A general criterion for factorial designs under model uncertainty

Pi Wen Tsai*, Steven G. Gilmour

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)231-242
Number of pages12
Issue number2
Publication statusPublished - 2010 May


  • Aberration
  • Design optimality criterion
  • Generalized minimum aberration
  • Model robust
  • Projection efficiency
  • Supersaturated design

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics


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