Generalized Bayesian D-optimal supersaturated multistratum designs

Abstract

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.

Keywords:

• potential terms
• primary terms
• split-plot
• staggered-level
• strip-plot

About the author

Chang-Yun Lin is a Professor in the Department of Applied Mathematics and Institute of Statistics at the National Chung Hsing University in Taiwan. He received his PhD degree from the Tsing Hua University in Taiwan in 2009. His research areas concern design of experiments, deep learning, Bayesian analysis, and genetic statistics.

Acknowledgments

The author thanks the anonymous referees for their many helpful comments and suggestions that led to substantial improvements to this article.

Additional information

Funding

This research was partially supported by the Central Taiwan Science Park (Grant no. 108RB08), the Ministry of Education, Taiwan (Grant no. PMS1080014), and the Ministry of Science and Technology, Taiwan (Grant no. MOST 107-2118-M-005-003-MY2).