The Mixture Problem for Categorized Components

Abstract

A method is developed for the design of experiments with mixtures in which the mixture components are categorized (acids, bases, etc.), and each category of components contributes a fixed proportion to the total mixture. The number of categories of mixture components is general (q < ∞), and each category is represented in every mixture by one or more of its member components.

The experimentation is to be performed in an ellipsoidal region chosen by the experimenter, subject to the constraints placed on the components. A transformation is made to a spherical region in order that rotatable response surface designs and polynomial models can be used for estimating the response.