Comparison of Box-Draper and D-Optimum Designs for Experiments with Mixtures

Abstract

In continuation of the study of [10] and [5], designs for quadratic regression are considered when the possible values of the controlable variable are mixtures x = (x 1, x 2, …, x q + 1) of nonnegative components x i with Σ q + 1 1 x i = I. The “all-boas” design of Box and Draper [1] for guarding against cubic bias, and the design that is optimum with respect to the D-optimality criterion ignoring the posaibility of such bias, are compared in terms of the average and the maximum of the variance and bias functions of the fitted repression. The D-optimum design performs well in terms of the Box-Draper criterion unless the sample size is fairly large, and is superior in terms of maximum variance and bias.