Fitting Models to Data from Mixture Experiments Containing other Factors

Abstract

People fit models to data for the purpose of screening out unimportant variables, or for quantifying the effects of important variables, or for just approximating the shape of a response surface. In mixture experiments containing other factors such as process variables and/or the amount of the mixture, the typical model-fitting strategy employed is to fit a combined model containing terms in the mixture components only along with terms involving crossproducts between the mixture components and the other factors. Such a model form allows one to measure the blending properties of the mixture components and to determine if the blending properties differ when changing the settings of the process variables and/or the amount of the mixture. The fitted model is assessed for adequacy of fit and, if found to be adequate, quite often the model is then used to generate contour plots of the predicted mixture surfaces at the settings of the other factors for display and interpretation purposes.In constrained-region mixture experiments, particularly when other factors (process variables or the amount of the mixture) are present, potential pitfalls await the unsuspecting model-builder. This paper discusses some of the potential pitfalls and illustrates them using two examples taken from the literature. Listed at the end of the paper are some general recommendations for designing experiments and fitting models to data from mixture experiments containing other factors.

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