DP-Optimality in Terms of Multiple Criteria and Its Application to the Split-Plot Design

Abstract

Recent arguments have been made that optimal design criteria should incorporate pure error degrees of freedom for estimating unknown variance components. In this paper, we incorporate pure error, along with traditional design criteria, using Pareto optimization to identify a collection of optimal designs. This strategy demonstrates the trade-offs between these conflicting objectives without having to resort to weighted combinations of the criteria. The proposed approach also allows extension of the criteria for purposes of selecting optimal split-plot designs based on the D-criterion and pure error degrees of freedom.

• D-Optimality
• Exchange Algorithm
• Lack-of-Fit
• Multi-Objective Optimization
• Optimal Design
• Pure Error
• Response Surface Model

Additional information

Notes on contributors

Yongtao Cao

Dr. Cao is Assistant Professor of Statistics in the Mathematics Department at Indiana University of Pennsylvania. He is a member of ASQ. His email address is [email protected].

Shaun S. Wulff

Dr. Wulff is Associate Professor of Statistics in the Department of Statistics at the University of Wyoming. His email address is [email protected].

Timothy J. Robinson

Dr. Robinson is Professor of Statistics in the Department of Statistics at the University of Wyoming. He is a Fellow of ASQ. His email address is [email protected].