Prediction Variance Properties of Third-Order Response Surface Designs in the Hypersphere

Abstract

The variance dispersion graphs (VDGs) and the fraction of design space (FDS) graphs are two graphical methods that effectively describe and evaluate the points of best and worst prediction capability of a design using the scaled prediction variance properties. These graphs are often utilized as an alternative to the single-value criteria such as D-and E-when they fail to describe the true nature of designs. In this paper, the VDGs and FDS graphs of third-order orthogonal uniform composite designs (OUCD 4 ) and orthogonal array composite designs (OACD 4 ) using the scaled-prediction variance properties in the spherical region for 2 to 7 factors are studied throughout the design region and over a fraction of space. Single-valued criteria such as D-, A-and G-optimality are also studied. The results obtained show that the OUCD 4 is more optimal than the OACD 4 in terms of D-, A-and G-optimality. The OUCD 4 was shown to possess a more stable and uniform scaled-prediction variance throughout the design region and over a fraction of design space than the OACD 4 although the stability of both designs slightly deteriorated towards the extremes.