Optimal Orthogonal Second-order Designs

Abstract

This paper extended the work of Chigbu and Nduka (2006), which obtained interesting results on closed form eigenvalues for comparing both orthogonal and rotatable Central Composite Designs (CCDs), by obtaining a majorization result. The majorization result is based on the principle of Schur’s ordering of designs and was used to compare the replicated cube plus one star orthogonal CCD and the replicated star plus one cube CCD. Based on our result the former CCD is better than the latter CCD.