Two-level factorial designs for searching dispersion factors and estimating location main effects

In factorial experiments, changing the level of a factor might, in certain applications, change the variance of the response variable. Such factors are called dispersion factors in this article. There have been several publications on the analysis methodology for identifying dispersion factors in unreplicated factorial experiments. However, the design optimality issues for the search and identification of dispersion factors seem to be relatively unexplored. In this study, we focus on the two-level factorial experiment in which there is at most one dispersion factor whose identity is not known a priori. The task is to estimate all location main effects and simultaneously identify the dispersion factor, if any. We propose a likelihood-based criterion for selecting the design from a class of competing designs using which one can estimate all location main effects and also correctly identify, with as high a probability as possible, the identity of the dispersion factor (if one exists). It is shown that, if attention is restricted to the class of regular 2n-p fractional factorial designs, then a large run size design of high resolution may be required to achieve our goal. As an alternative, we consider the class of simple arrays due to its appealing symmetry property and flexibility in run size. Additionally, the trade-off of efficiency between identification of the dispersion factor and estimation of the location main effects is under investigation. The situation involving multiple dispersion factors is also discussed.