The Usefulness of Optimum Experimental Designs

Abstract

SUMMARY Optimum experimental designs were originally developed by Kiefer, mainly for response surface models. This survey of recent developments emphasizes potential or actual usefulness. For linear models the construction of exact designs, particularly over irregular design regions, is stressed, as is the blocking of response surface designs. Other important areas include systematic designs that are robust against trend and designs for mixtures with irregular design regions: several industrial examples are mentioned. Both D- and c-optimum designs are found for a non-linear model of the economic response of cereal production to fertilizer level, the c-optimum design being for the conditions of maximum economic return. Locally optimum and Bayesian designs are both described. Similar results for generalized linear models lead to designs for the LD95 in a logistic model in which male and female subjects respond differently. Designs with structure in the variance suggest alternatives to the potentially wasteful product designs of Taguchi. Designs for sequential clinical trials to include random balance are presented. The last section outlines some applications, including life testing and models in which time is a factor.