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 I_wWLP and I_sWLP respectively, in the FFSP design. The authors further propose combined word length patterns C_wWLP and C_sWLP, in order to select good designs for different cases. The new criteria C_wWLP and C_sWLP 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.