Uniform Designs for Highly Constrained Mixture Experiments

The goal of a space-filling design is to uniformly scatter the design points in the experimental region of interest. For mixture experiment designs of reasonable size, as the dimensionality of the experimental region increases, space-filling design criteria (such as maximin and minimax) place most, if not all, design points at or near the boundary of the constrained region. This article introduces two number-theoretic methods for generating space-filling (specifically uniform) designs for constrained mixture experiments defined by single- and multiple-component constraints. The two methods are illustrated for a simple 3-component mixture problem and a more complicated 16-component waste-glass mixture problem. The uniform scatter of the points in the resulting designs is evaluated using three distance-based criteria.