A complementary design theory for doubling

Details A complementary design theory for doubling A complementary design theory for doubling

2008-03-14

arxiv.org/abs/0803.2118v1

Annals of Statistics 2008, Vol. 36, No. 1, 445-457

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/009005360700000712 the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009005360700000712

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.

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