标题： 加倍的互补设计理论 显示英文标题

标题： A complementary design theory for doubling

摘要： 陈和程[《统计年鉴》34 (2006) 546--558] 讨论了加倍法构造二水平部分因子设计的方法。他们证明了对于$9N/32\le n\le 5N/16$，所有具有$N$个运行次数和$n$个因子的最小混杂度设计都是由包含$5N/16$个因子的最大设计通过反复加倍$2^{5-1}$定义的设计投影而来，该设计由$I=ABCDE$定义。 本文发展了一种加倍的一般互补设计理论。对于任意通过反复加倍获得的设计，建立了普遍恒等式来连接每一对互补投影设计的字长模式。提出了从包含$5N/16$个因子的最大设计中选择最小混杂度投影设计的规则。 进一步表明，对于$17N/64\le n\le 5N/16$，所有具有$N$个运行次数和$n$个因子的最小离度设计都是具有$N$个运行次数和$5N/16$个因子的最大设计的投影。 显示英文摘要

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 $9N/32\le n\le 5N/16$, 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 $17N/64\le n\le 5N/16$, all minimum aberration designs with $N$ runs and $n$ factors are projections of the maximal design with $N$ runs and $5N/16$ factors.