Indicator function and its application in two-level factorial designs

• 成果类型: Article
• 署名作者: Ye, KQ
• 署名单位: State University of New York (SUNY) System; Stony Brook University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1056562470
• 发表日期: 2003
• 页码: 984-994
• 关键词: minimum g(2)-aberration; projection properties; plackett-burman; aberration; fractions

摘要

A two-level factorial design can be uniquely represented by a polynomial indicator function. Therefore, properties of factorial designs can be studied through their indicator functions. This paper shows that the indicator function is an effective tool in studying two-level factorial designs. The indicator function is used to generalize the aberration criterion of a regular two-level fractional factorial design to all two-level factorial designs. An important identity of generalized aberration is proved. The connection between a uniformity measure and aberration is also extended to all two-level factorial designs.