Robust design for mixture experiments: an efficient class of exchangeable designs for Scheffé polynomials

Abstract

Modern industry, engineering, and science seek to explore new methods to determine the composition that optimally describes certain product features. The goal of mixture design is to determine the proportions that optimize some property of the response. Most practitioners adopt a classical design approach since they vaguely know the model form prior to running their experiments. This work is focused on finding optimal designs for Scheffé polynomials where the parametric description of the response function may be inadequate. Our purpose is to obtain an analytical solution to the continuous problem (when possible) and to otherwise provide a numerical alternative. Theoretical results are proven for binary blends, while other strategies based on imposing restrictions and numerical approaches are provided for ternary blends. A real example illustrates the favorability of the results for a three-salt mixture setup. The geometrical properties observed in the designs encouraged the investigation of a class of exchangeable designs. The results reveal that this class of restricted designs may be widely recommended for their simplicity, high performance, and computational efficiency.