The D-Optimal Design of Blocked Experiments with Mixture Components

So far, the optimal design of blocked experiments involving mixture components has received scant attention in the literature. This paper describes the algorithmic approach to designing such experiments. For constrained and unconstrained experimental regions, the resulting experimental designs are shown to be statistically much more efficient than the orthogonally blocked design options presented in the literature. As an alternative to the algorithmic approach, a simple two-stage procedure to construct highly efficient blocked mixture experiments for unconstrained design regions in the presence of fixed and/or random blocks is presented. Finally, the similarities and differences between the design of blocked mixture experiments and mixture experiments in the presence of qualitative process variables are discussed in detail.