A complementary design theory for doubling

TL;DR

This paper introduces a comprehensive theory for the doubling method in fractional factorial designs, providing identities and rules to identify minimum aberration designs within a broad range of factors.

Contribution

It develops a general complementary design theory for doubling, linking wordlength patterns and guiding the selection of optimal projection designs.

Findings

Established identities linking wordlength patterns of complementary designs.

Developed a rule for selecting minimum aberration projections.

Showed all minimum aberration designs are projections of maximal designs within specified ranges.

Abstract

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.