Analyse de fiabilité des grands systèmes réparables markoviens stratifiés
Thèses d'Orsay, no. 585 (2000) , 130 p. 
@phdthesis{BJHTUP11_2000__0585__P0_0,
     author = {Paltanea, Eugen},
     title = {Analyse de fiabilit\'e des grands syst\`emes r\'eparables markoviens stratifi\'es},
     series = {Th\`eses d'Orsay},
     publisher = {Universit\'e de Paris-Sud U.F.R. Scientifique d'Orsay},
     number = {585},
     year = {2000},
     language = {fr},
     url = {https://www.numdam.org/item/BJHTUP11_2000__0585__P0_0/}
}
TY  - BOOK
AU  - Paltanea, Eugen
TI  - Analyse de fiabilité des grands systèmes réparables markoviens stratifiés
T3  - Thèses d'Orsay
PY  - 2000
IS  - 585
PB  - Université de Paris-Sud U.F.R. Scientifique d'Orsay
UR  - https://www.numdam.org/item/BJHTUP11_2000__0585__P0_0/
LA  - fr
ID  - BJHTUP11_2000__0585__P0_0
ER  - 
%0 Book
%A Paltanea, Eugen
%T Analyse de fiabilité des grands systèmes réparables markoviens stratifiés
%S Thèses d'Orsay
%D 2000
%N 585
%I Université de Paris-Sud U.F.R. Scientifique d'Orsay
%U https://www.numdam.org/item/BJHTUP11_2000__0585__P0_0/
%G fr
%F BJHTUP11_2000__0585__P0_0
Paltanea, Eugen. Analyse de fiabilité des grands systèmes réparables markoviens stratifiés. Thèses d'Orsay, no. 585 (2000), 130 p. https://www.numdam.org/item/BJHTUP11_2000__0585__P0_0/

[1] D. Aldous "Random walks on finite groups and rapidly mixing Markov chains", Séminaire de probabilités XVII, LNM 986, Springer, Berlin, 1983. | MR | Zbl | Numdam

[2] S. Asmussen Applied Probability and Queues, John Wiley & Sons Ltd., 1987. | MR | Zbl

[3] R.E. Barlow et A. W. Marshall "Tables of bounds for Distributions with monotone Hazard Rate", J. Amer. Statis. Assoc., vol. 60, pp. 872-890, 1965. | MR | DOI

[4] R.E. Barlow et F. Proschan Statistical Theory of Reliability and Life Testing, Holt, Reinhart and Winston, New York, 1975. | MR | Zbl

[5] R.E. Barlow et F. Proschan Mathematical Theory of Reliability, Classics in Applied Mathematics, SIAM, Philadelphia, 1996. | MR | Zbl

[6] P.J. Boland, E. El-Neweihi et F. Proschan "Schur Properties of Convolutions of Exponential and Geometric Random Variables", J. Multivariate Anal., vol. 48, pp. 157-167, 1994. | MR | Zbl | DOI

[7] P.J. Boland et E. El-Neweihi "Component Redundancy versus System Redundancy", IEEE Transaction on Reliability, vol. 44, 4, pp. 614-619, 1995. | DOI

[8] P.J. Boland, M. Shaked et J.G. Shanthikumar Handbook of Statistics, Academic Press, San Diego, CA, 1998.

[9] J.-L. Bon Fiabilité des Systèmes, Techniques Stochastiques, Masson, Paris, 1995.

[10] J.-L. Bon et J. Bretagnolle "Approximation of Reliability for a large system with non Markovian Repair-times", ESAIM-PS, vol.3, pp. 49-65, 1999. | MR | Zbl | Numdam | DOI

[11] J.-L. Bon, J. Bretagnolle, P. Pamphile et J.P. Raoult Calcul séquentiel de fiabilité à partir d'approximations exponentielles. Rapports Techniques, Université Paris -Sud, 1990

J.-L. Bon, J. Bretagnolle, P. Pamphile et J.P. Raoult Calcul séquentiel de fiabilité à partir d'approximations exponentielles. Rapports Techniques, Université Paris -Sud, 1991

J.-L. Bon, J. Bretagnolle, P. Pamphile et J.P. Raoult Calcul séquentiel de fiabilité à partir d'approximations exponentielles. Rapports Techniques, Université Paris -Sud, 1992

J.-L. Bon, J. Bretagnolle, P. Pamphile et J.P. Raoult Calcul séquentiel de fiabilité à partir d'approximations exponentielles. Rapports Techniques, Université Paris -Sud, 1993

[12] J.-L. Bon et J. Collet "An algorithm in order to implement reliability exponential approximations", Rel. Eng. and Safety Prob., vol.43, 3 pp.262-269, 1994.

[13] J.-L. Bon et E. Păltănea "Encadrement de la fiabilité d'un système markovien à partir des caractéristiques de ses composants", Actes des 29-èmes journées de statistique (ASU), pp. 169-173, 1997.

[14] J.-L. Bon et E. Păltănea "Ordering Properties of Convolutions of Exponential Random Variables", Lifetime Data Analysis, Kluwer Academic Publishers, vol. 5, pp. 185-189, 1999. | MR | Zbl | DOI

[15] K.L. Cheng Markov chains with stationary transition probabilities, Springer-Verlag, Berlin, 1967. | MR

[16] E. Çinlar Introduction to Stochastic Processes, Prentice Hall, Englewood Cliffs, New Jersey, 1975. | MR | Zbl

[17] C. Cocozza-Thivent Processus stochastiques et fiabilité des systèmes, SMAI, Springer, Berlin, 1997. | MR | Zbl

[18] C. Cocozza-Thivent et V. Kalashnikov "The failure rate in reliability. Numerical treatment", Journal of Applied Mathematics and Stochastic Analysis, vol. 10, pp. 21-45, 1997. | MR | Zbl | DOI

[19] C. Cocozza-Thivent et M. Roussignol "Comparaison des lois stationnaire et quasi-stationnaire d'un processus de Markov et applications à la fiabilité", Séminaire de Probabilités XXX, Lecture Notes in Mathematics, vol. 1626, pp. 24-39, 1996. | MR | Zbl | Numdam | DOI

[20] C. Cocozza-Thivent et M. Roussignol "Techniques de couplage en fiabilité", Ann. I.H.P. ", vol 31:1, pp. 119-141, 1995. | MR | Zbl | Numdam

[21] P.-J. Courtois et P. Semal, "Bound for transient characteristics of large or infinite Markov chains", Stewart [69], article 22, pp. 413-434. | MR | Zbl

[22] P. Diaconis et D. Stoock "Geometric bounds for eigenvalues of Markov chains", Ann. Appl. Prob., vol.1, pp. 36-61, 1991. | MR | Zbl

[23] P. Diaconis "The cutoff phenomenon in finite Markov chains", Proc Natl. Acad. Sci. USA, vol. 93, pp. 1659-1664, 1996. | MR | Zbl | DOI

[24] W. Feller An Introduction to Probability Theory and Its Applications, Wiley, New-York, 1968. | MR | Zbl

[25] I. Guikhman et A. Skorokhod Introduction à la théorie des processus aléatoires, Éditions Mir, Moscou, 1980. | Zbl

[26] L.J. Gleser "On the distribution of the number of successes in independent trials", Ann. Prob., vol. 3, pp. 182-188, 1975. | MR | Zbl

[27] B.V. Gnedenko, Y.K. Belyayev et A.D. Solovyev Mathematical Methods of Reliability Theory, Academic Press, New York and London, 1969. | MR | Zbl

[28] B.V. Gnedenko et A.D. Solovyev "Modèle de redondance", Kibernetica, 1974.

[29] B.V. Gnedenko et A.D. Solovyev Problèmes mathématiques de fiabilité, Radio i Sviaz, Moscou, 1983.

[30] W. Hoeffding "On the distribution of the number of successes in independent trials", Ann. Math. Statist., 27, pp. 713-721, 1959. | MR | Zbl | DOI

[31] M. Iosifescu Finite Markov Process and their applications, Wiley, New York, 1980. | MR | Zbl

[32] V.V. Kalashnikov Mathematical Methods in Queuing Theory, Kluwer Academic Publishers, 1994. | MR | Zbl | DOI

[33] S. Karlin and H.M. Taylor A first Course in Stochastic Processes, Academic Press, New York, 1975. | MR | Zbl

[34] J. Keilson Markov Chain Models - Rarity and Exponentiality, Springer-Verlag, New York, 1979. | MR | Zbl | DOI

[35] S. Kochar et C. Ma "Dispersive ordering of convolutions of exponential random variables", Statistics and Probability Letters, vol. 43, pp. 321-324, 1999. | MR | Zbl

[36] A.W. Marshall and I. Olkin Inequalities: Theory of Majorization and its Applications, Academic Press, New York, 1979. | MR

[37] P. Pamphile Calculs de la fiabilité de grands systèmes hautement fiables, Thèse de doctorat, Université Paris-Sud, Orsay, 1994.

[38] E. Păltănea "Étude de la fiabilité des modèles markoviens stratifiés", Proc. Conferinţa Societăţii de Şiinţe Matematice din România, Cluj, 1998.

[39] V. Petrov Limits Theorems of Probability Theory, Clarendon Press Oxford, 1995. | MR | Zbl

[40] O. Pourret Sur l'approximation lent-rapide pour les processus de Markov en fiabilité, Thèse de doctorat, Université Paris-Sud, Orsay, 1998.

[41] N. Ravichandran Stochastic Methods in Reliability Theory, Wiley Eastern Limited, New Delhi, 1990. | MR | Zbl

[42] S. Ross Stochastic Processes, Wiley, New York, 1983. | MR

[43] G. Rubino et B. Sericola "Sojourn Times in finite Markov Processes", J. Appl. Prob., 27, 1989. | MR | Zbl

[44] L. Saloff-Coste et al. Lecture on finite Markov Chains, École d'été de St-Flour, 1996. | MR | Zbl

[45] S.M. Samuels "On the number of successes in independent trials", Ann. Math. Statist., 36 1272-1278, 1965. | MR | Zbl | DOI

[46] M. Shaked et J.G. Shanthikumar Stochastic Orders and Their Applications, Academic Press, New York, 1994. | MR | Zbl

[47] J.G. Shanthikumar et D.D. Yao "Bivariate characterization of some Stochastic Order Relations", Adv. Appl. Prob., vol. 23, pp. 642-659, 1991. | MR | Zbl

[48] A.D. Soloviev et D.G. Konstant "Reliability of a complex renewable system with an unbounded number of repair units", J. Appl. Prob., 28, pp. 833-840, 1990. | MR | Zbl | DOI

[49] A.D. Soloviev et N.G. Karaseva "Evaluation du temps moyen de vie d'un système reparable", Vesthnik Mosc. Univ, Serie 1 math. et mécanique, 5, pp. 25-29, 1998. | Zbl

[50] R. Szekli Stochastic Ordering and Dependence in Applied Probability, Springer-Verlag, New York, 1995. | MR | Zbl | DOI

[51] M. Weba "Bounds for the total variation distance between the binomial and the Poisson distribution in case of medium sized success probabilities", J. Appl. Prob., vol. 36, pp. 97-104, 1999. | MR | Zbl | DOI

[52] B. Ycart "Cutoff for samples of Markov Chains", ESAIM-PS, vol.3, pp. 89-107, 1999. | MR | Zbl | Numdam | DOI