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ABSTRACT:
Chen and Cheng (2006a) 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.

SUGGESTED CITATION:
Hongquan Xu and Ching-Shui Cheng, "A Complementary Design Theory for Doubling" (August 11, 2006). Department of Statistics, UCLA. Department of Statistics Papers. Paper 2006081101.
http://repositories.cdlib.org/uclastat/papers/2006081101