Graphical evaluation of average slope variance for the family of three-level response surface designs

This is the authors' abstract. We don't add key points for this paper.

In experiments, estimation of the mean response is often considered, and the fraction of design space graph is a useful tool for assessing the prediction capabilities of designs for this purpose. In many experiments, interest might be in the slope (rate of change) of the mean response. Slope variance dispersion graphs and slope variance quantile plots have been presented to measure capabilities of response surface designs for estimating slopes. Slope variance quantile plots give the distribution of average slope variance at any chosen radius. However, different choices of radii can yield substantially different plots. In this article, we use the slope variance fraction of design space plot, analogous to the fraction of design space graph to assess the slope estimation capabilities of designs. Several three-level response surface designs are used to illustrate how the plot evaluates and compares the performance of designs. Orthogonal minimally aliased response surface designs, a new family of three-level response surface designs, perform comparably with other traditional response surface designs. However, some of its variations demonstrate superior slope estimation capabilities.