Skip to main content
SpringerLink
Log in

On the construction of E(s 2)-optimal supersaturated designs

  • Published:
Metrika Aims and scope Submit manuscript

Abstract

Supersaturated designs are an important class of factorial designs in which the number of factors is larger than the number of runs. These designs supply an economical method to perform and analyze industrial experiments. In this paper, we consider generalized Legendre pairs and their corresponding matrices to construct E(s 2)-optimal two-level supersaturated designs suitable for screening experiments. Also, we provide some general theorems which supply several infinite families of E(s 2)-optimal two-level supersaturated designs of various sizes.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Booth KHV and Cox DR (1962). Some systematic supersaturated designs. Technometrics 4: 489–495

    Article  MATH  MathSciNet  Google Scholar 

  2. Bulutoglu DA (2007). Cyclicly constructed E(s 2)-optimal supersaturated designs. J Stat Plann Inference 137: 2413–2428

    Article  MATH  MathSciNet  Google Scholar 

  3. Bulutoglu DA and Cheng CS (2004). Construction of E(s 2)-optimal supersaturated designs. Ann Stat 32: 1662–1678

    Article  MATH  MathSciNet  Google Scholar 

  4. Butler N, Mead R, Eskridge KM and Gilmour SG (2001). A general method of constructing E(s 2)-optimal supersaturated designs. J R Stat Soc B 63: 621–632

    Article  MATH  MathSciNet  Google Scholar 

  5. Cheng CS (1997). E(s 2)-optimal supersaturated designs. Stat Sinica 7: 929–939

    MATH  Google Scholar 

  6. Fletcher RJ, Gysin M and Seberry J (2001). Application of the discrete Fourier transform to the search for generalized Legendre pairs and Hadamard matrices. Australas J Combin 23: 75–86

    MATH  MathSciNet  Google Scholar 

  7. Georgiou S and Koukouvinos C (2002). On generalized Legendre pairs and multipliers of the corresponding supplementary difference sets. Utilitas Math 61: 47–63

    MATH  MathSciNet  Google Scholar 

  8. Geramita AV and Seberry J (1979). Orthogonal designs: quadratic forms and Hadamard matrices. Marcel Dekker, New York

    MATH  Google Scholar 

  9. Gysin M and Seberry J (1998). An experimental search and new combinatorial designs via a generalisation of cyclotomy. J Combin Math Combin Comput 27: 143–160

    MATH  MathSciNet  Google Scholar 

  10. Li WW and Wu CFJ (1997). Columnwise-pairwise algorithms with applications to the construction of supersaturated designs. Technometrics 39: 171–179

    Article  MATH  MathSciNet  Google Scholar 

  11. Lin DKJ (1993). A new class of supersaturated designs. Technometrics 35: 28–31

    Article  Google Scholar 

  12. Lin DKJ (1995). Generating systematic supersaturated designs. Technometrics 37: 213–225

    Article  MATH  Google Scholar 

  13. Liu M and Zhang R (2000). Construction of E(s 2) optimal supersaturated designs using cyclic BIBDs. J Stat Plann Inference 91: 139–150

    Article  MATH  Google Scholar 

  14. Liu Y and Dean AM (2004). k-circulant supersaturated designs. Technometrics 46: 32–43

    Article  MathSciNet  Google Scholar 

  15. Lu X and Meng Y (2000). A new method in the construction of two-level supersaturated designs. J Stat Plann Inference 86: 229–238

    Article  MATH  MathSciNet  Google Scholar 

  16. Nguyen NK (1996). An algorithmic approach to constructing supersaturated designs. Technometrics 38: 69–73

    Article  MATH  Google Scholar 

  17. Plackett RL and Burman JP (1946). The design of optimum multifactorial experiments. Biometrika 33: 303–325

    Google Scholar 

  18. Ryan KJ and Bulutoglu DA (2007). E(s 2)-optimal supersaturated designs with good minimax properties. J Stat Plann Inference 137: 2250–2262

    Article  MATH  MathSciNet  Google Scholar 

  19. Satterthwaite FE (1959). Random balance experimentation (with discussions). Technometrics 1: 111–137

    Article  MathSciNet  Google Scholar 

  20. Schroeder MR (1984). Number theory in science and communication. Springer, New York

    MATH  Google Scholar 

  21. Tang B and Wu CFJ (1997). A method for constructing supersaturated designs and its E(s 2)-optimality. Can J Stat 25: 191–201

    Article  MATH  MathSciNet  Google Scholar 

  22. Wallis WD, Street AP, Seberry JW (1972) Combinatorics: room squares, sum-free sets, Hadamard Matrices. Lecture Notes in Mathematics, Vol. 292, Springer, Berlin

  23. Wu CFJ (1993). Construction of supersaturated designs through partially aliased interactions. Biometrika 80: 661–669

    Article  MATH  MathSciNet  Google Scholar 

  24. Yamada S and Lin DKJ (1997). Supersaturated designs including an orthogonal base. Can J Statist 25: 203–213

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics and Actuarial-Financial Mathematics, University of the Aegean, Karlovassi, 83200, Samos, Greece

    Stelios D. Georgiou

Authors
  1. Stelios D. Georgiou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Stelios D. Georgiou.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Georgiou, S.D. On the construction of E(s 2)-optimal supersaturated designs. Metrika 68, 189–198 (2008). https://doi.org/10.1007/s00184-007-0151-6

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00184-007-0151-6

Keywords

Mathematics Subject Classification (2000)

Search

Navigation