Authors
Bradley Jones (1), Ryan Lekivetz (2), Dibyen Majumdar (3) & Christopher Nachtsheim (4)
Affiliations
(1) Adsurgo LLC, Cary, NC
(2) JMP Statistical Discovery LLC
(3) Department of Mathematics, Statistics, and Computer Science, University of Illinois, Chicago, Chicago, IL
(4) Carlson School of Management, University of Minnesota, Minneapolis, MN
Journal
Technometrics, VOL. 67, NO. 1, 1–10
Date Published
2025
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 ≥ 4. A key advantage is that these designs are available
for any even n ≥ 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 threelevel 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.
Citation
Bradley Jones, Ryan Lekivetz, Dibyen Majumdar & Christopher Nachtsheim
(2025) Screening Designs for Continuous and Categorical Factors, Technometrics, 67:1, 1-10, doi.org/10.1080/00401706.2024.2362149.