A series of search designs for 2m factorial designs of resolution V which permit search of one or two unknown extra three-factor interactions

Abstract

In the absence of four-factor and higher order interactions, we present a series of search designs for 2m factorials (m≥6) 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 ω (1≤ω≤3), are useful in obtaining search designs for k=2. Furthermore, it is shown that a search design obtained for each m≥6 is of the minimum number of treatments among balanced arrays of strenth 6. By modifying the results for m≥6, we also present a search design for m=5 and k=2.