Optimal mixed-level k-circulant supersaturated designs

Abstract Supersaturated designs (SSDs) offer a potentially useful way to investigate many factors with only few experiments in the preliminary stages of experimentation. This paper explores how to construct E ( f NOD ) -optimal mixed-level SSDs using k-cyclic generators. The necessary and sufficient conditions for the existence of mixed-level k-circulant SSDs with the equal occurrence property are provided. Properties of the mixed-level k-circulant SSDs are investigated, in particular, the sufficient condition under which the generator vector produces an E ( f NOD ) -optimal SSD is obtained. Moreover, many new E ( f NOD ) -optimal mixed-level SSDs are constructed and listed. The method here generalizes the one proposed by Liu and Dean [2004. k -circulant supersaturated designs. Technometrics 46, 32–43] for two-level SSDs and the one due to Georgiou and Koukouvinos [2006. Multi-level k-circulant supersaturated designs. Metrika 64, 209–220] for the multi-level case.

[1]  S. Georgiou,et al.  Multi-level k-circulant Supersaturated Designs , 2006 .

[2]  Fred J. Hickernell,et al.  MINIMUM DISCREPANCY IN 2-LEVEL SUPERSATURATED , 2003 .

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

[4]  R. Plackett,et al.  THE DESIGN OF OPTIMUM MULTIFACTORIAL EXPERIMENTS , 1946 .

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

[6]  C. Koukouvinos,et al.  Construction of some E ( f NOD ) optimal mixed-level supersaturated designs , 2005 .

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

[8]  F. E. Satterthwaite.  Random Balance Experimentation , 1959 .

[9]  Hal S. Stern,et al.  Neural networks in applied statistics , 1996 .

[10]  Dursun A. Bulutoglu,et al.  Cyclicly constructed E(s 2 )-optimal supersaturated designs , 2007 .

[11]  Yukun Liu,et al.  Construction of multi-level supersaturated design via Kronecker product , 2007 .

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

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

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

[15]  Stelios D. Georgiou,et al.  On multi-level supersaturated designs , 2006 .

[16]  C. Koukouvinos,et al.  Large supersaturated designs over prime fields , 2005 .

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

[18]  Yufeng Liu,et al.  k-Circulant Supersaturated Designs , 2004, Technometrics.

[19]  K. Fang,et al.  E ( ? 2 ) -optimal mixed-level supersaturated designs , 2007 .

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

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

[22]  Fred J. Hickernell,et al.  Connections Among Different Criteria for Asymmetrical Fractional Factorial Designs , 2006 .

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

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

[25]  Dennis K. J. Lin,et al.  A NOTE ON CYCLIC ORTHOGONAL DESIGNS , 2003 .

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

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

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

[29]  C. Wu,et al.  Construction of Optimal Multi-Level Supersaturated Designs , 2005, math/0603079.

[30]  Runchu Zhang,et al.  A method for screening active effects in supersaturated designs , 2007 .

[31]  Tomomi Matsui,et al.  A general construction method for mixed-level supersaturated design , 2006, Comput. Stat. Data Anal..

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

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