Nonlinear Models for Mixture Experiments Including Process Variables

Abstract

This present work is concerned with finding and assessing a class of models that flexibly fits data from mixture experiments and mixture-process variables experiments, and with providing guidelines for how to design mixture experiments and mixture-process variables experiments when these models are fitted. Most models in the literature are either based on polynomials and are therefore not very flexible, or have a large number of parameters that make the response surface interpretation difficult to understand. The modified fractional polynomial models are a recent class of models from the literature that are flexible and parsimonious but quite restrictive. We contribute to mixture experiments by proposing a new class of nonlinear models, the complement mixture fractional polynomial (CMFP) models, by making an additional transformation of the fractional polynomial, which results in less restrictive models while retaining (and indeed exceeding) the advantages of this class. Moreover, we suggest an extended form for the modified fractional polynomial models to fit data from mixture-process variables experiments.