Design Optimality Criteria of Reduced Models for Variations of Central Composite Design

Abstract

Choosing a response surface design to fit certain kinds of models is a difficult task. This work focuses on the reduced second order models having no quadratic and  no interaction terms for five variations of Central Composite Design (SCCD, RCCD, OCCD, Slope-R and FCC) using the D-, G- and A- optimality criteria. Results show that for models having no quadratic terms that G- and A-optimality criteria are equivalent and replication of the axial portion with increase in center points tends to decrease the D-, A- and G-optimality criteria values of the CCDs while for models having no interaction terms, replication of the axial portion with increase in center points increases the D-optimality criterion values of SCCD, RCCD and OCCD in all the factors considered. Finally, the work have shown that replication of the axial portion reduces the performance of the CCDs with models having no quadratic terms and Slope-R is a better design with respect to D- and A-optimality criteria.