Quantile plots of the prediction variance for response surface designs

Giovannitti-Jensen and Myers (1989) used variance dispersion graphs (VDG's) to assess the overall prediction capability of a response surface design inside a region of interest, R. The VDG's consist of plots of the maximum and minimum prediction variance values on concentric spheres inside R against their radii. These plots provide useful information about the amount of dispersion in the prediction variance throughout the region R. They do not, however, account for values of the prediction variance on a sphere other than its maximum and minimum. Quite often, information concerning the prediction variance distribution on a sphere will provide a more comprehensive and accurate assessment of the quality of prediction than can be obtained from the VDG's. In this article, we describe such a distribution by using a plot of its quantiles. A method for deriving these quantiles is given. Two examples are presented to illustrate the utility of the proposed approach.