Prediction Variance Assessment of Variations of Two Second-Order Response Surface Designs

Abstract

Two second-order response surface designs have been evaluated. The designs are the small composite designs and the minimum-run resolution V designs. The cube and star portions of these second-order designs are replicated with different amounts and the variations of the designs generated by replication are compared independently to assess the performance of the prediction variances for each of the second-order design under consideration. Two optimality criteria, G- and I-optimality, that are prediction variance-oriented are used to evaluate the maximum and average prediction variance of the designs while fraction of designs space plots are constructed to track the prediction variance performance of these designs throughout the design space. For the two second-order designs, the results indicate that it is advantageous to replicate the star than replicating the cube.

Keywords: Optimality criteria, fraction of design space plot, small composite design, minimum-run resolution V design, design replication, cube, star.