Supersaturated multistratum designs

Supersaturated designs have gained much attention in the past two decades. Such designs can reduce substantial cost in the initial stage of experiments to identify the few important factors from many of interest. Most exiting supersaturated designs in the literature are developed for completely randomized experiments, which have single-stratum structures. However, in many cases, complete randomization is infeasible and hence designs with more complicated structures are needed. In this article, we study the supersaturated designs in multistratum structures. We propose the generalized Df criterion and develop the multistratum columnwise-pairwise exchange algorithm for constructing and selecting efficient supersaturated multistratum designs. The supersaturated split-plot, strip-plot, and staggered-level designs are constructed and their sensitivity, power, and type I error rate are studied. An example with SAS and R codes is provided to demonstrate how to conduct data analysis for supersaturated multistratum designs.