Construction of mixed-level screening designs using Hadamard matrices

Abstract

Modern experiments typically involve a very large number of variables. Screening designs allow experimenters to identify active factors in a minimum number of trials. To save costs, only low-level factorial designs are considered for screening experiments, especially two- and three-level designs. In this article, we provide a systematic method to construct screening designs that contain both two- and three-level factors based on Hadamard matrices with the fold-over structure. The proposed designs have good performance in terms of D-optimal and A-optimal criteria, and the estimates of the main effects are unbiased by the second-order effects, making them very suitable for screening experiments. Besides, some theoretical results on D- and A-optimality are obtained as a by-product.