具有最小象差的区组正则部分析因设计
Blocked regular fractional factorial designs with minimum aberration
摘要：
本文考虑最小象差区组析因设计的构造。基于编码理论，提出了最小矩像差的概念。Sinica 13（2003）691--708]的非区组化设计方法推广到区组化设计。编码理论方法以逐行方式研究设计，因此将块设计与非规则和过饱和设计联系起来。建立了分块字长模式的下界。证明了一个区组设计具有MA，如果它起源于一个非区组MA设计并达到下界。它还表明，一个正规设计可以划分成极大块当且仅当它包含一个行没有零。给出了由非区组MA设计构造MA区组设计的充分条件。该理论，然后应用于构建MA块组设计的所有32个运行，64运行多达32个因素，和所有81个运行相对于四个组合字长模式。
英文摘要：
This paper considers the construction of minimum aberration (MA) blocked factorial designs. Based on coding theory, the concept of minimum moment aberration due to Xu [Statist. Sinica 13 (2003) 691--708] for unblocked designs is extended to blocked designs. The coding theory approach studies designs in a row-wise fashion and therefore links blocked designs with nonregular and supersaturated designs. A lower bound on blocked wordlength pattern is established. It is shown that a blocked design has MA if it originates from an unblocked MA design and achieves the lower bound. It is also shown that a regular design can be partitioned into maximal blocks if and only if it contains a row without zeros. Sufficient conditions are given for constructing MA blocked designs from unblocked MA designs. The theory is then applied to construct MA blocked designs for all 32 runs, 64 runs up to 32 factors, and all 81 runs with respect to four combined wordlength patterns.
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