Exchange Algorithms for Constructing Model-Robust Experimental Designs

Abstract

Optimal experimental design procedures, utilizing criteria such as D-optimality, are useful for producing designs for quantitative responses, often under nonstandard conditions such as constrained design spaces. However, these methods require a priori knowledge of the exact form of the response function, an often unrealistic assumption. Model-robust designs are those that, from our perspective, are efficient with respect to a set of possible models. In this paper, we develop a model-robust technique motivated by a connection to multiresponse D-optimal design. This link spawns a generalization of the modified Fedorov exchange algorithm, which is then used to construct exact model-robust designs. We also study the effectiveness of designs robust for a small set of models compared with designs that account for much larger sets. We give several examples and compare our designs with two model-robust procedures in the literature.

• D-Optimality
• Model Space
• Multiresponse Design
• Robust Design

Additional information

Notes on contributors

Byran J. Smucker

Dr. Smucker is an Assistant Professor of Statistics at Miami University and a Full Member of ASQ. His email address is [email protected].

Enrique Del Castillo

Dr. del Castillo is a Distinguished Professor of Industrial and Manufacturing Engineering and a Professor of Statistics at the Pennsylvania State University. His email address is [email protected].

James L. Rosenberger

Dr. Rosenberger is a Professor of Statistics at the Pennsylvania State University. His email address is [email protected].