Exact Calculation of Integrated Prediction Variance for Response Surface Designs on Cuboidal and Spherical Regions

Abstract

Over the years, design optimality evaluation of response surface designs focused mainly on D-optimality and G-optimality criteria. The apparent limited use of the IV-optimality criterion appears to be influenced by the computational challenges associated with the criterion. The lack of available computer code appears to be the main reason for limited use of the IV-optimality criterion. In addition, the IV-optimality criterion appears more difficult to code than the D-optimality criterion because of the integration required over the specified design region. In this paper, an efficient and exact method is presented for computing the IV-optimality criterion for selected response surface designs. The pseudo-code for the computer program is also presented. The investigation examines both spherical and cuboidal regions of interest. In addition, an analytical approach is outlined for computing the IV-optimality criterion for second-order split-plot designs. A particular feature of the analytical expressions is that they are derived using the design parameters. In addition, several comparisons of second-order response surface designs are illustrated for completely randomized designs and split-plot designs.

• Design Optimality
• IV-Criterion
• Region Moments
• Restricted Randomization

Additional information

Notes on contributors

Wayne R. Wesley

Dr. Wesley is Program Director for Industrial Engineering in the Faculty of Engineering and Computing. He is a senior member of ASQ. His email addresses are [email protected] and [email protected].

James R. Simpson

Dr. Simpson is Group Operations Analyst at Eglin Air Force Base. He is a senior member of ASQ. His email address is [email protected].

Peter A. Parker

Dr. Parker is Research Scientist in the Systems Engineering Directorate. He is a senior member of ASQ. His email address is [email protected].

Joseph J. Pignatiello

Dr. Pignatiello is an Associate Professor, Department of Industrial and Manufacturing Engineering. He is a Fellow of ASQ. His email address is [email protected].