Q_B-Optimal Two-Level Designs

2025/04/07 by Pi-Wen Tsai, Steven G. Gilmour, Tsai, Pi-Wen +1 · 1 citation
Computer Science · Decision Sciences · Mathematics · #Advanced Multi-Objective Optimization Algorithms #FOS: Computer and information sciences #Methodology (stat.ME) #Optimal Experimental Design Methods #Statistical Methods in Clinical Trials

paper · pdf · doi:10.48550/arxiv.2504.05072

openalex publication_date 2025/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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