The Algebraic Structure of Eight-Run Minimum Aberration Two-Level Fractional Factorial Designs

Abstract

This paper is concerned with the eight-run minimum aberration fractional factorial designs at two levels. The design is characterised by run size economy and aliasing effects. The paper aims to describe the features of the design from an algebraic perspective. It is found that the group formed by the aliasing sets of the design is a non-cyclic finite Abelian p−group. It is shown by examples that the partitioned aliasing subsets of the group, which are constructed according to the number of possible ways the identity relation can be obtained, are not subgroups and that a mapping defined on the maximum word length of an aliased set is not a homomorphism.