An algorithm for generating good mixed level factorial designs

Abstract

An algorithm for the creation of mixed level arrays with generalized minimum aberration (GMA) is proposed. GMA mixed level arrays are particularly useful for experiments involving qualitative factors: for these, the number of factor levels is often a consequence of subject matter requirements, while a priori assumptions on a statistical model are not made, apart from assuming lower order effects to be more important than higher order effects. The proposed algorithm creates GMA arrays using mixed integer optimization with conic quadratic constraints. Fully achieving GMA is feasible for small problems; for larger problems, the optimization task is reduced to considering the confounding of low-order effects only. Lower bounds for the lowest-order confounding are provided (given the number of experimental runs). Where one of these bounds is actually attainable, the algorithm is often fast in providing an array which attains it. Examples illustrate the scope and usefulness of the algorithm, which is implemented in an R package, using one of two commercial optimizers.