Optimal two-level regular designs under baseline parametrization via cosets and minimum moment aberration

Abstract

We consider two-level fractional factorial designs under a baseline parametrization that arises naturally when each factor has a control or baseline level. While the criterion of minimum aberration can be formulated as usual on the basis of the bias that interactions can cause in the estimation of main effects, its study is hindered by the fact that level permutation of any factor can impact such bias. This poses a serious challenge especially in the practically important highly fractionated situations where the number of factors is large. We address this problem for regular designs via explicit consideration of the principal fraction and its cosets, and obtain certain rank conditions which, in conjunction with the idea of minimum moment aberration, are seen to work well. The role of simple recursive sets is also examined with a view to achieving further simplification. Details on highly fractionated minimum aberration designs having up to 256 runs are provided.