Definitive screening designs with added two-level categorical factors

Recently, Jones and Nachtsheim (2011) proposed a new class of designs called definitive screening designs (DSDs). These designs have three levels, provide estimates of main effects that are unbiased by any second-order effect, require only one more than twice as many runs as there are factors, and avoid confounding of any pair of second-order effects. For designs having six factors or more, these designs project to efficient response surface designs with three or fewer factors. A limitation of these designs is that all factors must be quantitative. In this paper, we develop column-augmented DSDs that can accommodate any number of two-level qualitative factors using two methods. The DSD-augment method provides highly efficient designs that are still definitive in the sense that the estimates of all main effects continue to be unbiased by any active second-order effects. An alternative procedure, the ORTH-augment approach, leads to designs that are orthogonal linear main effects plans; however, some partial aliasing between main effects and interactions involving the categorical factors is present.