A note on generalized aberration in factorial designs

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Space-Filling Fractional Factorial Designs (2014, methodology): “Fang and Mukerjee (2000) derived an expression of CD for two-level regular designs in terms of word length pattern; Ma and Fang (2001) extended their result to nonregular fractional designs and also showed that WD can be expressed by the generalized word length pattern (GWP) for two- or three-level…”
Construction of Optimal Multi-Level Supersaturated Designs (2005, background): “Generalized minimum aberration (GMA) criteria, extensions of the minimum aberration criterion [14], have been proposed to assess regular or nonregular designs. See [12, 23 , 28, 33, 34].”
A note on optimal foldover design (2003, background): “where c is de2ned in (1) and (A1(T ( )); : : : ; A g s (T ( ))) is the generalized word length pattern of T ( ) (proposed by Ma and Fang, 2001; Xu and Wu, 2001). It is well known that the criterion of minimum generalized aberration, independently proposed by Ma and Fang (2001) and Xu and Wu (2001) i”
Minimum moment aberration for nonregular designs and supersaturated designs (2001, background): “(1999), Tang and Deng (1999), Xu and Wu (2001) and Ma and Fang (2001) .”
Connections Among Different Criteria for Asymmetrical Fractional Factorial Designs (2006, background): “Aberration has been generalized to nonregular FFDs (Tang and Deng (1999), Ma and Fang (2001) and Xu and Wu (2001)).”