Advances in Applied Probability

On the equivalence of systems of different sizes, with applications to system comparisons

Bo H. Lindqvist, Francisco J. Samaniego, and Arne B. Huseby

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

The signature of a coherent system is a useful tool in the study and comparison of lifetimes of engineered systems. In order to compare two systems of different sizes with respect to their signatures, the smaller system needs to be represented by an equivalent system of the same size as the larger system. In the paper we show how to construct equivalent systems by adding irrelevant components to the smaller system. This leads to simpler proofs of some current key results, and throws new light on the interpretation of mixed systems. We also present a sufficient condition for equivalence of systems of different sizes when restricting to coherent systems. In cases where for a given system there is no equivalent system of smaller size, we characterize the class of lower-sized systems with a signature vector which stochastically dominates the signature of the larger system. This setup is applied to an optimization problem in reliability economics.

Article information

Source
Adv. in Appl. Probab., Volume 48, Number 2 (2016), 332-348.

Dates
First available in Project Euclid: 9 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.aap/1465490751

Mathematical Reviews number (MathSciNet)
MR3511764

Zentralblatt MATH identifier
1344.60084

Subjects
Primary: 60K10: Applications (reliability, demand theory, etc.)
Secondary: 62N05: Reliability and life testing [See also 90B25] 90B50: Management decision making, including multiple objectives [See also 90C29, 90C31, 91A35, 91B06]

Keywords
Coherent system system signature $k$-out-of-$n$ system mixed system reliability polynomial irrelevant component cut set critical path vector stochastic order reliability economics

Citation

Lindqvist, Bo H.; Samaniego, Francisco J.; Huseby, Arne B. On the equivalence of systems of different sizes, with applications to system comparisons. Adv. in Appl. Probab. 48 (2016), no. 2, 332--348. https://projecteuclid.org/euclid.aap/1465490751


Export citation

References

  • Barlow, R. E. and Proschan, F. (1981). Statistical Theory of Reliability and Life Testing. Holt, Rinehart and Winston, New York.
  • Boland, P. J. (2001). Signatures of indirect majority systems. J. Appl. Prob. 38, 597–603.
  • Lindqvist, B. H., Samaniego, F. J. and Huseby, A. B. (2014). On the equivalence of systems of different sizes. Preprint Statistics No. 2/2014, Department of Mathematical Sciences, Norwegian University of Science and Technology.
  • Navarro, J. and Rubio, R. (2010). Computations of signatures of coherent systems with five components. Commun. Statist. Simul. Comput. 39, 68–84.
  • Navarro, J., Samaniego, F. J., Balakrishnan, N. and Bhattacharya, D. (2008). On the application and extension of system signatures in engineering reliability. Naval Res. Logistics 55, 313–327.
  • Nering, E. D. and Tucker, A. W. (1993). Linear Programs and Related Problems. Academic Press, Boston, MA.
  • Randles, R. H. and Wolfe, D. A. (1991). Introduction to the Theory of Nonparametric Statistics. Krieger, Malabar, FL.
  • Samaniego, F. J. (1985). On closure of the IFR class under formation of coherent systems. IEEE Trans. Reliability 34, 69–72.
  • Samaniego, F. J. (2007). System Signatures and Their Applications in Engineering Reliability (Internat. Ser. Operat. Res. Manag. Sci. 110). Springer, New York.