Dispersion effects in unreplicated two-level factorial designs

This dissertation focuses on obtaining information about process variation from experimental data through unreplicated two-level design of experiments (DOE). The objective of this research is to develop statistical tools to study the dispersion effects in unreplicated two-level factorial designs. The two most common design plans found in industrial settings, completely randomized designs (CRD) and split plot designs, are considered in developing the tools to study dispersion effects.; In the situation of confounding between location and dispersion effects we extend the model discrimination (MD) criterion of Meyer, Steinberg and Box (1996) by allowing the models to have dispersion effect. We initially modified the bayesian part of the method of finding active factors to accommodate non-structured models and then use the resultant posterior probabilities in the next step of discriminating the concurrent models. We also established a procedure to transform the experimental data to ensure homogeneous variance and then apply the MD criterion. The proposed method provides guidance to where the next set of additional experimental runs should be executed to allow maximum discrimination among the models.; We also develop a method to estimate the residuals in unreplicated two-level split-plot designs. The goal of estimating the residuals is to be able to check the model assumptions, particularly, the study of dispersion effects. We provide a procedure to test the dispersion effects in split-plot configuration, including an approach to examine the dispersion effect in the whole plot stratum when there is dispersion at the subplot level. This methodology is based on the conditional whole plot dispersion analysis on each level of the subplot dispersion effect. Since it is key the proper identification of location models in the investigation of dispersion effects we developed a method to identify the active factors in the whole plot and subplot stratum. The method is based on the Bayesian procedure of Box and Meyer for CRD.