The construction of exact D-optimum experimental designs with application to blocking response surface designs

Anthony C. Atkinson · Alexander N. Donev

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

Abstract

The properties of optimum designs are investigated when there are both qualitative and quantitative factors. Algorithms for the construction of exact designs are described, which are of general applicability. The case when the qualitative factors represent blocking variabes is given special treatment; a modified algorithm provides the opportunity to divide the experimental trials into blocks of specified sizes. Examples are given of second-order models in the quantitative factors divided into two or three blocks of a variety of sizes. Use of the adjustment algorithm to improve such designs generated from a list of candidate points is demonstrated.

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2000An Algorithm for the Construction of "D-Optimal" Experimental Designs 1980A Comparison of Algorithms for Constructing Exact D-Optimal Designs 1972Results in the Theory and Construction of D -Optimum Experimental Designs 1957MULTIFACTOR EXPERIMENTAL DESIGN FOR EXPLORING THE RESPONSE SURFACES 1988Response-Surface Designs for Quantitative and Qualitative Variables 1982Branch-and-Bound Search for Experimental Designs Based onDOptimality and Other Criteria 1974Planning Experiments for Discriminating between Models 1980Time- and Space-Saving Computer Methods, Related to Mitchell's DETMAX, for Finding D-Optimum Designs

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1989Computer-Aided Blocking of Factorial and Response-Surface Designs 2002Optimal Split-Plot Designs 2001Multistratum Response Surface Designs 2004Outperforming Completely Randomized Designs 2001Optimal Split-Plot Designs 2020A-optimal versus D-optimal design of screening experiments

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