Nonregular two-level designs of resolutin Ⅳ or more containing clear two-factor interactions

摘要

In this paper,the concepts of clear effects,alias sets and grid representations are generalized to nonregular two-level designs.Many good generalized join designs of n runs with resolution Ⅳ or more containing many generalized clear two-factor interactions are given for n=48 up to 192 and n being a multiple of 16.The type-A join designs contain more generalized clear two-factor interactions than any regular resolution Ⅳ design with the same number of factors and less runs.The type-B join designs have the minimum possible number of runs for m-factor designs to be of resolution Ⅳ or more and to contain generalized clear two-factor interactions.The designs constructed are shown to have concise generalized two-factor interaction grid representations.Finally,theoretical results for the necessary and sufficient conditions under which there exist nonregular two-level designs of resolution Ⅳ or more containing generalized clear two-factor interactions are proved.