A complementary design theory for doubling

• 成果类型: Article
• 署名作者: Xu, Hongquan; Cheng, Ching-Shui
• 署名单位: University of California System; University of California Los Angeles; University of California System; University of California Berkeley
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009005360700000712
• 发表日期: 2008
• 页码: 445-457
• 关键词: aberration

摘要

Chen and Cheng [Ann. Statist. 34 (2006) 546-558] discussed the method of doubling for constructing two-level fractional factorial designs. They showed that for 9N/32 <= n <= 5N/16, all minimum aberration designs with N runs and n factors are projections of the maximal design with 5N/16 factors which is constructed by repeatedly doubling the 2(5-1) design defined by I = ABCDE. This paper develops a general complementary design theory for doubling. For any design obtained by repeated doubling, general identities are established to link the wordlength patterns of each pair of complementary projection designs. A rule is developed for choosing minimum aberration projection designs from the maximal design with 5N/16 factors. It is further shown that for 17N/64 <= n <= 5N/16, all minimum aberration designs with N runs and n factors are projections of the maximal design with N runs and 5N/16 factors.