A Class of Three-Level Designs for Definitive Screening in the Presence of Second-Order Effects

Abstract

Screening designs are attractive for assessing the relative impact of a large number of factors on a response of interest. Experimenters often prefer quantitative factors with three levels over two-level factors because having three levels allows for some assessment of curvature in the factor—response relationship. Yet, the most familiar screening designs limit each factor to only two levels. We propose a new class of designs that 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. Moreover, for designs having six factors or more, our designs allow for the efficient estimation of the full quadratic model in any three factors. In this respect, our designs may render follow-up experiments unnecessary in many situations, thereby increasing the efficiency of the entire experimentation process. We also provide an algorithm for design construction.

• Alias
• Confounding
• Coordinate Exchange Algorithm
• D-Efficiency
• Response Surface Designs
• 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 Operations and Management Science 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].