A General Criterion for Factorial Designs Under Model Uncertainty

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(s) 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.