Advertisement

Reliability Analysis of Coherent Systems with Exchangeable Components

  • M. V. KoutrasEmail author
  • I. S. Triantafyllou
Chapter
Part of the Springer Optimization and Its Applications book series (SOIA, volume 91)

Abstract

In this paper we study reliability properties of coherent systems consisting of n exchangeable components. We focus on the aging behavior of a reliability structure and several results are reached clarifying whether a system displays the IFR/DFR property or not. More specifically, a necessary and sufficient condition is deduced for a system’s lifetime to be IFR, while additional signature-based conditions aiming at the same direction are also delivered. For illustration purposes, special cases of well-known reliability systems and specific lifetimes’ distributions are considered and studied in detail.

Keywords

Coherent systems Increasing failure rate Samaniego’s signature Minimal and maximal signatures 

References

  1. 1.
    Chao, M. T., Fu, J. C. and Koutras, M. V.: Survey of reliability studies of consecutive−k−out−of−n: F & Related Systems, IEEE Transactions on Reliability, 44, 120–127 (1995).Google Scholar
  2. 2.
    David, H. A. and Nagaraja, H. N.: Order Statistics, 3rd Edition, John Wiley & Sons, N. J (2003).Google Scholar
  3. 3.
    Eryilmaz, S.: Review of recent advances in reliability of consecutive-k-out-of-n: F and related systems, Proceedings of the Institution of Mechanical Engineering-Part O- Journal of Risk and Reliability, 224, 225–237 (2010).Google Scholar
  4. 4.
    Eryilmaz, S.: Reliability properties of systems with two exchangeable log-logistic components, Communication in Statistics-Theory and Methods, 41, 3416–3427 (2012).Google Scholar
  5. 5.
    Kuo, W. and Zuo, M. J.: Optimal Reliability Modeling: Principles and Applications, John Wiley & Sons, N.J (2003).Google Scholar
  6. 6.
    Navarro, J. and Rychlik, T.: Reliability and expectation bounds for coherent systems with exchangeable components, Journal of Multivariate Analysis, 98, 102–113 (2007).CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Navarro, J. and Eryilmaz, S.: Mean residual lifetimes of consecutive-k-out-of-n: F systems, Journal of Applied Probability, 44, 82–98 (2007).CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Navarro, J., Ruiz, J. M. and Sandoval, C. J.: Properties of coherent systems with dependent components, Communication in Statistics- Theory and Methods, 36, 175–191 (2007).CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Samaniego, F. J.: System Signatures and their Applications in Engineering Reliability, Vol.110, Springer, N. Y (2007).Google Scholar
  10. 10.
    Samaniego, F. J.: On closure of the IFR class under formation of coherent systems, IEEE Transactions on Reliability,34, 69–72 (1985).Google Scholar
  11. 11.
    Steele, J. M.: The Cauchy-Schwarz Master Class, Cambridge University Press, N. Y (2004).CrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of Statistics and Insurance ScienceUniversity of PiraeusPiraeusGreece

Personalised recommendations