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

Abstract

There 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 and Xiao et al. 2012. 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 matrix
• definitive screening designs
• Hadamard matrix
• Kronecker products

Data availability statement

The authors confirm that the data supporting the findings of this study are available within the Supplementary Materials.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Bradley Jones

Bradley Jones is a Distinguished Research Fellow at JMP Statistical Discovery LLC where he does research in design of experiments and statistical methods.

Ryan Lekivetz

Ryan 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 Nachtsheim

Christopher 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.