Skip to main content
SpringerLink
Log in

Testing Systems of Identical Components

  • Published:
Journal of Combinatorial Optimization Aims and scope Submit manuscript

Abstract

We consider the problem of testing sequentially the components of a multi-component reliability system in order to figure out the state of the system via costly tests. In particular, systems with identical components are considered. The notion of lexicographically large binary decision trees is introduced and a heuristic algorithm based on that notion is proposed. The performance of the heuristic algorithm is demonstrated by computational results, for various classes of functions. In particular, in all 200 random cases where the underlying function is a threshold function, the proposed heuristic produces optimal solutions.

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

  • L. Arseneau, “Optimal testing strategies for s,t-series parallel systems,” Master's thesis, Combinatorics and Optimization, University of Waterloo, 1996.

  • Y. Ben-Dov, “Optimal testing procedures for special structures of coherent systems,” Management Science, vol. 27, no. 12, pp. 1410–1420, 1981.

    Article  MATH  Google Scholar 

  • E. Boros and T. Ünlüyurt, “Diagnosing double regular systems,” Annals of Mathematics and Artificial Intelligence, vol. 26, pp. 171–191, 1999.

    Article  ISI  MathSciNet  MATH  Google Scholar 

  • E. Boros and T. Ünlüyurt, “Sequential testing of series-parallel systems of small depth,” in M. Laguna and J.L.G. Velarde (eds.), OR Computing Tools for the New Millennium, Kluwer, 2000, pp. 39–74.

  • Y. Breitbart and A. Reiter, “A branch-and-bound algorithm to obtain an optimal evaluation tree for monotonic boolean functions,” Acta Informatica, vol. 4, pp. 311–319, 1975.

    MathSciNet  MATH  Google Scholar 

  • Y. Breitbart and S. Gal, “Analysis of algorithms for the evaluation of monotonic Boolean functions,” IEEE Transactions on Computers, vol. 27, no. 11, pp. 1083–1087, 1978.

    ISI  MathSciNet  MATH  Google Scholar 

  • Y. Breitbart and A. Reiter, “Algorithms for fast evaluation of boolean expressions,” Acta Informatica, vol. 4, pp. 107–116, 1975.

    Google Scholar 

  • M. Chang, W. Shi, and W.K. Fuchs, “Optimal diagnosis procedures for k-out-of-n structures,” IEEE Transactions on Computers, vol. 39, no. 4, pp. 559–564, 1990.

    Article  ISI  Google Scholar 

  • L.A. Cox, S.Y. Chiu, and X. Sun, “Least-cost failure diagnosis in uncertain reliability systems,” Reliability Engineering and System Safety, vol. 54, pp. 203–216, 1996.

    Article  Google Scholar 

  • S.O. Duffuaa and A. Raouf, “An optimal sequence in multicharacteristics inspection,” Journal of Optimization Theory and Applications, vol. 67, no. 1, pp. 79–87, 1990.

    Article  ISI  MathSciNet  MATH  Google Scholar 

  • M.R. Garey, “Optimal task sequencing with precedence constraints,” Discrete Mathematics, vol. 4, pp. 37–56, 1973.

    Article  MATH  MathSciNet  Google Scholar 

  • R. Greiner, “Finding optimal derivation strategies in redundant knowledge bases,” Artificial Intelligence, vol. 50, pp. 95–115, 1990.

    ISI  MathSciNet  Google Scholar 

  • E. Gudes and A. Hoffman, “A note on an optimal evaluation of boolean expressions in an online query system,” Short Communications, Artificial Intelligence/Language Processing, vol. 22, no. 10, pp. 550–553, 1979.

    MathSciNet  Google Scholar 

  • J.Y. Halpern, “Evaluating Boolean function with random variables,” International Journal of Systems Science, vol. 5, no. 6, pp. 545–553, 1974.

    MATH  ISI  MathSciNet  Google Scholar 

  • M.Z. Hanani, “An optimal evaluation of boolean expressions in an online query system,” Short Communications, Artificial Intelligence/Language Processing, vol. 20, no. 5, pp. 344–347, 1977.

    MATH  MathSciNet  Google Scholar 

  • L.A. Cox Jr., Y. Qiu, and W. Kuehner, “Heuristic least-cost computation of discrete classification functions with uncertain argument values,” Annals of Operations Research, vol. 21, pp. 1–21, 1989.

    Article  MathSciNet  MATH  Google Scholar 

  • H.A. Simon and J.B. Kadane, “Optimal problem-solving search: All-or-none solutions,” Artificial Intelligence, vol. 6, pp. 235–247, 1975.

    Article  ISI  MathSciNet  MATH  Google Scholar 

  • D.E. Smith, “Controlling backward inference,” Artificial Intelligence, vol. 39, pp. 145–208, 1989.

    Article  MATH  ISI  MathSciNet  Google Scholar 

  • T. Ünlüyurt, Sequential Testing of Complex Systems. PhD thesis, Rutgers University, 1999.

  • T. Ünlüyurt, “Sequential testing of complex systems: A review,” Discrete Applied Mathematics, vol. 142, nos. (1–3), pp. 189–205, 2004.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Engineering and Natural Sciences, Sabanci University, Orhanlı, Tuzla, 34956, İstanbul, Turkey

    Tonguç Ünlüyurt

Authors
  1. Tonguç Ünlüyurt
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tonguç Ünlüyurt.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ünlüyurt, T. Testing Systems of Identical Components. J Comb Optim 10, 261–282 (2005). https://doi.org/10.1007/s10878-005-4106-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10878-005-4106-4

Keywords

Search

Navigation