Modelling in mixture experiments including interaction with process variables

In many practical situations where experiments with mixtures are carried out, it is sometimes necessary to consider running the experiment at different levels, or combinations of levels, of one or more process variables. It is common practice to use a polynomial model for the responses produced from a mixtures simplex centroid or simplex lattice design with quadratic or cubic terms to describe the effects of the mixture ingredients. It is also usual to investigate the process variables using a factorial design, or a suitable response surface design such as a central composite design, with a model including main effects and interaction terms. There are various ways of combining these models to investigate the joint behaviour of the mixture ingredients and the process variables simultaneously. In this paper, we consider several such models and propose a particular model involving polynomial terms for the mixture and process variables and first and second order interaction terms involving both mixture and process variables. The model building strategy is illustrated using an example involving three mixture ingredients and two process variables in a bread making experiment.