Approximation of Reliability for a large system with non-markovian repair-times

Jean-Louis Bon; Jean Bretagnolle

ESAIM: Probability and Statistics (2010)

  • Volume: 3, page 49-65
  • ISSN: 1292-8100

Abstract

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Consider a system of many components with constant failure rate and general repair rate. When all components are reliable and easily reparable, the reliability of the system can be evaluated from the probability q of failure before restoration. In [14], authors give an asymptotic approximation by monotone sequences. In the same framework, we propose, here, a bounding for q and apply it in the ageing property case.

How to cite

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Bon, Jean-Louis, and Bretagnolle, Jean. "Approximation of Reliability for a large system with non-markovian repair-times." ESAIM: Probability and Statistics 3 (2010): 49-65. <http://eudml.org/doc/197749>.

@article{Bon2010,
abstract = { Consider a system of many components with constant failure rate and general repair rate. When all components are reliable and easily reparable, the reliability of the system can be evaluated from the probability q of failure before restoration. In [14], authors give an asymptotic approximation by monotone sequences. In the same framework, we propose, here, a bounding for q and apply it in the ageing property case. },
author = {Bon, Jean-Louis, Bretagnolle, Jean},
journal = {ESAIM: Probability and Statistics},
keywords = { Reliability; ageing repair; minimal cut.; harmonic new better than used in expectation; constant failure rate; general repair rate; HNBUE},
language = {eng},
month = {3},
pages = {49-65},
publisher = {EDP Sciences},
title = {Approximation of Reliability for a large system with non-markovian repair-times},
url = {http://eudml.org/doc/197749},
volume = {3},
year = {2010},
}

TY - JOUR
AU - Bon, Jean-Louis
AU - Bretagnolle, Jean
TI - Approximation of Reliability for a large system with non-markovian repair-times
JO - ESAIM: Probability and Statistics
DA - 2010/3//
PB - EDP Sciences
VL - 3
SP - 49
EP - 65
AB - Consider a system of many components with constant failure rate and general repair rate. When all components are reliable and easily reparable, the reliability of the system can be evaluated from the probability q of failure before restoration. In [14], authors give an asymptotic approximation by monotone sequences. In the same framework, we propose, here, a bounding for q and apply it in the ageing property case.
LA - eng
KW - Reliability; ageing repair; minimal cut.; harmonic new better than used in expectation; constant failure rate; general repair rate; HNBUE
UR - http://eudml.org/doc/197749
ER -

References

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  1. R.E. Barlow and F. Proschan, Statistical Theory of Reliability and Life Testing. Holt, Rhineart and Winston, New York (1975).  Zbl0379.62080
  2. J.-L. Bon, Méthodes Mathématiques de Fiabilité, Éditions Masson, Paris (1995).  
  3. J.-L. Bon and E. Paltanea, Encadrement de la fiabilité d'un système markovien à partir des caractéristiques de ses composants, Actes des XXIXes Journées de Statistique, ASU (1997).  
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  8. V.V. Kalashnikov, Geometric sums: Bounds for rare events with applications, Kluwer academic Publishers (1997).  Zbl0881.60043
  9. G.P. Klimov, Stokastiskie systemi obslujivanie, Nauka (in Russian) (1966).  
  10. J. Keilson, Stochastic models in reliability theory, in Teoria dell affidabilita, Proc. Int. School Enrico Fermi, North-Holland (1984).  Zbl0704.60086
  11. I.N. Kovalenko, N.Yu. Kuznetsov and P.A. Pegg, Mathematical Theory of Reliability of Time dependent Systems with Practical Applications, J. Wiley (1997).  
  12. P. Pamphile, Calcul de fiabilité de grands systèmes hautement fiables. Thèse université Paris-Sud (Orsay), Paris (1994).  
  13. A.D. Solovyev, Voprosi Matematicheskoi Teorii Nadejnosti, Gnedenko B.V., Ed., Radio i Sviaz, Moscow (1983) (in Russian).  
  14. A.D. Solovyev and D.G. Konstant, Reliability estimation of a complex renewable system with an unbounded number of repair units. J. Appl. Probab.28 (1991) 833-842.  Zbl0746.60087

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