On the equivalence of definitions for regular fractions of mixed-level factorial designs |
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Authors: | PM van de Ven A Di Bucchianico |
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Institution: | 1. EURANDOM, The Netherlands;2. Department of Mathematics and Computer Science, Eindhoven University of Technology, The Netherlands |
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Abstract: | The notion of regularity for fractional factorial designs was originally defined only for two-level factorial designs. Recently, rather different definitions for regular fractions of mixed-level factorial designs have been proposed by Collombier 1996. Plans d’Expérience Factoriels. Springer, Berlin], Wu and Hamada 2000. Experiments. Wiley, New York] and Pistone and Rogantin 2008. Indicator function and complex coding for mixed fractional factorial designs. J. Statist. Plann. Inference 138, 787–802]. In this paper we prove that, surprisingly, these definitions are equivalent. The proof of equivalence relies heavily on the character theory of finite Abelian groups. The group-theoretic framework provides a unified approach to deal with mixed-level factorial designs and treat symmetric factorial designs as a special case. We show how within this framework each regular fraction is uniquely characterized by a defining relation as for two-level factorial designs. The framework also allows us to extend the result that every regular fraction is an orthogonal array of a strength that is related to its resolution, as stated in Dey and Mukerjee 1999. Fractional Factorial Plans. Wiley, New York] to mixed-level factorial designs. |
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Keywords: | Factorial designs Mixed-level designs Regular fractions Orthogonal arrays |
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