Connections Among Different Criteria for Asymmetrical Fractional Factorial Designs

In recent years, there has been increasing interest in the study of asym- metrical fractional factorial designs. Various new optimality criteria have been proposed from dieren t principles for design construction and comparison, such as generalized minimum aberration, minimum moment aberration, minimum projec- tion uniformity and the 2 (D) (for design D) criteria. In this paper, these criteria are reviewed and the 2 (D) criterion is generalized to the so-called minimum 2 criterion. Connections among dieren t criteria are investigated. These connections provide strong statistical justication for each of them. Some general optimality results are developed, which not only unify several results (including results for the symmetrical case), but also are useful for constructing asymmetrical supersaturated designs.

[1]  I. Olkin,et al.  Inequalities: Theory of Majorization and Its Applications , 1980 .

[2]  Runze Li,et al.  Majorization framework for balanced lattice designs , 2005, math/0603082.

[3]  Rahul Mukerjee,et al.  On the existence of saturated and nearly saturated asymmetrical orthogonal arrays , 1995 .

[4]  Dennis K. J. Lin,et al.  A new class of supersaturated designs , 1993 .

[5]  Ching-Shui Cheng,et al.  Regular fractional factorial designs with minimum aberration and maximum estimation capacity , 1998 .

[6]  David M. Steinberg,et al.  Minimum aberration and model robustness for two‐level fractional factorial designs , 1999 .

[7]  Min-Qian Liu,et al.  Some theory and the construction of mixed-level supersaturated designs , 2004 .

[8]  F. J. Hickernell,et al.  Uniform designs limit aliasing , 2002 .

[9]  Hongquan Xu,et al.  A catalogue of three-level regular fractional factorial designs , 2005 .

[10]  Kenny Q. Ye,et al.  Geometric isomorphism and minimum aberration for factorial designs with quantitative factors , 2004, math/0503678.

[11]  Dursun A. Bulutoglu,et al.  Construction of E(s^2)-optimal supersaturated designs , 2004 .

[12]  Boxin Tang,et al.  Theory of J-characteristics for fractional factorial designs and projection justification of minimum G2-aberration , 2001 .

[13]  Dennis K. J. Lin,et al.  Construction of mixed-level supersaturated design , 2002 .

[14]  F. J. Hickernell,et al.  ${E(s^2)}$-Optimality and Minimum Discrepancy in 2-level Supersaturated Designs , 2002 .

[15]  W. G. Hunter,et al.  Minimum Aberration 2 k–p Designs , 1980 .

[16]  Dennis K. J. Lin,et al.  On the construction of multi-level supersaturated designs , 2000 .

[17]  Gennian Ge,et al.  Construction of optimal supersaturated designs by the packing method , 2004 .

[18]  S. Yamada,et al.  Optimality of mixed-level supersaturated designs , 2002 .

[19]  Dennis K. J. Lin,et al.  Optimal mixed-level supersaturated design , 2003 .

[20]  Lih-Yuan Deng,et al.  Minimum $G_2$-aberration for nonregular fractional factorial designs , 1999 .

[21]  Gennian Ge,et al.  Uniform supersaturated design and its construction , 2002 .

[22]  Yong Zhang,et al.  Uniform Design: Theory and Application , 2000, Technometrics.

[23]  Kai-Tai Fang,et al.  A note on generalized aberration in factorial designs , 2001 .

[24]  Hongquan Xu.  Minimum moment aberration for nonregular designs and supersaturated designs , 2001 .

[25]  Kai-Tai Fang,et al.  Construction of minimum generalized aberration designs , 2003 .

[26]  Hong Qin,et al.  Combinatorial constructions for optimal supersaturated designs , 2004, Discret. Math..

[27]  W. G. Hunter,et al.  Minimum Aberration 2k-p Designs , 1980 .

[28]  Changbao Wu,et al.  Fractional Factorial Designs , 2022 .