Extensions of D-optimal Minimal Designs for Symmetric Mixture Models.

The purpose of mixture experiments is to explore the optimum blends of mixture components, whichwill provide the desirable response characteristics in finished products. D-optimal minimal designs have been considered for a variety of mixture models, including Scheffe's linear, quadratic, and cubic models. Usually, these D-optimal designs are minimally supported since they have just as many design points as the number of parameters. Thus, they lack the degrees of freedom to perform the lack-of-fit (LOF) tests. Also, the majority of the design points in D-optimal minimal designs are on the boundary: vertices, edges, or faces of the design simplex. In this article, extensions of the D-optimal minimal designs are developed for a general mixture model to allow additional interior points in the design space to enable prediction of the entire response surface. Also a new strategy for adding multiple interior points for symmetric mixture models is proposed. We compare the proposed designs with Cornell (1986) two 10-point designs for the LOF test by simulations.