Descriptions des systèmes et dépendances stochastiques en théorie de la « fiabilité »
Cahiers du Bureau universitaire de recherche opérationnelle Série Recherche, Tome 39-40 (1982), pp. 3-99.
@article{BURO_1982__39-40__3_0,
     author = {Mazars, N.},
     title = {Descriptions des syst\`emes et d\'ependances stochastiques en th\'eorie de la {\guillemotleft} fiabilit\'e {\guillemotright}},
     journal = {Cahiers du Bureau universitaire de recherche op\'erationnelle S\'erie Recherche},
     pages = {3--99},
     publisher = {Institut Henri Poincar\'e - Institut de Statistique de l'Universit\'e de Paris},
     volume = {39-40},
     year = {1982},
     language = {fr},
     url = {http://archive.numdam.org/item/BURO_1982__39-40__3_0/}
}
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Mazars, N. Descriptions des systèmes et dépendances stochastiques en théorie de la « fiabilité ». Cahiers du Bureau universitaire de recherche opérationnelle Série Recherche, Tome 39-40 (1982), pp. 3-99. http://archive.numdam.org/item/BURO_1982__39-40__3_0/

[1] Barlow R.E. and Proshan F., "Mathematical Theory of Reliability", (1965), John Wiley and Sons, New-York. | MR | Zbl

[2] Barlow R.E. and Proshan F., "Statistical Theory of Reliability and Life Testing", Vol.1 : "Probability Models", (1975), HOLT, RINEHART and WINSTON, New-York. | MR | Zbl

[3] Barnett S., "Matrix Differential Equations and Kronecker Products", (January 1973), SIAM, Journal on Applied Mathematics, Vol.24, N° 1, pp. 1-5. | MR | Zbl

[4] Bellman R. "An Introduction to Matrix Analysis", (1960), MAC GRAW HILL book Company, New-York. | MR | Zbl

[5] Birnbaum Z.W., "On the Importance of Different Components of a Multicomponent System", (1969), Multivariate Analysis II, Pr KRISHNAIAH Editor, Academic press, pp. 581-592. | MR

[6] Birnbaum Z.W. and Esary J.D., "Modules of Binary Coherent Systems", (June 1965), SIAM Journal on Applied Mathematics, Vol. 13, n° 2, pp. "444-462 | Zbl

[7] Birnbaum Z.W., Esary J.D. and Marshall A.W., "A Stochastic Characterization of Wear Out for Components and Systems", (1966), The Annals of Mathematical Statistics, Vol. 37, pp. 816-825. | MR | Zbl

[8] Birnbaum Z.W., Esary J.D. and Saunders S.C., "Multicomponent Systems and Structures and Their Reliability", (February 1961), Technometrics, Vol. 3, N°1, pp. 55-77. | MR | Zbl

[9] Bodin L.D., "Approximations to System Reliability Using a Modular Decomposition", (May 1970), Technometrics, Vol. 12, N°2, p. 335-344. | MR | Zbl

[10] Brewer J.W., "Kronecker Products and Matrix Calculus in System Theory", (September 1978), IEEE Transactions on Circuits and Systems, Vol. CAS-25, N°9, pp. 772-781 | MR | Zbl

[11] Brindley E.C. and Thompson W.A., "Dependence and Aging Aspects of Multivariate Survival", (December 1972), Journal of the American Statistical Association, Vol. 67, pp. 822-830 | MR | Zbl

[12] Bryson M.C. and Siddiqui M.M., "Some Criteria for Aging", (1969), Journal of the American Statistical Association, Vol. 64, pp. 1472-1483. | MR

[13] Buchanan W.B. and Singpurwalla N.D., "Some Stochastic Characterizations of Multivariate Survival", (1977), The Theory and Applications of Reliability with Emphasis on Bayesian and Non Parametric Methods, Vol.1, Academic press, pp. 329-348. | MR

[14] Buzacott J.A. "Markov Approach to Finding Failure Times of Repairable Systems", (1970), IEEE Transactions on Reliability, Vol.R-19, pp. 128-134.

[15] Chatterjee P., "Fault Tree Analysis : Reliability Theory and Systems Safety Analysis", (November 1974), ORC 74-34, Operations Research Center, University of California, Berkeley.

[16] Chung K.L., "Markov Chains with Stationnary Transition Probabilities", Second Edition, (1967), Springer Verlag, Berlin. | MR | Zbl

[17] Cinlar E., "Introduction to Stochastic Processes", (1975), Prentice Hall Inc., New Jersey. | MR | Zbl

[18] Corraza M., "Contributions à l'Etude de la Fiabilité des Systèmes", (Février 1974), Thèse de Doctorat ès Sciences Physiques, Université Paul Sabatier, Toulouse,

[19] Cox D.R. and Miller H.D., "The Theory of Stochastic Processes", (1965), Methuen books, London. | MR | Zbl

[20] El Neveihi, Proshan F. and Sethuraman J., "Multistate Coherent Systems", (1978), Journal of Applied Probability, Vol.15, pp. 675-688. | MR | Zbl

[21] Esary J.D. and Marshall A.W., "System Structure and the Existence of a System Life", (November 1964), Technometrics, Vol. 6, N° 4, pp. 459-463 | Zbl

[22] Esary J.D. and Marshall A.W., "Coherent Life functions", (June 1970), SIAM Journal on Applied Mathematics, Vol.18, N°4, pp, 810-814. | MR | Zbl

[23] Esary J.D. and Marshall A.W., "Multivariate Distributions with Exponential Minimums", (1974), The Annals of Statistics, Vol. 2, N° 1, pp, 84-98. | MR | Zbl

[24] Esary J.D. Marshall A.W. and Proshan F., "Some Reliability Applications of the Hazard Transforms, (June 1970), SIAM, Journal on Applied Mathematics, Vol. 18, N° 4, pp. 849-860. | MR | Zbl

[25] Esary J.D. and Proshan F., "Coherent Structures and Non Identical Components", (May 1963), Technometrics, Vol. 5, N° 2, pp. 191-209, | MR | Zbl

[26] Esary J.D. and Proshan F., "A Reliability Bound for Systems of Maintained Interdependent Components", (March 1970), Journal of the American Statistical Association, Vol. 65, N° 29, pp. 329-338, | Zbl

[27] Esary J.D. and Proshan F., "Relationships Among some Concepts of Bivariate Dependence", (1972), The Annals of Mathematical Statistics, Vol. 43, N° 2, pp. 651-655, | MR | Zbl

[28] Esary J.D. and Proshan F. and Walkup A.W., "Association of Random Variables with Applications", (1967), The Annals of Mathematical Statistics, Vol.38, pp. 1466-1474. | MR | Zbl

[29] Fussel J.B., Powers G.J. and Bennetts R.G., "Fault Tree Analysis A State of the Art Discussion", (April 1974 ), IEEE Transactions on Reliability, Vol.R-23, N° 2, pp. 51-55.

[30] Gantmacher F.R., "Theorie des Matrices", (1966), Editions Dunod, Paris, | Zbl

[31] Gnedenko B., Belaiev Y. and Soloviev A., "Méthodes Mathématiques en Théorie de la Fiabilité", (1972), Editions MIR, Moscou. | Zbl

[32] Gondran M. et Pages A., "Fiabilité des Systèmes", (1980), Collection des Etudes et Recherches-EDF, Editions Eyrolles, Paris. | MR | Zbl

[33] Harris R., "A Multivariate Definition for Increasing Hazard Rate Distribution Functions", (1970), The Annals of Mathematical Statistics, Vol.41, pp. 713-717. | MR | Zbl

[34] Henze E., Masse J.C. and Theodorescu R., "On Multiple Markov Chains", (1977), Journal of Multivariate Analysis, Vol. 7, pp. 589-593. | MR | Zbl

[35] Hirsh W.M., Meisner M. and Boll C., "Cannibalization in Multicomponent Systems and the Theory of Reliability", (1968), Naval Research Logistic Quartely, Vol.15, pp. 331-359. | Zbl

[36] Kemeny J. and Snell J.L., "Finite Markov Chains", (1960), D. Van Nostrand Company, Inc., Princeton. | MR | Zbl

[37] Langberg N., Proshan F. and Quinzi A.J., "Converting Dependent Models into Independent Ones with Applications in Reliability" (1977), The Theory and Applications of Reliability with Emphasis on Bayesian and Non Parametric Methods, Vol. I, Academic press, pp. 259-276. | MR

[38] Lemmann E.L., "Some Concepts of Dependence", (1966), The Annals of Mathematical Statistics, Vol. 37, pp. 1137-1153. | MR | Zbl

[39] Marshall A.W. and Olkin I., "A Multivariate Exponential Distribution", (March 1967), Journal of the American Statistical Association, Vol. 62, N° 1, pp. 30-44. | MR | Zbl

[40] Mazars N. "Des Algorithmes d'Analyse des Arbres d'Evénements" (à paraître) Note de la Direction des Etudes et Recherches - E.D.F.

[41] Natvig B., "Improved Bounds for the Availability and Unavailability in a Fixed Time Interval for Systems of Maintained Interdependent Components", (March 1980), Advances in Applied Probability, Vol.12, pp. 200-221. | MR | Zbl

[42] Nijenhuis A. and Wilf H.S. "Combinatorial Algorithms" (1978) Academic press - New-York - (Chapter 15). | MR | Zbl

[43] Pande P.K., Spector M.E. and Chatterjee P., "Computerized Fault Tree Analysis : TREEL and MICSUP", (April 1975), ORC 75-3, Operations Research Center, University of California, Berkeley.

[44] Papazoglou I.A., "Markovian Reliability under Uncertainty", Sc. D. Thesis, (September 1977), M.I.T. Nuclear Engeeneering Department.

[45] Pyke R., "Markov Renewal Processes : Definitions and Preliminary Properties", (1961), The Annals of Mathematical Statistics, Vol.32, pp. 1231-1242. | MR | Zbl

[46] Queysanne, "Algèbre", (1966), Collection U, Editions A. Colin, Paris. | Zbl

[47] Renyi A., "Calcul des Probabilités", (1966), Editions Dunod, Paris. | MR | Zbl

[48] Rosenthal A., "A Computer Scientist Look at Reliability Computations", (1975), Reliability and Fault Tree Analysis, SIAM Conference Volume, pp. 133-152. | MR

[49] Styan G.P.H., "Hadamard Products and Multivariate Statistics Analysis", (1973), Linear Algebra and its Applications", Vol.6, pp. 217-240. | MR | Zbl