Small run size design for model identification in 3m factorial experiments

Abstract

An active interaction in a main effect plan may cause biased estimation of the parameters in an analysis of variance (ANOVA) model. A fractional factorial design (FFD) with higher order resolution can resolve the alias problem, however, with a considerable number of runs. Alternatively, a search design (SD), the so-called main effect plus k plan (MEP.k), with much less number of runs than FFD, is able to search for k possible active interactions and estimate them in addition to estimating the main effects. However, the existing MEP.k's for 3m factorial experiments are either proposed for a large m (e.g. m≥13) or have a large number of runs. In this paper, we proposed an irregular design for 3m factorial experiments, which is able to identify the active two-factor interactions and estimate them along with estimating the general mean and main effects for 3≤m≤14. The obtained design has fewer runs than the previous designs; meanwhile, it is also comparable and competitive in the discrimination and estimation performances with them. By simulation studies, it is shown that the proposed design does well in model identification and variable selection. © 2020 John Wiley & Sons, Ltd.