On the Prediction Variance Performance of Replicated Minimum-Run Resolution V Designs

Abstract

The Minimum-run resolution V (MinResV) central composite designs used in response surface exploration offer a smaller number of experimental runs when compared to the standard central composite design (CCD), which is an advantage when considering the cost of experimentation. However, the evaluation of the MinResV design has focused on replicating only the centre point for error estimation. Replicating the other portions of the design and the implications have not yet been considered in previous related studies. The cube and star portions of the Minimum-run resolution V (MinResV) designs have been replicated, evaluated and compared using the A-, D-, G- and I-optimality criteria. The stability and prediction capabilities of the designs generated by partial replication of the portions of the MinResV designs are tracked using the fraction of design space (FDS) graph. In this study, these graphs were plotted for the scaled and unscaled prediction variances of the partially replicated variations of the MinResV designs in the spherical regions. For the k=6, 7, 8, 9 and 10 factors considered in this study, the MinResV CCDs with star-replicated designs performed better than the cube-replicated designs in terms of minimum spread of scaled and unscaled prediction variances.