Optimal split-plot designs under individual word length patterns

Abstract

For multi-factor experiments that cannot run all the factors in a completely random order, fractional factorial split-plot (FFSP) designs are often used in practice. When some prior knowledge has shown that some factors are more likely to be significant than others, Han et al. (2023) proposed the individual word length patterns (IWLPs) of whole-plot (WP) and sub-plot (SP), denoted by the I${}_w$WLP and I${}_s$WLP respectively, in the FFSP design. In this paper, we propose a construction method for optimal FFSP designs based on these two criteria, where the key of the method is to construct generating matrices for different FFSP designs from the generating matrix of a fractional factorial design, and hence we get a class of effective FFSP designs. These designs are more applicable in many situations. The results for 16-run two-level FFSP designs are tabulated in the supplementary material for possible use by practitioners.