MathLAB Journal

Comparisons of Alternative Axial Distances for Cuboidal Regions of Central Composite Designs Using D and G Efficiencies

Abstract

Onyishi, Linus Ifeanyi M.E. Nja E.O. Effanga F.C. Eze

In this study, three axial distances are proposed as alternatives to the existing axial distances of the Central
Composite Design (CCD) in cuboidal design regions with the aim of providing formidable alternatives to the
existing axial distances of the CCD whose prediction properties are less extreme and more stable in the cuboidal
design regions. The three alternative axial distances, namely the arithmetic, harmonic and geometric axial
distances for cuboidal regions, were developed algebraically based on the concepts of the three Pythagorean
means. The strengths and weaknesses of the alternative axial distances were validated by comparing their
performances with the existing axial distances in the cuboidal regions. The D- and G-efficiencies are used for
comparison. The cuboidal region shows that the three alternative axial distances are consistently better in terms
of the D- and G-efficiencies.<