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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.05072 |
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| _version_ | 1866910905434898432 |
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| author | Tsai, Pi-Wen Gilmour, Steven G. |
| author_facet | Tsai, Pi-Wen Gilmour, Steven G. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_05072 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $Q_B$-Optimal Two-Level Designs Tsai, Pi-Wen Gilmour, Steven G. Methodology 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. |
| title | $Q_B$-Optimal Two-Level Designs |
| topic | Methodology |
| url | https://arxiv.org/abs/2504.05072 |