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Minimum aberration and model robustness for two-level fractional factorial designs

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Abstract:

The performance of minimum aberration two-level fractional factorial designs is studied under two criteria of model robustness. Simple sufficient conditions for a design to dominate another design with respect to each of these two criteria are derived. It is also shown that a minimum aberration design of resolution III or higher maximizes the number of two-factor interactions which are not aliases of main effects and, subject to that condition, minimizes the sum of squares of the sizes of alias sets of two-factor interactions. This roughly says that minimum aberration designs tend to make the sizes of the alias sets very uniform. It follows that minimum aberration is a good surrogate for the two criteria of model robustness that are studied here. Examples are given to show that minimum aberration designs are indeed highly efficient.

Keywords: Estimation capacity; Resolution; Suspect two-factor interaction; Upper weak majorization; Word length pattern

Document Type: Original Article

DOI: https://doi.org/10.1111/1467-9868.00164

Affiliations: 1: University of California, Berkeley, USA, 2: University of Tel Aviv, Israel, 3: Bell Laboratories, Murray Hill, USA

Publication date: 1999-01-01

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