematical Reviews, 2006b)

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