Computer Construction of "D-Optimal" First-Order Designs

Toby J. Mitchell

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Optimal Experimental Design Methods Simulation Techniques and Applications Advanced Statistical Methods and Models

Abstract

This paper presents the results of a study in which the computer algorithm DETMAX was used for the purpose of constructing n-run “D-optimal” designs over a cubic region of interest for the first-order model E(y) = β0 + β0 x 1 + … + β p x p . These results suggest some general “rules” (actually conjectures) for the construction of such designs. For p ≤ 9, all but 12 combinations of n and p are covered by these “rules;” the 12 exceptions are discussed separately. The resolution IV designs obtained by folding over these “D-optimal” first-order designs are also discussed and are shown to compare favorably with designs previously published.

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References

1951On the Experimental Attainment of Optimum Conditions 1946THE DESIGN OF OPTIMUM MULTIFACTORIAL EXPERIMENTS 1992On the Experimental Attainment of Optimum Conditions 1970The Sequential Generation of $D$-Optimum Experimental Designs 2000The 2 k-p Fractional Factorial Designs Part I 1961The 2 k-p Fractional Factorial Designs Part I 1958On the Nonrandomized Optimality and Randomized Nonoptimality of Symmetrical Designs 1971Factorial Designs, the |X′X| Criterion, and Some Related Matters

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1980Time- and Space-Saving Computer Methods, Related to Mitchell's DETMAX, for Finding D-Optimum Designs 1980$D$-Optimum Weighing Designs 2004Comparison of designs for computer experiments 1982Developments in the Design of Experiments, Correspondent Paper 1994Algorithm AS 295: A Fedorov Exchange Algorithm for D-Optimal Design 2005Large Factorial Designs for Product Engineering and Marketing Research Applications

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