Weigthed Design Optimality Criteria for Spherical Response Surface Designs

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Published: Nov 12, 2018
Keywords:
design optimality criteria, spherical response surface design, reduced models

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Boonorm Chomtee
Department of Statistics, Kasetsart University, Bangkok, Thailand
John J. Borkowski
Department of Mathematical Sciences, Montana State University, USA.

Abstract

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 pq


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


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


 

Article Details

Issue
Vol. 5 No. 1 (2005)
Section
Original Research Articles

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References

[1] Chipman, Hugh A. 1996 Bayesian Variable Selection with Related Predictors, The Canadian Journal of Statistics, 24, 17-36.
[2] Borkowski, John J., 2002 Using Prior Probabilities to Calculate Weighted Design Optimality Criteria for Response Surface Designs in the Hypercube, Technical Report, 08-08-02.
[3] Chipman, Hugh A. and Hamada, Michael S. 1996 Discussion: Factor-Based or Effect-Based Modelingg? Implication for Design, Technometrics, 38, 317-320.
[4] Borkowski, John J. and Valeroso, Elsie S. 2001 Comparison of Design Optimality Criteria of Reduced Models for Response Surface Designs in the Hypercube, Technometrics, 43, 468-477.