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

Jean-Louis Bon; Jean Bretagnolle

ESAIM: Probability and Statistics (1999)

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

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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 (1999): 49-65. <http://eudml.org/doc/104257>.

@article{Bon1999,
author = {Bon, Jean-Louis, Bretagnolle, Jean},
journal = {ESAIM: Probability and Statistics},
keywords = {harmonic new better than used in expectation; constant failure rate; general repair rate; HNBUE},
language = {eng},
pages = {49-65},
publisher = {EDP Sciences},
title = {Approximation of reliability for a large system with non-markovian repair-times},
url = {http://eudml.org/doc/104257},
volume = {3},
year = {1999},
}

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
PY - 1999
PB - EDP Sciences
VL - 3
SP - 49
EP - 65
LA - eng
KW - harmonic new better than used in expectation; constant failure rate; general repair rate; HNBUE
UR - http://eudml.org/doc/104257
ER -

References

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  1. [1] R.E. Barlow and F. Proschan, Statistical Theory of Reliability and Life Testing. Holt, Rhineart and Winston, New York ( 1975). Zbl0379.62080MR438625
  2. [2] J.-L. Bon, Méthodes Mathématiques de Fiabilité, Éditions Masson, Paris ( 1995). 
  3. [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). 
  4. [4] K. Chen and Z. He, Reliability bounds for NBUE and NWUE distributions. Acta Mat. Appli. Sinica 4 ( 1989). Zbl0682.62078MR1003622
  5. [5] D.R. Cox, Renewal Theory, J. Wiley ( 1967). Zbl0168.16106
  6. [6] I.B. Gertsbakh, Asymptotic methods in reliability theory: A review. Adv. in Appl. Prob. 16 ( 1984) 47-175. Zbl0528.60085MR732135
  7. [7] D.B. Gnedenko and A.D. Solovyev, Estimation de la fiabilité des systèmes réparables complexes. Teknicheskaia Kibernetika 3 ( 1975) 121-128 (en russe). Zbl0312.90022MR423732
  8. [8] V.V. Kalashnikov, Geometric sums: Bounds for rare events with applications, Kluwer academic Publishers ( 1997). Zbl0881.60043MR1471479
  9. [9] G.P. Klimov, Stokastiskie systemi obslujivanie, Nauka (in Russian) ( 1966). MR207064
  10. [10] J. Keilson, Stochastic models in reliability theory, in Teoria dell affidabilita, Proc. Int. School Enrico Fermi, North-Holland ( 1984). Zbl0704.60086MR891218
  11. [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). Zbl0899.60074
  12. [12] P. Pamphile, Calcul de fiabilité de grands systèmes hautement fiables, Thèse université Paris-Sud (Orsay), Paris ( 1994). 
  13. [13] A.D. Solovyev, Voprosi Matematicheskoi Teorii Nadejnosti, Gnedenko B.V., Ed., Radio i Sviaz, Moscow ( 1983) (in Russian). 
  14. [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. Zbl0746.60087MR1133791

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