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Combinatorial Equivalence of Fractional Factorial Designs

Two symmetrical fractional factorial designs are said to be combinatorially equivalent if one design can be obtained from another by reordering the runs, relabeling the factors and relabeling the levels of one or more factors. This article presents concepts of ordered distance frequency matrix, distance frequency vector, and reduced distance frequency vector for a design. Necessary conditions for two designs to be combinatorial equivalent based on these concepts are presented. A new algorithm based on the results obtained is proposed to check combinatorial non-equivalence of two factorial designs and several illustrating examples are provided.