# 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

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topBon, 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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- J. Keilson, Stochastic models in reliability theory, in Teoria dell affidabilita, Proc. Int. School Enrico Fermi, North-Holland (1984). Zbl0704.60086
- I.N. Kovalenko, N.Yu. Kuznetsov and P.A. Pegg, Mathematical Theory of Reliability of Time dependent Systems with Practical Applications, J. Wiley (1997).
- P. Pamphile, Calcul de fiabilité de grands systèmes hautement fiables. Thèse université Paris-Sud (Orsay), Paris (1994).
- A.D. Solovyev, Voprosi Matematicheskoi Teorii Nadejnosti, Gnedenko B.V., Ed., Radio i Sviaz, Moscow (1983) (in Russian).
- 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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