A Note on Model Reduction for Experiments With Both Mixture Components and Process Variables

Abstract

In mixture experiments containing process variables, the traditional Scheffe-type model contains terms in the mixture components and crossproducts between the mixture components and the process variables. The crossproduct coefficients estimate the effects of the process variables on the blending properties of the mixture components only and do not provide any overall measure of the main effects and interactions of the process variables by themselves. In this note a reparametrized model form is presented that enables the effects of the process variables to be separated from the blending effects of the mixture components. Reduced model forms are obtained using a subset-selection procedure. The model-reduction technique is illustrated using data from a six-factor fish-patty experiment.