Author | Goos, Peter. author |
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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 |
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 2mโf 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 2mโf factorial designs -- 9.3 2m and 2mโf split-plot designs -- 9.4 Discussion -- 10 Summary and Future Research