Hegang H. Chen | Searcharxiv

arXiv2009

Some results on $2^{n-m}$ designs of resolution IV with (weak) minimum aberration

It is known that all resolution IV regular $2^{n-m}$ designs of run size $N=2^{n-m}$ where $5N/16<n<N/2$ must be projections of the maximal even design with $N/2$ factors and, therefore, are even designs. This paper derives a general and explicit relationship between the wordlength pattern of any even $2^{n-m}$ design and that of its complement in the maximal even design. Using these identities, we identify some (weak) minimum aberration $2^{n-m}$ designs of resolution IV and the structures of their complementary designs. Based on these results, several families of minimum aberration $2^{n-m}$ designs of resolution IV are constructed.

math.ST↗

arXiv2006

Doubling and projection: a method of constructing two-level designs of resolution iv

Given a two-level regular fractional factorial design of resolution IV, the method of doubling produces another design of resolution IV which doubles both the run size and the number of factors of the initial design. On the other hand, the projection of a design of resolution IV onto a subset of factors is of resolution IV or higher. Recent work in the literature of projective geometry essentially determines the structures of all regular designs of resolution IV with $n\geq N/4+1$ in terms of doubling and projection, where $N$ is the run size and $n$ is the number of factors. These results imply that, for instance, all regular designs of resolution IV with $5N/16<n\leq N/2$ must be projections of the regular design of resolution IV with $N/2$ factors. We show that, for $9N/32\leq n\leq 5N/16$, all minimum aberration designs are projections of the design with $5N/16$ factors which is constructed by repeatedly doubling the 2$^{5-1}$ design defined by $I=\mathit{ABCDE}$. To prove this result, we also derive some properties of doubling, including an identity that relates the wordlength pattern of a design to that of its double and a result that does the same for the alias patterns of two-factor interactions.

math.ST↗