Theory of minimum aberration blocked regular mixed factorial designs

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• 作者：Ai ; Mingyao ; Zhang ; Runchu
• 关键词：primary 62K15 ; secondary 62K05 ; Blocking ; Coding theory ; Mixed-level ; Minimum aberration ; Regular ; Blocked consulting design
• 刊名：Journal of Statistical Planning and Inference
• 出版年：2004
• 期刊代码：36_03783758
• 类别：mt
• 出版时间：November 1, 2004
• 卷：126
• 期：1
• 页码：305-323
• 文件大小：306 K

摘要

Chen and Cheng (Ann. Statist. 27 (1999) 1948) got the relationships between a blocked symmetrical factorial design and its residual design. In this paper, we extend the study to the case of blocked mixed-level factorial designs. By introducing a concept of blocked consulting design and using MacWilliams identities and Krawtchouk polynomials in coding theory, we obtain combinatorial identities that govern the relationships between the partitioned wordlength patterns of a blocked regular mixed factorial design and that of its blocked consulting design. Based on these identities, we furthermore establish some general rules for identifying minimum aberration blocked mixed factorial designs in terms of their blocked consulting designs. As applications, some blocked 4¹2ⁿ and 4²2ⁿ designs with 16 and 32 runs are tabulated.