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A series of search designs for 2m factorial designs of resolution V which permit search of one or two unknown extra three-factor interactions
Authors:Teruhiro Shirakura  Shinsei Tazawa
Institution:(1) Department of Mathematics, Kobe University, Nada-ku, 657 Kobe, Japan;(2) Department of Mathematics, Kinki University, 577 Higashi-Osaka, Japan
Abstract:In the absence of four-factor and higher order interactions, we present a series of search designs for 2m factorials (mge6) which allow the search of at most k (=1,2) nonnegligible three-factor interactions, and the estimation of them along with the general mean, main effects and two-factor interactions. These designs are derived from balanced arrays of strength 6. In particular, the nonisomorphic weighted graphs with 4 vertices in which two distinct vertices are assigned with integer weight ohgr (1leohgrle3), are useful in obtaining search designs for k=2. Furthermore, it is shown that a search design obtained for each mge6 is of the minimum number of treatments among balanced arrays of strenth 6. By modifying the results for mge6, we also present a search design for m=5 and k=2.
Keywords:Search design  minimum treatment  balanced array  strength 6  weighted graph  isomorphic graph
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