Theory and Construction Methods for Large Regular Resolution IV Designs

Abstract : The author defines 2 (super k-p) fractional factorial designs that use all of their degrees of freedom to estimate main effects and two-factor interactions as second order saturated (SOS) designs. He proves that resolution IV SOS designs project to every other resolution IV design, and shows the details of these projections for every n = 32 and n = 64 run fraction. For k greater than (5/l6)n, all resolution IV designs are a projection from the even SOS design at k = n/2. For k less than or equal to (5/l6)n the minimum aberration design resolution IV designs are projections of SOS designs with both even and odd words in the defining relation. While even resolution IV designs are limited to estimating fewer than n/2 two-factor interactions (in addition to the k main effects), resolution IV designs with odd-length words in the defining relation may devote more than half of their degrees of freedom to two-factor interactions. The author proposes a method to search for good resolution IV designs using naive projections from even/odd SOS designs. He introduces the alias length pattern as a tool to help characterize designs, and he describes how the matrix T = DD for a design D is useful in searching for designs. He lists the resolution IV even/odd minimum aberration designs for n = 128 and provides a catalog of the best resolution IV even/odd designs for n = 128. These results are based on an isomorphic check using a convenient function of T, as well as the set of projections of a design. Finally, the author suggests a new method for finding good regular resolution IV designs for large n (greater than 128) and provides a preliminary table of good resolution IV even/odd designs for n = 256. (19 tables, 7 figures, 26 refs.)

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