Permuting regular fractional factorial designs for screening quantitative factors

• 成果类型: Article
• 署名作者: Tang, Yu; Xu, Hongquan
• 署名单位: Soochow University - China; University of California System; University of California Los Angeles
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/ast073
• 发表日期: 2014
• 页码: 333350
• 关键词: minimum aberration; 2-level; catalog

摘要

Fractional factorial designs arewidely used in screening experiments. They are often chosen by the minimum aberration criterion, which regards factor levels as symbols. For designs with quantitative factors, however, permuting the levels for one or more factors could alter their geometrical structures and statistical properties. We provide a justification of the minimum beta-aberration criterion for quantitative factors and study level permutations for regular fractional factorial designs in order to improve their efficiency for screening quantitative factors. We show how regular designs can be linearly permuted to reduce contamination of nonnegligible interactions on the estimation of linear effects without increasing the run size. We further show that such linear permutations are unique under the minimum beta-aberration criterion and the best level permutations can be determined without an exhaustive search. We establish additional theoretical results for three-level designs and obtain the best level permutations for regular designs with 27 and 81 runs. We illustrate the practical benefits of level permutation with an antiviral drug combination experiment.