Fraction of Design Space to Assess Prediction Capability of Response Surface Designs

Abstract

Variance Dispersion Graphs (VDGs) are useful summaries for comparing competing designs on a fixed design space. However, they do not give all useful information about the prediction capability of a design. We propose the Fraction of Design Space (FDS) technique, which addresses some of the shortcomings of VDGs. The new technique gives the researcher more detailed information by quantifying the fraction of design space where the scaled prediction variance (SPV) is less than or equal to any pre-specified value. The FDS graph gives the researcher information about the distribution of the SPV in the region based on the ranges and proportions of possible SPV values. Several variations on the graph, including plotting the variance of the estimated mean response, are also presented to allow for specialized consideration of different designs. The FDS technique complements the use of VDGs to give the researcher more insight into the prediction capability of a design. Several standard designs with different numbers of factors are studied with both methods.