Graphical Summaries to Compare Prediction Variance Performance for Variations of the Central Composite Design for 6 to 10 Factors

Abstract

Three readily available second-order response surface designs for a relatively large number of factors are examined and compared. The number of factors in this study range from 6 < k < 10 for both spherical and cuboidal regions of interest. As the number of factors in an experiment increases, the number of terms in the second-order model, as well as the total number of observations can increase quite rapidly. Hence finding economical designs that still predict well in the region of interest is an important objective. The scaled and unscaled prediction variances are investigated over the design region for the central composite design (CCD), small composite design (SCD), and minimum-run resolution (MinRes) V designs. For each of the cuboidal and spherical regions, several choices of axial values are compared. Fraction of design space (FDS) plots and box plots are constructed to characterize the prediction variance properties for the designs in this study.