Modelagem da variabilidade em experimentos com misturas

Abstract

In industrial experiments, controlling variability is of paramount importance to ensure product quality. Classical regression models are widely used in industry for mixture experiments; however, when the assumption of constant variance is not satisfied, the building of procedures that allow to minimize the variability becomes necessary and other methods of statistical modeling should be considered. The approach considered in this thesis uses the class of generalized linear models. This class is very general and quite flexible, generalizing some of the most important probability distributions and allowing to model variability through of the joint modeling for mean and dispersion (JMMD). The JMMD provides an efficient method for estimating the parameters of the joint models of mean and dispersion; however, the variable selection process is not clear and is based on subjective criteria for choosing the terms of the models. In this thesis the variable selection problem in JMMD is solved. A variable selection procedure, based on hypothesis testing and the goodness of fit of the model is proposed. Simulation methods are used to verify the efficiency of the procedure. The variable selection procedure is adapted for the case of experiments with mixtures and results in a very efficient method for obtaining the mean and variance models. The theory of optimal design of experiments is presented to the JMMD and applied to mixture experiments. The results obtained in this thesis through the application of JMMD in mixture experiments are very encouraging, indicating that the theory promises to be of great utility in modeling and conducting industrial experiments involving mixtures.