A general theory of minimum aberration and its applications

• 成果类型: Article
• 署名作者: Cheng, CS; Tang, BX
• 署名单位: Academia Sinica - Taiwan; University of California System; University of California Berkeley; Simon Fraser University; University of Memphis
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053604000001228
• 发表日期: 2005
• 页码: 944-958
• 关键词: fractional factorial-designs; optimal blocking; 2-level

摘要

Minimum aberration is an increasingly popular criterion for comparing and assessing fractional factorial designs, and few would question its importance and usefulness nowadays. In the past decade or so, a great deal of work has been done on minimum aberration and its various extensions. This paper develops a general theory of minimum aberration based on a sound statistical principle. Our theory provides a unified framework for minimum aberration and further extends the existing work in the area. More importantly, the theory offers a systematic method that enables experimenters to derive their own aberration criteria. Our general theory also brings together two seemingly separate research areas: one on minimum aberration designs and the other on designs with requirement sets. To facilitate the design construction, we develop a complementary design theory for quite a general class of aberration criteria. As an immediate application, we present some construction results on a weak version of this class of criteria.