Folded over non-orthogonal designs |
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Authors: | C Devon Lin A Miller RR Sitter |
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Institution: | 1. Department of Statistics and Actuarial Science, Simon Fraser University, Burnaby, BC, Canada V5A 1S6;2. Department of Statistics, University of Auckland, Private Bag 92019, Auckland, New Zealand |
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Abstract: | In this article, we use the notion of minimal dependent sets (MDS) to introduce MDS-resolution and MDS-aberration as criteria for comparing non-orthogonal foldover designs, and discuss the ideas and their usefulness. We also develop a fast isomorphism check that uses a cyclic matrix defined on the design before it is folded over. By doing so, the speed of the check for comparing two isomorphic designs is increased relative to merely applying an isomorphism check to the foldover design. This relative difference becomes greater as the design size increases. Finally, we use the isomorphism check to obtain a catalog of minimum MDS-aberration designs for some useful n and k and discuss an algorithm for obtaining “good” larger designs. |
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Keywords: | Aberration Fractional factorial Hadamard matrix Minimal dependent sets Plackett&ndash Burman designs Resolution Isomorphism Equivalence |
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