A complementary design theory for doubling

TLDR: Xu and Cheng as discussed by the authors developed a general complementary design theory for doubling and developed a rule for choosing minimum aberration projection designs from the maximal design with 5N/16 factors.

Abstract: A COMPLEMENTARY DESIGN THEORY FOR DOUBLING By Hongquan Xu 1 and Ching-Shui Cheng 2 University of California, Los Angeles, and University of California, Berkeley August 11, 2006 Chen and Cheng (2006a) discussed the method of doubling for con- structing 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 the- ory 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. AMS 2000 subject classifications. Primary 62K15. Key words and phrases. Maximal design, minimum aberration, Pless power moment identity, wordlength pattern. Running title. Doubling and Complementary Designs Supported in part by NSF Grant DMS-0505728 Supported in part by NSF Grant DMS-0505556