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Biometrika Advance Access originally published online on January 30, 2009
Biometrika 2009 96(1):95-106; doi:10.1093/biomet/asn062
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© 2009 Biometrika Trust

Articles

Bayesian-inspired minimum aberration two- and four-level designs

V. Roshan Joseph

H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0205, U.S.A. roshan{at}isye.gatech.edu

Mingyao AI

Laboratory of Mathematics and Applied Mathematics, School of Mathematical Sciences, Peking University, Beijing 100871, China myai{at}math.pku.edu.cn

C. F. Jeff Wu

H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0205, U.S.A. jeffwu{at}isye.gatech.edu

Received for publication 1 March 2008. Revision received 1 October 2008.
  Abstract

Motivated by a Bayesian framework, we propose a new minimum aberration-type criterion for designing experiments with two- and four-level factors. The Bayesian approach helps in overcoming the ad hoc nature of effect ordering in the existing minimum aberration-type criteria. The approach is also capable of distinguishing between qualitative and quantitative factors. Numerous examples are given to demonstrate its advantages.

Key Words: Bayesian method • Fractional factorial design • Qualitative factor • Quantitative factor


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