Generating and Assessing Exact G-Optimal Designs

Abstract

We introduce a new algorithm for generating near G-optimal designs for second-order models over cuboidal regions. The algorithm involves the use of Brent's minimization algorithm with coordinate exchange to create designs for 2 to 5 factors. Designs created using this new method either match or exceed the G-efficiency of previously reported designs. We also introduce a new graphical tool, the variance ratio fraction of design space (VRFDS) plot, which is useful for easy comparison of the prediction variance for competing designs over a given region of interest. Using the VRFDS plot to compare G-optimal designs to I-optimal designs shows that the G-optimal designs have higher prediction variance over the vast majority of the design region. This suggests that, for many response surface studies, G-optimal designs may not be the best choice.