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2012 | 22 | 3 | 585-600
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Bayesian reliability models of Weibull systems: State of the art

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In the reliability modeling field, we sometimes encounter systems with uncertain structures, and the use of fault trees and reliability diagrams is not possible. To overcome this problem, Bayesian approaches offer a considerable efficiency in this context. This paper introduces recent contributions in the field of reliability modeling with the Bayesian network approach. Bayesian reliability models are applied to systems with Weibull distribution of failure. To achieve the formulation of the reliability model, Bayesian estimation of Weibull parameters and the model's goodness-of-fit are evoked. The advantages of this modelling approach are presented in the case of systems with an unknown reliability structure, those with a common cause of failures and redundant ones. Finally, we raise the issue of the use of BNs in the fault diagnosis area.
Opis fizyczny
  • LACS, National School of Engineering of Tunis, BP 37, 1002 Belvedere, Tunisia
  • LAGIS, Polytech'Lille, University of Lille Nord de France, 59650 Villeneuve d'Ascq, France
  • LACS, National School of Engineering of Tunis, BP 37, 1002 Belvedere, Tunisia
  • Agena (2011). Website,
  • Almond, R.G. (1992). An extended example for testing graphical-belief, Technical report, Statistical Sciences Inc., Seattle, WA.
  • Anderson, M., Anderson, R. and Wheeler, K. (2004). Filtering in hybrid dynamic Bayesian networks, International Conference on Acoustics, Speech and Signal Processing, Montreal, Canada, Vol. 5, pp. 773-776.
  • Andrews, J.D. and Moss, T.R. (1993). Reliability and Risk Assessment, Longman Scientific & Technical, John Wiley, Hoboken, NJ.
  • Arroyo-Figueroa, G. and Sucar, L. E. (1999). A temporal Bayesian network for diagnosis and prediction, Uncertainty in Artificial Intelligence. Proceedings of the 15th UAI Conference, Stockholm, Sweden, pp. 13-20.
  • Ben Salem, A., Muller, A. and Weber, P. (2006). Dynamic Bayesian networks in system reliability analysis, 6th IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes, Beijing, China, Vol. 6, pp. 481-486.
  • Bobbio, A., Portinale, L., Minichino, M. and Ciancamerla, E. (2001). Improving the analysis of dependable systems by mapping fault trees into Bayesian networks, Reliability Engineering and System Safety 71(3): 249-260.
  • Boudali, H. and Dugan, J.B. (2005). A discrete-time Bayesian network reliability modeling and analysis framework, Reliability Engineering and System Safety 87(3): 337-349.
  • Boudali, H. and Dugan, J.B. (2006). A continuous-time Bayesian network reliability modeling and analysis framework, IEEE Transactions on Reliability 55: 86-97.
  • Bousquet, N. (2006). Une mthodologie d'analyse baysienne pour la prvision de la dure de vie de composants industriels, Ph.D. thesis, University of Paris XI, Paris.
  • Boyen, X. and Koller, D. (1998). Tractable inference for complex stochastic processes, 14th Annual Conference on Uncertainty in AI (UAI), Madison, WI, USA, pp. 33-42.
  • Casella, G. (1985). An introduction to empirical Bayes data analysis, The American Statistician 39(2): 83-87.
  • Cholewa, W., Korbicz, J., Koscielny, M., Patan, K., Rogala, T., Syfert, M. and Witczak, M. (2010). Diagnostic methods, in J. Korbicz and J.M. Kościelny (Eds.), Modeling, Diagnostics and Process Control: Implementation in the DiaSter System, Springer-Verlag, Berlin, pp. 206-231.
  • CoreTeam, R.D. (2008). R: A language and environment for statistical computing, foundation for statistical computing,
  • David, J.L., Thomas, A., Best, N. and Spiegelhalter, D. (2000). Winbugs-a Bayesian modelling framework: Concepts, structure, and extensibility, Statistics and Computing 10(4): 325-337.
  • Deely, J.J. and Lindley, D.V. (1981). Empirical Bayes, Journal of the American Statistical Association 76(376): 833-841.
  • Galan, S.F. and Diez, F.J. (2000). Modeling dynamic causal interactions with Bayesian networks: Temporal noisy gates, 2nd International Workshop on Causal Networks (CaNew'2000), Berlin, Germany, pp. 1-5.
  • Galan, S.F. and Diez, F.J. (2002). Networks of probabilistic events in discrete time, International Journal of Approximate Reasoning 30: 181-202.
  • Gilks, W.R. and Wild, P. (1992). Adaptive rejection sampling for Gibbs sampling, Applied Statistics 41(2): 337-348.
  • Hamada, M.S., Wilson, A.G., Reese, C. and Martz, H. (2008). Bayesian Reliability, Springer Series in Statistics, Springer, New York, NY.
  • Hongbin, L., Qing, Z. and Zhenyu, Y. (2007). Reliability modeling of fault tolerant control systems, International Journal of Applied Mathematics and Computer Science 17(4): 491-504, DOI: 10.2478/v10006-007-0041-0.
  • Hugin (2011). Website,
  • Jeffreys, H. (1961). Theory of Probability, Oxford University Press, Oxford.
  • Jensen, F. (2001). Bayesian Networks and Decision Graphs, Springer-Verlag, New York, NY.
  • Johnson, V.E., Graves, T.L., Hamada, M.S. and Reese, C.S. (2003). A hierarchical model for estimating the reliability of complex systems, in J.M. Bernardo, A.P. Dawid, J.O. Berger and M. West (Eds.), Bayesian Statistics 7, Oxford University Press, London, pp. 199-213.
  • Kelly, D.L. and Smith, C.L. (2009). Bayesian inference in probabilistic risk assessment: The current state of the art, Reliability Engineering and System Safety 94(2): 628-643.
  • Khelassi, A., Theilliol, D. and Weber, P. (2011). Reconfigurability analysis for reliable fault-tolerant control design, International Journal of Applied Mathematics and Computer Science 21(3): 431-439, DOI: 10.2478/v10006-011-0032z.
  • Koller, D. and Lerner, U. (2000). Sampling in factored dynamic systems, in A. Doucet, J.F.G. de Freitas and N. Gordon (Eds.), Sequential Monte Carlo Methods in Practice, Springer-Verlag, New York, NY, pp. 445-464.
  • Koller, D., Lerner, U. and Angelov, D. (1999). A general algorithm for approximate inference and its application to hybrid Bayes nets, 15th Annual Conference on Uncertainty in Artificial Intelligence, UAI-99, Stockholm, Sweden, pp. 324-333.
  • Kozlov, A.V. and Koller, D. (1997). Nonuniform dynamic discretization in hybrid networks, in D. Geiger and P.P. Shenoy (Eds.), Uncertainty in Artificial Intelligence, Vol. 13, Morgan Kaufmann, San Francisco, CA, pp. 314-325.
  • Langseth, H. and Portinale, L. (2007). Bayesian networks in reliability, Reliability Engineering and System Safety 92(1): 92-108.
  • Lauritzen, S. and Jensen, F. (1999). Stable local computation with conditional Gaussian distributions, Technical Report R-99-2014, Department of Mathematical Sciences, Aalborg University, Aalborg.
  • Lerner, U., Segal, E. and Koller, D. (2001). Exact inference in networks with discrete children of continuous parents, in J. Breese and D. Koller (Eds.), Uncertainty in Artificial Intelligence, Vol. 17, Morgan Kaufmann, San Francisco, CA, pp. 319-328.
  • Lynch, S.M. (2007). Introduction to Applied Bayesian Statistics and Estimation for Social Scientists, Springer, New York, NY.
  • Marquez, D., Neil, M. and Fenton, N.E. (2007). A new Bayesian network approach to reliability modeling, 5th International Mathematical Methods in Reliability Conference (MMR 07), Glasgow, UK, pp. 1-4.
  • Martz, H.F. and Waller, R.A. (1990). Bayesian reliability analysis of complex series/parallel systems of binomial subsystems and components, Technometrics Archive 32(4): 407-416.
  • Mehranbod, N., Soroush, M. and Panjapornpon, C. (2005). A method of sensor fault detection and identification, Journal of Process Control 15(3): 321-339.
  • Moral, S., Rumi, R. and Salmeron, A. (2001). Mixtures of truncated exponentials in hybrid bayesian networks, in P. Besnard and S. Benferhart (Eds.), 6th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, Lecture Notes in Artificial Intelligence, Vol. 2143, Springer-Verlag, Heidelberg, pp. 145-167.
  • Morris, C.N. (1983). Parametric empirical Bayes inference: Theory and applications, Journal of the American Statistical Association 78: 47-55.
  • Murphy, K. (2002). Dynamic Bayesian Networks: Representation, Inference and Learning, Ph.D. thesis, UC Berkley, CA.
  • Neil, M., Tailor, M. and Marquez, D. (2007). Inference in hybrid Bayesian networks using dynamic discretization, Statistics and Computing 17(3): 219-233.
  • Neil, M., Tailor, M., Marquez, D., Fenton, N. E. and Hearty, P. (2008). Modelling dependable systems using hybrid bayesian networks, Reliability Engineering and System Safety 93(7): 933-939.
  • Netica (2011). Website,
  • Nodelman, U., Shelton, C. and Koller, D. (2002). Continuous time Bayesian networks, Proceedings of the 18th Conference on Uncertainty in Artificial Intelligence (UAI), Alberta, Canada, pp. 378-387.
  • Pearl, J. (1988). Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference, Morgan Kaufmann, San Mateo, CA.
  • Portinale, L., Bobbio, A. and Montani, S. (2005). Modern Statistical and Mathematical Methods in Reliability, World Scientific, London, Chapter 26, pp. 365-382.
  • Portinale, L., Bobbio, A., Raiteri, D.C. and Montani, S. (2007). Compiling dynamic fault trees into dynamic Bayesian nets for reliability analysis: The Radyban tool, CEUR Workshop Proceedings, Vancouver, British Columbia, Canada, Vol. 268.
  • Reese, S.C., Johnson, V., Hamada, M.S. and Wilson, A.G. (2005). A hierarchical model for the reliability of an antiaircraft missile system, UT MD Anderson Cancer Center Department of Biostatistics Working Paper Series, Houston, TX.
  • Rinne, H. (2008). The Weibull Distribution: A Handbook, CRC Press, New York, NY.
  • Robinson, D. G. (2001). A hierarchical Bayes approach to system reliability analysis, Sandia Report Sand 2001-3513, Sandia National Laboratories, Albuquerque, NM/Livermore, CA.
  • Roychoudhury, I., Biswas, G. and Koutsoukos, X. (2006). A Bayesian approach to efficient diagnosis of incipient faults, 17th International Workshop on Principles of Diagnosis (DX 06), Peñaranda de Duero, Burgos, Spain, pp. 243-250.
  • Sullivan, K.J., Dugan, J.B. and Coppit, D. (1999). The Galileo fault tree analysis tool, 29th Annual International Symposium on Fault-Tolerant Computing, Madison, WI, USA, pp. 232-235.
  • Torres-Toledano, J.G. and Sucar, L.E. (1998). Bayesian networks for reliability analysis of complex systems, in H. Coelho (Ed.), IBERAMIA'98, Lecture Notes in Artificial Intelligence, Vol. 1484, Springer, London, pp. 195-206.
  • Weber, P. and Jouffe, L. (2003). Reliability modelling with dynamic Bayesian networks, 5th IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes, Washington, DC, USA.
  • Weber, P. and Jouffe, L. (2006). Complex system reliability with dynamic object oriented Bayesian networks, Reliability Engineering & Systems Safety 91(2): 149-162.
  • Weber, P., Theilliol, D., Aubrun, C. and Evsukoff, A. (2006). Increasing effectiveness of model-based fault diagnosis: A dynamic Bayesian network design for decision making, 6th IFAC Symposium on Fault Detection Supervision and Safety for Technical Processes SAFEPROCESS, Beijing, China.
  • Wilson, A.G., Graves, T.L., Hamada, M.S. and Reese, C.S. (2006). Advances in data combination, analysis and collection for system reliability assessment, Statistical Science 21(4): 514-531.
  • Wilson, A.G. and Huzurbazar, A.V. (2007). Bayesian networks for multilevel system reliability, Reliability Engineering and Systems Safety 92(10): 1413-1420.
  • Zaidi, A., Tagina, M. and Ould-Bouamama, B. (2010). Reliability data for improvement of decision-making in analytical redundancy relations bond graph based diagnosis, 2010 IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Montreal, Canada, pp. 790-795.
  • Zhang, X. and Hoo, K. A. (2011). Effective fault detection and isolation using bond graph-based domain decomposition, Computers and Chemical Engineering 35(1): 132-148.
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