A family of orthogonal main effects screening designs for mixed-level factors

AbstractAbstractThere is limited literature on screening when some factors are at three levels and others are at two levels. This topic has seen renewed interest of late following the introduction of the definitive screening design structure by Jones and Nachtsheim 2011 Jones, B., and C. J. Nachtsheim. 2011. A class of three-level designs for definitive screening in the presence of second-order effects. Journal of Quality Technology 43 (1):1–15. doi: 10.1080/00224065.2011.11917841.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar] and Xiao et al. 2012 Xiao, L., Dennis, K. J. Lin, and F. Bai. 2012. Constructing definitive screening designs using conference matrices. Journal of Quality Technology 44 (1):2–8. doi: 10.1080/00224065.2012.11917877.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]. Two well-known examples are Taguchi's L18 and L36 designs. However, these designs are limited in two ways. First, they only allow for either 18 or 36 runs, which is restrictive. Second, they provide no protection against bias of the main effects due to active two-factor interactions. In this article, we introduce a family of orthogonal, mixed-level screening designs in multiples of eight runs. Our 16-run design can accommodate up to four continuous three-level factors and up to eight two-level factors. The three-level factors must be continuous, whereas the two-level factors can be either continuous or categorical. All of our designs supply substantial bias protection of the main effects estimates due to active two-factor interactions.Keywords: conference matrixdefinitive screening designsHadamard matrixKronecker products Disclosure statementNo potential conflict of interest was reported by the authors.Data availability statementThe authors confirm that the data supporting the findings of this study are available within the Supplementary Materials.Additional informationNotes on contributorsBradley JonesBradley Jones is a Distinguished Research Fellow at JMP Statistical Discovery LLC where he does research in design of experiments and statistical methods.Ryan LekivetzRyan Lekivetz is an Advanced Analytics Manager at JMP Statistical Discovery LLC where he manages the team that implements features in the design of experiments and reliability platforms for JMP software. His research interests include design of experiments, combinatorial testing, and the intersection of the two.Christopher NachtsheimChristopher Nachtsheim is the Frank A. Donaldson Chair of operations management in the Carlson School of Management. He does research in design of experiments and related statistical methods.