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

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.