Theory of optimal blocking of 2n-m designs

• 成果类型: Article
• 署名作者: Chen, HG; Cheng, CS
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities; University of California System; University of California Berkeley
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1999
• 页码: 1948-1973
• 关键词: minimum aberration; RESOLUTION

摘要

In this paper, we define the blocking wordlength pattern of a blocked fractional factorial design by combining the wordlength patterns of treatment-defining words and block-defining words. The concept of minimum aberration can be defined in terms of the blocking wordlength pattern and provides a good measure of the estimation capacity of a blocked fractional factorial design. By blending techniques of coding theory and finite projective geometry, we obtain combinatorial identities that govern the relationship between the blocking wordlength pattern of a blocked 2(n-m) design and the split wordlength pattern of its blocked residual design. Based on these identities, we establish general rules for identifying minimum aberration blocked 2(n-m) designs in terms of their blocked residual designs. Using these rules, we study the structures of some blocked 2(n-m) designs with minimum aberration.