Weigthed Design Optimality Criteria for Spherical Response Surface Designs

In this paper, D. A, G, and IV optimality criteria are developed by using prior probability assignments to model effects. Hence, one and three center point for response surface designs for three design variables (K = 3) in a spherical design region are considered over sets of reduced models for weak and strong heredity. These two specific classes of reduced models are formed by removing terms based on hierarchical structures. The spherical response surface designs are central composite design (CCDs), Box-Behnken design (BBDs), small composite design (SCDs), uniform shell design (UNFSDs), and hybrid 310, 311A, 311B designs. The results of weak and strong heredity models provide reliable interpolation estimates of weighted optimality criterion values for other choices of p₁, p₁, p₂, and p_q

Keywords:  design optimality criteria, spherical response surface design, reduced models

Corresponding author: E-mail: fsciboc@ku.ac.th , jobo@math.montana.edu