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 Q_B criterion, which aims to improve the estimation in as many models as possible by incorporating experimenters’ prior knowledge along with an approximation to the A_s 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 Q_B and other criteria for different situations are explored. It is shown that the E(s²) criterion is a special case of Q_B and several aberration-type criteria are limiting cases of our criterion, so that Q_B provides a bridge between alphabetic optimality and aberration. The two case studies illustrate the potential benefits of the Q_B criterion. R programs for calculating Q_B are available online as supplemental materials.

Keywords:  :

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