Equivalence of symmetric factorial designs and characterization and ranking of two-level Split-lot designs

TLDR: In this paper, the problems of combinatorial and geometric equivalence of symmetric factorial experiments, as well as characterization and ranking of two-level Split-plot and Split-lot designs are considered.

Abstract: The problems of combinatorial and geometric equivalence of symmetric factorial experiments, as well as characterization and ranking of two-level Split-plot and Splitlot designs are considered. Two fractional factorial symmetric designs with qualitative factors are said to be combinatorially equivalent if one can be obtained from the other by reordering the runs, relabeling the factors and relabeling factor levels. If the only permissible relabeling of factors levels is reversal of symbols, geometric equivalence is obtained. Existing criteria for detecting combinatorial and geometric equivalence or non-equivalence of symmetric factorial designs are described and evaluated via computer algorithms. Some new necessary and sufficient criteria for both types of equivalence are presented. All results generalize to designs with factors having different number of levels. A characterization method for two-level Split-plot and Split-lot designs based on nonregular fractional factorial designs is given. As an application, a new ranking method is proposed for general two-level Split-plot and Split-lot designs which suggests that existing ranking criteria overlook some aspects of the designs.