Screening Designs for Continuous and Categorical Factors

Screening experiments often require both continuous and categorical factors. In this article we develop a new class of saturated designs containing m three-level continuous factors and m–1 two-level categorical or continuous factors in (Formula presented.) runs, where (Formula presented.). A key advantage is that these designs are available for any even (Formula presented.). With effect sparsity or by not making use of all of the two-level columns of the design, we demonstrate via simulation that it is possible to identify up to three active quadratic effects. When n is a multiple of 8, the designs are orthogonal. When n is a multiple of four and not a multiple of 8, the three-level factors are orthogonal to each other and to the two-level factors, and the two-level factors are nearly orthogonal to each other. Finally, when n is a multiple of two, and not a multiple of four or 8, the three-level and two-level factors are nearly orthogonal within those groupings, and orthogonal to each other. We show that even in this latter case, the designs typically have power near one for identifying up to m active main effects when the signal-to-noise ratio is greater than 1.5.