Definitive Screening Designs with Added Two-Level Categorical Factors^*

Abstract

Recently, Jones and Nachtsheim (2011) proposed a new class of designs called definitive screening designs (DSDs). These designs have three levels, provide estimates of main effects that are unbiased by any second-order effect, require only one more than twice as many runs as there are factors, and avoid confounding of any pair of second-order effects. For designs having six factors or more, these designs project to efficient response surface designs with three or fewer factors. A limitation of these designs is that all factors must be quantitative. In this paper, we develop column-augmented DSDs that can accommodate any number of two-level qualitative factors using two methods. The DSD-augment method provides highly efficient designs that are still definitive in the sense that the estimates of all main effects continue to be unbiased by any active second-order effects. An alternative procedure, the ORTH-augment approach, leads to designs that are orthogonal linear main effects plans; however, some partial aliasing between main effects and interactions involving the categorical factors is present.

• Alias
• Conference Matrix
• Confounding
• Coordinate Exchange Algorithm
• D-Efficiency
• Robust Designs
• Screening Designs

Additional information

Notes on contributors

Bradley Jones

Dr. Jones is Principal Research Fellow for the JMP Division of SAS and Guest Professor at the University of Antwerp. His email address is [email protected].

Christopher J. Nachtsheim

Dr. Nachtsheim is the Frank A. Donaldson Chair of Operations Management, Chair of the Supply Chain and Operations Department at the Carlson School of Management and is a member of the Graduate Faculty of the School of Statistics at the University of Minnesota. His email address is [email protected].