Design Selection and Classification for Hadamard Matrices Using Generalized Minimum Aberration Criteria

TLDR: This article considers the problem of classifying and ranking designs that are based on Hadamard matrices and finds that generalized aberration performs quite well under these familiar criteria.

Abstract: Deng and Tang (1999) and Tang and Deng (1999) proposed and justified two criteria of generalized minimum aberration for general two-level fractional factorial designs. The criteria are defined using a set of values called J characteristics. In this article, we examine the practical use of the criteria in design selection. Specifically, we consider the problem of classifying and ranking designs that are based on Hadamard matrices. A theoretical result on J characteristics is developed to facilitate the computation. The issue of design selection is further studied by linking generalized aberration with the criteria of efficiency and estimation capacity. Our studies reveal that generalized aberration performs quite well under these familiar criteria.