D-optimal Rotatable Central Composite Designs Constructed through Resolutions

Abstract

Response surface methodology is widely used for developing, improving, and optimizing processes in various fields. A design is of resolution  if no  factors effect is confounded with any other effect containing less than  factors. In this study, a method for constructing second order rotatable designs based on resolution R, in particular resolution III and IV for three and four factors respectively, argumented with star points is presented. Attention is given to the moment matrices and the related information surfaces based on the parameter subsystem of interest on the second-order Kronecker model and their corresponding rotatable Central Composite Designs (CCDs). Weighted Central Composite Designs (WCCDs) are derived by assigning different weights to two portions of the CCD namely the cube and star portion. The derived designs achieve the property of rotatability and high efficiency and are shown to be D-optimal. Experimental runs are reduced hence economical and the resulting designs are improved in terms of optimality and estimation efficiency. The results show that the cube portion is of great importance in D-optimal resolution III design while the two portions are of equall importance in resolution IV design.

Key Words:  Resolution R, Kronecker model, Optimality Criterion, Weighted Central Composite Designs, Second – Order designs, Moment matrices, Information matrices