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 e↵ects that are unbiased by any second-order e↵ect, require only one more than twice as many runs as there are factors, and avoid confounding of any pair of second-order e↵ects. For designs having six factors or more, these designs project to e cient 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 e cient designs that are still definitive in the sense that the estimates of all main e↵ects continue to be unbiased by any active second-order e↵ects. An alternative procedure, the ORTH-augment approach, leads to designs that are orthogonal linear main e↵ects plans; however, some partial aliasing between main e↵ects and interactions involving the categorical factors is present.