Quantile plots of the average slope variance for response surface designs

Abstract

This article is concerned with the comparison of designs on the basis of their capabilities to estimate the slope of a response function. Jang and Park (1993) used slope variance dispersion graphs (SVDG's) to assess the so-called slope rotatability over all directions of a response surface design. Although these graphs provide useful information about the dispersion in the average slope variance (ASV) throughout a region of interest, their utility is somewhat limited since they only account for the maximum and minimum values of the ASV on a hypersphere inside the region of interest. In this article, a method is proposed for estimating the ASV distribution on a hypersphere by using a plot of its quantiles. This method provides more information than can be obtained from considering only the maximum and minimum values of the ASV. Two examples are given to illustrate the usefulness of the proposed method.

Keywords:

• Slope rotatability over all directions
• slope estimation capability
• slope variance dispersion graphs
• spherical coordinates