Optimal two-level fractional factorial designs with pure dispersion factors

Abstract

The problem of finding optimal designs when pure dispersion factors are present in the class of regular single replicated two-level fractional factorial design of resolution III and higher is studied. When a single dispersion factor is present, D-optimal and A-optimal designs depend on the number of length three words involving the dispersion factor in the defining relation for resolution III designs. When two dispersion factors with equal dispersion main effect are present, D-optimal designs depend not only on the number of length three and length four words involving the dispersion factors in the defining relation but also on the values of the dispersion mean and main effects and the structures of the words. Tables are given to show how D-optimality ordering of designs changes when the values of the dispersion mean and main effects and the word structure change.