Construction of minimum generalized aberration designs

Supersaturated designs have become increasingly popular in recent years because of their potential in saving run size and the technical novelty. In this paper, the minimum generalized aberration (MGA) criterion proposed by Ma and Fang (2001) (and another two equivalent criteria proposed by Xu and Wu (2001) and Xu (2001b) respectively) for comparing non-regular symmetrical designs is used for evaluating supersaturated designs. A new construction method for MGA symmetrical supersaturated designs via resolvable balanced incomplete block designs is proposed, and some infinite classes for the existence of such MGA designs are obtained simultaneously, along with the investigation of properties of the resulting designs. The construction method shows a strong connection between these two different kinds of designs.

[1]  Y. Ikebe,et al.  Construction of three-level supersaturated design , 1999 .

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

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

[4]  Ching-Shui Cheng,et al.  E(s 2 )-OPTIMAL SUPERSATURATED DESIGNS , 1997 .

[5]  Lih-Yuan Deng,et al.  GENERALIZED RESOLUTION AND MINIMUM ABERRATION CRITERIA FOR PLACKETT-BURMAN AND OTHER NONREGULAR FACTORIAL DESIGNS , 1999 .

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

[7]  Boxin Tang,et al.  A method for constructing supersaturated designs and its Es2 optimality , 1997 .

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

[9]  Jiahua Chen,et al.  Some Results on $2^{n - k}$ Fractional Factorial Designs and Search for Minimum Aberration Designs , 1992 .

[10]  Douglas R. Stinson,et al.  Frames with Block Size Four , 1992, Canadian Journal of Mathematics.

[11]  Howard M. Proskin,et al.  Theory of Block Designs , 1989 .

[12]  M. F. Franklin.  Constructing Tables of Minimum Aberration pn-m Designs , 1984 .

[13]  Dennis K. J. Lin.  Generating Systematic Supersaturated Designs , 1995 .

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

[15]  Jiahua Chen,et al.  A catalogue of two-level and three-level fractional factorial designs with small runs , 1993 .

[16]  Min-Qian Liu,et al.  Construction of E(s2) optimal supersaturated designs using cyclic BIBDs , 2000 .

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

[18]  Lih-Yuan Deng,et al.  A RESOLUTION RANK CRITERION FOR SUPERSATURATED DESIGNS , 1999 .

[19]  Nam-Ky Nguyen.  An algorithmic approach to constructing supersaturated designs , 1996 .

[20]  Changbao Wu,et al.  Construction of supersaturated designs through partially aliased interactions , 1993 .

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

[22]  Dennis K. J. Lin,et al.  Three-level supersaturated designs , 1999 .

[23]  William Li,et al.  Columnwise-pairwise algorithms with applications to the construction of supersaturated designs , 1997 .

[24]  R. Julian R. Abel,et al.  Resolvable balanced incomplete block designs with block size 5 , 2001 .

[25]  Alan Hartman,et al.  The existence of resolvable Steiner quadruple systems , 1987, J. Comb. Theory, Ser. A.

[26]  C. Colbourn,et al.  The CRC handbook of combinatorial designs , edited by Charles J. Colbourn and Jeffrey H. Dinitz. Pp. 784. $89.95. 1996. ISBN 0-8493-8948-8 (CRC). , 1997, The Mathematical Gazette.

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

[28]  K. H. Booth,et al.  Some Systematic Supersaturated Designs , 1962 .

[29]  Hongquan Xu.  Optimal factor assignment for asymmetrical fractional factorial designs: Theory and applications. , 2001 .

[30]  S. Yamada,et al.  Supersaturated design including an orthogonal base , 1997 .

[31]  J HickernellF,et al.  The Uniform Design and Its Applications , 1995 .

[32]  Xuan Lu,et al.  A new method in the construction of two-level supersaturated designs , 2000 .