@article{9ec820663ed34448b11f94f6236f91e8,
title = "A general criterion for factorial designs under model uncertainty",
abstract = "Motivated by two industrial experiments in which rather extreme prior knowledge was used to choose the design, we show that the QB criterion, which aims to improve the estimation in as many models as possible by incorporating experimenters' prior knowledge along with an approximation to the As criterion, is more general and has a better statistical interpretation than many standard criteria. The generalization and application of the criterion to different types of designs are presented. The relationships between QB and other criteria for different situations are explored. It is shown that the E(s2) criterion is a special case of QB and several aberration-type criteria are limiting cases of our criterion, so that QB provides a bridge between alphabetic optimality and aberration. The two case studies illustrate the potential benefits of the QB criterion. R programs for calculating QB are available online as supplemental materials.",
keywords = "Aberration, Design optimality criterion, Generalized minimum aberration, Model robust, Projection efficiency, Supersaturated design",
author = "Tsai, {Pi Wen} and Gilmour, {Steven G.}",
note = "Funding Information: The authors thank, and acknowledge financial support from, Queen Mary, University of London, the U.K. Engineering and Physical Sciences Research Council and the Isaac Newton Institute for Mathematical Sciences. The first author{\textquoteright}s research was partly supported by a grant from the National Science Council of Taiwan. We also thank Academia Sinica for inviting the second author to visit and Ching-Shui Cheng for encouraging us to continue our work on this topic. We thank the referees for thoughtful and constructive comments that led to considerable changes in the way we present this work.",
year = "2010",
month = may,
doi = "10.1198/TECH.2010.08093",
language = "English",
volume = "52",
pages = "231--242",
journal = "Technometrics",
issn = "0040-1706",
publisher = "American Statistical Association",
number = "2",
}