Optimal split-plot orthogonal arrays

It is well known that many industrial experiments have split-plot structures. Compared to completely randomised experiments, split-plot designs are more economical and thus have received much attention among researchers. Much work has been done for two-level split-plot designs. In this article, we consider split-plot designs with factors of three, more than three, or mixed levels and with both qualitative and quantitative factors. We show that if two designs with both qualitative and quantitative factors are geometrically isomorphic, then their generalised wordlength patterns are identical. Three design scenarios are considered for optimal designs. The corresponding wordlength patterns are defined and the minimum aberration mixed-level split-plot designs having 18 and 36 runs are tabulated. This article provides a method for constructing split-plot designs with factors of three, more than three, or mixed levels and with qualitative and quantitative factors.