Journal of Applied Probability

Signature-based representations for the reliability of systems with heterogeneous components

Jorge Navarro, Francisco J. Samaniego, and N. Balakrishnan

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

Signature-based representations of the reliability functions of coherent systems with independent and identically distributed component lifetimes have proven very useful in studying the ageing characteristics of such systems and in comparing the performance of different systems under varied criteria. In this paper we consider extensions of these results to systems with heterogeneous components. New representation theorems are established for both the case of components with independent lifetimes and the case of component lifetimes under specific forms of dependence. These representations may be used to compare the performance of systems with homogeneous and heterogeneous components.

Article information

Source
J. Appl. Probab., Volume 48, Number 3 (2011), 856-867.

Dates
First available in Project Euclid: 23 September 2011

Permanent link to this document
https://projecteuclid.org/euclid.jap/1316796920

Digital Object Identifier
doi:10.1239/jap/1316796920

Mathematical Reviews number (MathSciNet)
MR2884821

Zentralblatt MATH identifier
1250.62052

Subjects
Primary: 60E15: Inequalities; stochastic orderings
Secondary: 60K10: Applications (reliability, demand theory, etc.)

Keywords
Coherent system k-out-of-n system order statistic signature mixture copula stochastic order

Citation

Navarro, Jorge; Samaniego, Francisco J.; Balakrishnan, N. Signature-based representations for the reliability of systems with heterogeneous components. J. Appl. Probab. 48 (2011), no. 3, 856--867. doi:10.1239/jap/1316796920. https://projecteuclid.org/euclid.jap/1316796920


Export citation

References

  • Agrawal, A. and Barlow, R. E. (1984). A survey of network reliability and domination theory. Operat. Res. 32, 478–492.
  • Barlow, R. E. and Proschan, F. (1975). Statistical Theory of Reliability and Life Testing. Holt, Rinehart and Winston, New York.
  • Belzunce, F., Franco, M., Ruiz, J.-M. and Ruiz, M. C. (2001). On partial orderings between coherent systems with different structures. Prob. Eng. Inf. Sci. 15, 273–293.
  • Bhattacharya, D. and Samaniego, F. J. (2010). On estimating component characteristics from system failure-time data. Naval Res. Logistics 57, 380–389.
  • Boland, P. J. (2001). Signatures of indirect majority systems. J. Appl. Prob. 38, 597–603.
  • De Finetti, B. (1931). Sul concetto di media. Giornale Ist. Ital. Attuari 2, 369–396.
  • Esary, J. D. and Proschan, F. (1963). Relationship between system failure rate and component failure rates. Technometrics 5, 183–189.
  • Hardy, G. H., Littlewood, J. E. and Pólya, G. (1934). Inequalities. Cambridge University Press, London.
  • Jasiński, K., Navarro, J. and Rychlik, T. (2009). Bounds on variances of lifetimes of coherent and mixed systems. J. Appl. Prob. 46, 894–908.
  • Khaledi, B.-E. and Shaked, M. (2007). Ordering conditional lifetimes of coherent systems. J. Statist. Planning Infer. 137, 1173–1184.
  • Kochar, S., Mukerjee, H. and Samaniego, F. J. (1999). The “signature” of a coherent system and its application to comparisons among systems. Naval Res. Logistics 46, 507–523.
  • Navarro, J. (2008). Likelihood ratio ordering of order statistics, mixtures and systems. J. Statist. Planning Infer. 138, 1242–1257.
  • Navarro, J. and Hernandez, P. J. (2008). Mean residual life functions of finite mixtures, order statistics and coherent systems. Metrika 67, 277–298.
  • Navarro, J. and Rubio, R. (2010). Comparisons of coherent systems using stochastic precedence. Test 19, 469–486.
  • Navarro, J. and Rychlik, T. (2010). Comparisons and bounds for expected lifetimes of reliability systems. Europ. J. Operat. Res. 207, 309–317.
  • Navarro, J. and Shaked, M. (2006). Hazard rate ordering of order statistics and systems. J. Appl. Prob. 43, 391–408.
  • Navarro, J. and Shaked, M. (2010). Some properties of the minimum and the maximum of random variables with joint logconcave distributions. Metrika 71, 313–317.
  • Navarro, J. and Spizzichino, F. (2010). Comparisons of series and parallel systems with components sharing the same copula. Appl. Stoch. Models Business Industry 26, 775–791.
  • Navarro, J., Ruiz, J. M. and Sandoval, C. J. (2007). Properties of coherent systems with dependent components. Commun. Statist. Theory Meth. 36, 175–191.
  • Navarro, J., Samaniego, F. J. and Balakrishnan, N. (2010). The joint signature of coherent systems with shared components. J. Appl. Prob. 47, 235–253.
  • Navarro, J., Spizzichino, F. and Balakrishnan, N. (2010). Applications of average and projected systems to the study of coherent systems. J. Multivariate Anal. 101, 1471–1482.
  • 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.
  • Nelsen, R. B. (2006). An Introduction to Copulas, 2nd edn. Springer, New York.
  • Rychlik, T. (2001). Projecting Statistical Functionals (Lecture Notes Statist. 160). Springer, New York.
  • Samaniego, F. J. (1985). On closure of the IFR class under formation of coherent systems. IEEE Trans. Reliab. 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.
  • Satyanarayana, A. and Prabhakar, A. (1978). New topological formula and rapid algorithm for reliability analysis of complex networks. IEEE Trans. Reliab. 27, 82–100.
  • Shaked, M. and Shanthikumar, J. G. (2007). Stochastic Orders. Springer, New York.
  • Shaked, M. and Suarez–Llorens, A. (2003). On the comparison of reliability experiments based on the convolution order. J. Amer. Statist. Assoc. 98, 693–702.
  • Zhang, Z. (2010). Mixture representations of inactivity times of conditional coherent systems and their applications. J. Appl. Prob. 47, 876–885.