THE USEFULNESS OF OPTIMUM EXPERIMENTAL-DESIGNS

Optimum experimental designs were originally developed by Kiefer, main ly for response surface models. This survey of recent developments emp hasizes potential or actual usefulness. For linear models the construc tion of exact designs, particularly over irregular design regions, is stressed, as is the blocking of response surface designs. Other import ant areas include systematic designs that are robust against trend and designs for mixtures with irregular design regions: several industria l examples are mentioned. Both D- and c-optimum designs are found for a non-linear model of the economic response of cereal production to fe rtilizer level, the c-optimum design being for the conditions of maxim um economic return. Locally optimum and Bayesian designs are both desc ribed. Similar results for generalized linear models lead to designs f or the LD(95) in a logistic model in which male and female subjects re spond differently. Designs with structure in the variance suggest alte rnatives to the potentially wasteful product designs of Taguchi. Desig ns for sequential clinical trials to include random balance are presen ted. The last section outlines some applications, including life testi ng and models in which time is a factor.