Metrika

, Volume 68, Issue 1, pp 99–110 | Cite as

A general construction of E(s2)-optimal large supersaturated designs

Article

Abstract

A general method for construction of E(s2)-optimal, two-level supersaturated designs (SSDs) with the equal occurrence property, from supplementary difference sets is introduced. It is proved that SSDs constructed in this way are E(s2)-optimal. Comparisons are made with previous works and it is shown that the proposed method gives promising results for the construction of E(s2)-optimal large SSDs.

Keywords

Cyclotomy Difference sets E(s2)-optimality Supersaturated designs Supplementary difference sets 

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References

  1. Baumert LD (1971) Cyclic difference sets. Springer, BerlinMATHGoogle Scholar
  2. Booth KHV, Cox DR (1962) Some systematic supersaturated designs. Technometrics 4:489–495MATHCrossRefMathSciNetGoogle Scholar
  3. Box GEP, Meyer RD (1986) An analysis for unreplicated fractional factorials. Technometrics 28:11–18MATHCrossRefMathSciNetGoogle Scholar
  4. Bulutoglu DA (2007) Cyclicly constructed E(s 2)-optimal supersaturated designs. J Stat Plan Inference 137:2413–2428MATHCrossRefMathSciNetGoogle Scholar
  5. Bulutoglu DA, Cheng CS (2004) Construction of E(s 2)-optimal supersaturated designs. Ann Stat 32:1662–1678MATHCrossRefMathSciNetGoogle Scholar
  6. Butler N, Mead R, Eskridge KM, Gilmour SG (2001) A general method of constructing E(s 2)-optimal supersaturated designs. J R Stat Soc B 63:621–632MATHCrossRefMathSciNetGoogle Scholar
  7. Cheng CS (1997) E(s 2)-optimal supersaturated designs. Stat Sin 7:929–939MATHGoogle Scholar
  8. Cheng CS, Tang B (2001) Upper bounds on the number of columns in supersaturated designs. Biometrika 88:1169–1174MATHCrossRefMathSciNetGoogle Scholar
  9. Eskridge KM, Gilmour SG, Mead R, Butler NA, Travnicek DA (2004) Large supersaturated designs. J Stat Comput Simul 74:525–542MATHCrossRefMathSciNetGoogle Scholar
  10. Geramita AV, Seberry J (1979) Orthogonal designs: quadratic forms and Hadamard matrices. Marcel Dekker, New York, BaselMATHGoogle Scholar
  11. Gilmour SG (2006) Factor screening via supersaturated designs. In: Dean A, Lewis S (eds) Screening methods for experimentation in industry, drug discovery, and genetics. Springer, New York, pp 169–190Google Scholar
  12. Gysin M, Seberry J (1998) On new families of supplementary difference sets over rings with short orbits. J Combin Math Combin Comput 28:161–186MATHMathSciNetGoogle Scholar
  13. Holcomb DR, Montgomery DC, Carlyle WM (2007) The use of supersaturated experiments in turbine engine development. Qual Eng 19:17–27CrossRefGoogle Scholar
  14. Koukouvinos C, Mylona K, Simos DE (2007) Exploring k-circulant supersaturated designs via genetic algorithms. Comput Stat Data Anal 51:2958–2968CrossRefMathSciNetGoogle Scholar
  15. Li WW, Wu CFJ (1997) Columnwise-pairwise algorithms with applications to the construction of supersaturated designs. Technometrics 39:171–179MATHCrossRefMathSciNetGoogle Scholar
  16. Lin DKJ (1993) A new class of supersaturated designs. Technometrics 35:28–31CrossRefGoogle Scholar
  17. Lin DKJ (1995) Generating systematic supersaturated designs. Technometrics 37:213–225MATHCrossRefGoogle Scholar
  18. Liu YF, Dean A (2004) k-circulant supersaturated designs. Technometrics 46:32–43CrossRefMathSciNetGoogle Scholar
  19. Liu M, Zhang R (2000) Construction of E(s 2) optimal supersaturated designs using cyclic BIBDs. J Stat Plan Inference 91:139–150MATHCrossRefGoogle Scholar
  20. Lu X, Meng Y (2000) A new method in the construction of two-level supersaturated designs. J Stat Plan Inference 86:229–238MATHCrossRefMathSciNetGoogle Scholar
  21. Nguyen NK (1996) An algorithmic approach to constructing supersaturated designs. Technometrics 38: 69–73MATHCrossRefGoogle Scholar
  22. Nguyen NK, Cheng CS (2007) New E(s 2)-optimal supersaturated designs constructed from incomplete block designs. Technometrics (to appear)Google Scholar
  23. Plackett RL, Burman JP (1946) The design of optimum multifactorial experiments. Biometrika 33:303–325Google Scholar
  24. Ryan KJ, Bulutoglu DA (2007) E(s 2)-optimal supersaturated designs with good minimax properties. J Stat Plan Inference 137:2250–2262MATHCrossRefMathSciNetGoogle Scholar
  25. Satterthwaite FE (1959) Random balance experimentation (with discussions). Technometrics 1:111–137CrossRefMathSciNetGoogle Scholar
  26. Seberry Wallis J (1973) Some remarks on supplementary difference sets. Colloquia Marhematica Societatis Janos Bolyai Hungary 10:1503–1526Google Scholar
  27. Tang B, Wu CFJ (1997) A method for constructing supersaturated designs and its Es 2-optimality. Can J Stat 25:191–201MATHCrossRefMathSciNetGoogle Scholar
  28. Wallis WD, Street AP, Seberry Wallis J (1972) Combinatorics: room squares, sum-free sets, Hadamard matrices. Lecture notes in mathematics, vol 292. Springer, BerlinGoogle Scholar
  29. Wu CFJ (1993) Construction of supersaturated designs through partially aliased interactions. Biometrika 80:661–669MATHCrossRefMathSciNetGoogle Scholar
  30. Yamada S, Lin DKJ (1997) Supersaturated designs including an orthogonal base. Can J Stat 25:203–213MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of MathematicsNational Technical University of AthensAthensGreece
  2. 2.National Statistical Service of GreecePiraeusGreece

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