SummaryA connection between a balanced fractional 2 ~ factorial design of resolution V and a balanced array of strength 4 with index set {Z0, Z~, /~2,/~3, Z~} has been established by Srivastava [3]. The purpose of this paper is to generalize his results by investigating the combinatorial property of a fraction T and the algebraic structure of the information matrix of the fractional design. Main results are: A necessary and sufficient condition for a fractional 2 ~ factorial design T of resolution 2/+1 to be balanced is that T is a balanced array of strength 2l with index set {/~0,/~1,/~,"',/~2t} provided the information matrix M is nonsingular.
We consider a fractional 2 m factorial design derived from a simple array (SA) such that the ( + 1)-factor and higher-order interactions are negligible, where 2 ≤ m. The purpose of this article is to give a necessary and sufficient condition for an SA to be a balanced fractional 2 m factorial design of resolution 2 + 1. Such a design is concretely characterized by the suffixes of the indices of an SA.
It is shown that the characteristic roots of the information matrix of a balanced fractional 2 ~ factorial design T of resolution 2l § are the same as those of its complementary design T. Necessary conditions for the existence of such a design T are also given.BALANCED FRACTIONAL 2 m FACTORIALS 383
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