$Q_B$-Optimal Two-Level Designs

Pi-Wen Tsai; Steven G. Gilmour

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arXiv · 2504.05072

$Q_B$-Optimal Two-Level Designs

Pi-Wen Tsai·Steven G. Gilmour

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Abstract

Two-level designs are widely used for screening experiments where the goal is to identify a few active factors which have major effects. Orthogonal two-level designs in which all factors are level-balance and each of the four level combinations of any pair of factors appears equally often are commonly used. In this paper, we apply the model-robust $Q_B$ criterion introduced by Tsai, Gilmour and Mead (2007) to the selection of optimal two-level screening designs without the requirements of level-balance and pairwise orthogonality. The criterion incorporates experimenter's prior belief on how likely a factor is to be active and recommends different designs under different priors, and without the requirement of level-balance and pairwise orthogonality, a wider range of designs is possible. A coordinate exchange algorithm is developed for the construction of $Q_B$-optimal designs for given priors.

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Pi-Wen Tsai, Steven G. Gilmour. 2025-04-07. $Q_B$-Optimal Two-Level Designs. https://arxiv.org/abs/2504.05072

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