Optimal prediction variance properties of some central composite designs in the hypercube

Abstract

Measures of the prediction variance performances of three variations of central composite designs when the region is hypercube were examined and compared using the G-efficiency and I-optimality criterion so as to determine the economical design(s) that perform(s) better than the other. The hypercube is the multidimensional cuboidal region with the axial distance, $\alpha =1.0$. The designs are the standard central composite designs (CCD), the small composite design (SCD) and minimum run resolution V (minResV) design. Two prediction variance based optimality criteria, I-optimality and G-efficiency were determined, a plot of variance dispersion graph and fraction of design space are used to give a comprehensive picture of the behavior of the prediction variance throughout the region of interest. Comparing the three designs mentioned above for 3, 4, and 5 factors on cuboidal region, the result showed that CCD performed better than SCD and MinResVdesign considering 2, 3, and 5 center points.

Keywords:

• Prediction variance
• optimality criteria
• factorial portion
• axial point