SPHERICAL PREDICTION-VARIANCE PROPERTIES OF CENTRAL COMPOSITE AND BOX-BEHNKEN DESIGNS

For quadratic regression on the hypercube, a single-number criterion, such as a G efficiency that is based on the prediction variance, is often included as one of the criteria when selecting a response surface design. As an alternative to the single-number-criterion approach, the variance dispersion graph, presented by Giovannitti-Jensen and Myers, is a graphical technique for evaluating prediction-variance properties throughout the experimental region. Three properties of interest are the maximum, minimum, and average spherical prediction variances, given the spherical radius. As an alternative to the computer-based approach requiring an optimization algorithm to evaluate these properties, the maximum, minimum, and spherical prediction variances for central composite and Box-Behnken designs can be determined analytically and are functions only of the radius and the design parameters. These functions yield the exact values of the spherical prediction-variance properties of central composite and Box-Behnken designs, thereby removing the need for extensive computing involving algorithms that do not guarantee finding global optima. Results are presented for spherical and cuboidal regions.