Comparison of the Three Types of Central Composite Designs Over Subsets of Reduced Models by Design Optimality Criteria

Abstract

The purpose of this article is to compare the 3 important types of central composite designs (CCDs) consisting of central composite circumscribed design (CCCD), central composite inscribed design (CCID), and central composite face-centroid design (CCFD) in response surface methodology (RSM). The difference among these designs is the distance from the center design to the axial points. The comparison was performed across the full second-order response surface model and across a set of reduced models for 3, 4, and 5 design factors (k = 3, 4, and 5) including 1, 3, and 5 center runs (nc = 1, 3, and 5). This study used D-, A-, and G-optimality criteria to evaluate the performance of CCDs by presenting the design optimality criteria comparison ranking throughout the reduced-model subsets of 43, 224, and 839 models for 3, 4, and 5 design variables, respectively. The results showed that CCCD was superior to CCID and CCFD according to A-and D-optimality criteria, while CCCD and CCID performed better than CCFD based on G-optimality criterion over a set of reduced models for 3, 4, and 5 design factors. It was observed that D-, A-, and G-optimality efficiencies were robust to changes in the linear and cross-product terms and sensitive to deviation in the square terms. The study will provide recommendations to assist the experimenters in the choice of the best design among the candidate designs for practice applications when some model effects may be insignificant.