Screening Designs for Continuous and Categorical Factors

Abstract

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 $n=2m$ runs, where $m\ge 4$. A key advantage is that these designs are available for any even $n\ge 8$. 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.

Keywords:

• Conference matrix
• Definitive screening designs
• Hadamard matrix

Supplementary Materials

Supplementary materials are comprised of

1. A description of the power comparisons of SCCDs and Hadamard-matrix-based designs for identifying main effects, along with the associated plots.

2. The set of SCCDs ranging in size from 8 through 32 in Excel (.xlsx) files.

3. Three simulation codes, written in R, that produce the simulation results for main-effects power, for the comparisons with Hadamard matrices, and for quadratic-effects power. These codes also automatically generate the graphical summaries in Figures 3, 4, and Figure 1 of the supplementary materials.

Acknowledgments

We thank the referees, the associate editor and the editor for suggestions that led to significant improvements in our article.

Disclosure Statement

The authors report that there are no competing interests to declare.