Identification of Dispersion Effects in 2k Factorial Design

Abstract

The identification of dispersion effects is a very important stage in developing robust products and processes. Several methods to identify dispersion effects are present in statistical and quality engineering literature, especially methods which use 2K or 2K-p
unreplicated factorial designs, such as Box-Meyer, Harvey, Brenemann-Nair and Bergman- Hynén methods. In this paper we considered generalizations of these methods for replicated
experiments, and compare them by Monte Carlo simulations, analyzing sensitivity and specificity indicators. We also included joint generalized linear models (joint GLMs) in our comparison. The joint GLMs provides an interesting general framework to fit mean and variance models and it is recommend for this proposal, but it needs specialized software. If the main focus is found only in one or two higher effects, then the Box-Meyer method is an efficient and very simple method. When only one non-null dispersion effect is present, our simulation showed that the Box-Meyer method is the best, even when compared with
the joint GLMs. When two non-null dispersion effects are present, the Box-Meyer method is biased, but surprisingly our simulation showed that this method works well.