Individual Word Length Patterns for Fractional Factorial (Split-Plot) Designs

Fractional factorial (FF) designs are commonly used for factorial experiments in many fields. When some prior knowledge has shown that some factors are more likely to be significant than others, Li, et al. (2015) proposed a new pattern, called the individual word length pattern (IWLP), which, defined on a column of the design matrix, measures the aliasing of the effect assigned to this column and effects involving other factors. In this paper, the authors first investigate the relationships between the IWLP and other popular criteria for regular FF designs. As we know, fractional factorial split-plot (FFSP) designs are important both in theory and practice. So another contribution of this paper is extending the IWLP criterion from FF designs to FFSP designs. The authors propose the IWLP of a factor from the whole-plot (WP), or sub-plot (SP), denoted by the IwWLP and IsWLP respectively, in the FFSP design. The authors further propose combined word length patterns CwWLP and CsWLP, in order to select good designs for different cases. The new criteria CwWLP and CsWLP apply to the situations that the potential important factors are in WP or SP, respectively. Some examples are presented to illustrate the selected designs based on the criteria established here.

Automated summary

In this paper, a new pattern called the individual word length pattern (IWLP) is proposed to measure the aliasing between the effect assigned to a column of the design matrix and effects involving other factors. The IWLP criterion is extended from regular fractional factorial (FF) designs to fractional factorial split-plot (FFSP) designs. The authors further propose combined word length patterns (CwWLP and CsWLP) to select good designs for different cases based on the potential important factors being in whole-plot or sub-plot.