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.