Methods for Identifying Dispersion Effects in Unreplicated Factorial Experiments

Abstract

There has been considerable interest recently in the use of statistically designed experiments to identify both location and dispersion effects for quality improvement. Analysis of dispersion effects usually requires replications that can be expensive or time consuming. Several recent articles have considered identification of both location and dispersion effects from unreplicated fractional factorial experiments. In this article, we provide a systematic study of various methods that are commonly used or have been proposed recently. Both theoretical and simulation results are used to characterize the properties. Although all methods suffer from some degree of bias, some have serious problems when the bias remains large even as the design run size increases to infinity. Based on these analyses, we propose some iterative strategies for model selection and estimation of the dispersion effects. A real example and simulations as well are used to illustrate the results.