Comparison of Optimality Criteria of Reduced Models for Response Surface Designs with Restricted Randomization

Abstract

In this work, $D-$, $G-$, and $A-$ efficiencies and the scaled average prediction variance, $IV$ criterion, are computed and compared for second-order split-plot central composite design. These design optimality criteria are evaluated across the set of reduced split-plot central composite design models for three design variables under various ratios of the variance components (or degrees of correlation $d$). It was observed that $D$, $A$, $G$, and $IV$ for these models strongly depend on the values of $d$; they are robust to changes in the interaction terms and vary dramatically with the number of, and changes in the squared terms.