Two-level augmented definitive screening designs

Definitive screening designs (DSDs) constitute a well-known class of screening designs for three-level factors. DSDs are comprised of orthogonal main effects plans for which main effects estimates are statistically independent of estimates of two-factor interactions. Jones and Nachtsheim (2013) proposed two methods for augmenting DSDs with two-level categorical factors, namely the DSD-augment and the ORTH-augment approaches. However, these two versions produce distinct features that are not sufficiently flexible to accommodate versatile performance preferences in practice. In this paper, we provide a comprehensive overview of the augmented designs with DSD structures and show how to construct compromise designs that share the desirable traits of both DSD-augment and ORTH-augment designs. In addition to the DSD-augment and ORTH-augment designs, we suggest routine consideration of nondominated compromise designs as described in the paper. Additionally, we provide some theoretical properties of randomly assigned augmented DSDs.