Generalized Bayesian D-optimal supersaturated multistratum designs

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Supersaturated designs are useful in the initial stage of experiments to identify important factors from many of interest with a small number of runs. Traditional supersaturated designs were mainly constructed for completely randomized experiments, which have single-stratum structures. They cannot be used for experiments that have multistratum structures, such as the split-plot, strip-plot, and staggered-level experiments. How to construct supersaturated multistratum designs for complex experiments has gained much attention recently. In this paper, we consider the situation in which the experimenters have prior knowledge of which factors are more likely to be important (called the primary factors) than the others (called the potential factors). By taking primary and potential factors into account, we propose an approach using the generalized Bayesian D (GBD) criterion to construct a new class of supersaturated multistratum designs. The GBD-optimal supersaturated multistratum designs provide guidelines on how to assign factors to the designs, which enhances efficiency on identifying active factors. A case study shows that the proposed supersaturated design (32 runs with 19 factors) is as effective as the full 26 factorial design (64 runs with 6 factors) to identify important factors in a battery cell experiment.