Author | Goos, Peter. author |
---|---|

Title | The Optimal Design of Blocked and Split-Plot Experiments [electronic resource] / by Peter Goos |

Imprint | New York, NY : Springer New York : Imprint: Springer, 2002 |

Connect to | http://dx.doi.org/10.1007/978-1-4613-0051-9 |

Descript | XIII, 264 p. online resource |

SUMMARY

This book provides a comprehensive treatment of the design of blocked and split-plot experiments, two types of experiments that are extremely popular in practice. The traget audience includes applied statisticians and academics. The optial design approach advocated in the book will help applied statisticians from industry, medicine, agriculture, chemistry, and many other fields of study in setting up tailor-made experiments. This is illustrated by a number of examples. The book also contains a theoretical background, a thorough review of the recent work in the area of blocked and split-plot experiments, and a number of interesting theoretical results

CONTENT

1 Introduction -- 1.1 A practical design problem -- 1.2 Analysis of experiments -- 1.3 Design of experiments -- 1.4 Optimal designs -- 1.5 Standard response surface designs -- 1.6 Categorical designs -- 1.7 The D-optimality criterion -- 1.8 Updating the information matrix, its inverse and its determinant -- 1.9 Constructing discrete D-optimal designs -- 2 Advanced Topics in Optimal Design -- 2.1 Heterogeneous variance -- 2.2 Correlated observations -- 2.3 Blocking experiments -- 3 Compound Symmetric Error Structure -- 3.1 Restricted randomization -- 3.2 Model -- 3.3 Analysis -- 3.4 Information matrix -- 3.5 Equivalence of OLS and GLS -- 3.6 Small sample properties of the design criterion -- 4 Optimal Designs in the Presence of Random Block Effects -- 4.1 Introduction -- 4.2 The random block effects model -- 4.3 Optimal designs that do not depend on ? -- 4.4 Optimal designs when ? ? + ? -- 4.5 The general case -- 4.6 Computational results -- 4.7 Pastry dough mixing experiment. -- 4.8 More than three factor levels -- 4.9 Efficiency of blocking -- 4.10 Optimal number of blocks and block sizes -- 4.11 Optimality of orthogonal blocking -- Appendix A. Design construction algorithm -- Appendix B. Adjustment algorithm -- 5 Optimal Designs for Quadratic Regression on One Variable and Blocks of Size Two -- 5.1 Introduction -- 5.2 Optometry experiment -- 5.3 Model -- 5.4 Continuous D-optimal designs -- 5.5 Exact D-optimal designs -- 5.6 Discussion -- 6 Constrained Split-Plot Designs -- 6.1 Introduction -- 6.2 Model -- 6.3 Analysis of a split-plot experiment -- 6.4 Design of a split-plot experiment -- 6.5 Some theoretical results -- 6.6 Design construction algorithm -- 6.7 Computational results -- 6.8 The protein extraction experiment -- 6.9 Algorithm evaluation -- 6.10 Cost efficiency and statistical efficiency -- Appendix A. Optimality of crossed split-plot designs -- Appendix B. V-optimality of 2m and 2mโ{128}{147}f designs -- Appendix C. The construction algorithm -- Appendix D. Estimated expected efficiency -- 7 Optimal Split-Plot Designs in the Presence of Hard-to-Change Factors -- 7.1 Introduction -- 7.2 Model -- 7.3 Design construction algorithm -- 7.4 Computational results -- Appendix A. The construction algorithm -- Appendix B. Saturated designs with correlated observations -- 8 Optimal Split-Plot Designs -- 8.1 Introduction -- 8.2 Increasing the number of level changes -- 8.3 Design construction -- 8.4 Computational results -- 8.5 Discussion -- Appendix. The construction algorithm -- 9 Two-Level Factorial and Fractional Factorial Designs -- 9.1 Introduction -- 9.2 Blocking 2m and 2mโ{128}{147}f factorial designs -- 9.3 2m and 2mโ{128}{147}f split-plot designs -- 9.4 Discussion -- 10 Summary and Future Research

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