The imprecise dirichlet model for multilevel system reliability

Journal of Statistical Theory and Practice

Volumn 3, Issue 1, 2009, Pages 211-223

  Wilson, Alyson G ^a   Huzurbazar, Aparna V ^b   Sentz, Kari ^b  

^a Iowa State University   (United States)

^b LOS ALAMOS NATIONAL LABORATORY   (United States)

Author keywords

Bayesian network; Fault tree; Imprecise Dirichlet model; Multilevel data; Multinomial Dirichlet model; Reliability

Indexed keywords

EID: 85008826289     PISSN: 15598608     EISSN: 15598616     Source Type: Journal    
DOI: 10.1080/15598608.2009.10411921     Document Type: Article

References (24)

1. Bernard, J.M., 2005. An introduction to the imprecise Dirichlet model for multinomial data. International Journal of Approximate Reasoning, 39(2-3), 123–150.
2. Bobbio, A., Portinale, L., Minichino, M., Ciancamerla, E., 2001. Improving the analysis of dependable systems by mapping fault trees into Bayesian networks. Reliability Engineering & Systems Safety, 71(3), 249–260.
3. Coolen, F.P.A., 2004. On the use of imprecise probabilities in reliability. Quality and Reliability Engineering International, 20(3), 193–202. 15th Advances in Reliability Technology Symposium (ARTS), Loughborough, England, APR 08-10, 2003.
4. Gelman, W.R., Richardson, S., Spiegelhalter, D.J., 1995. Markov Chain Monte Carlo in Practice, Chapman & Hall, London.
5. Hamada, M., Martz, H., Reese, C.S., Graves, T. Johnson, V., Wilson, A.G., 2004. A fully Bayesian approach for combining multilevel failure information in fault tree quantification and optimal follow-on resource allocation. Reliability Engineering & Systems Safety, 86(3), 297–305.
6. Hamada, M., Wilson, A., Reese, C.S., Martz, H., 2008. Bayesian Reliability. Springer, New York.
7. Kozine, I.O., Utkin, L.V., 2005. Constructing imprecise probability distributions. International Journal of General Systems, 34(4), 401–408.
8. Lee, B.H., 2001. Using Bayes belief networks in industrial FMEA modeling and analysis. In Proceedings: Annual Reliability and Maintainaability Symposium, Philadelphia, PA, January 22-25, 2001.
9. Neal, R.M., 2003. Slice sampling. Annals of Statistics, 31(3), 705–741.
10. Portinale, L., Bobbio, A., Montani, S., 2005. From artificial intelligence to dependability: modeling and analysis with Bayesian networks. In Modern Statistical and Mathematical Methods in Reliability, Wilson, A.G., Limnios, N., Keller-McNulty, S.A. and Armijo, Y.M. (editors), 365–381. World Scientific, Singapore.
11. Rausand, M., Høyland, A., 2004. System Reliability Theory: Models, Statistical Methods, and Applications. 2nd edition. Wiley-Interscience: John Wiley & Sons, Hoboken, NJ.
12. Sigurdsson, J.H., Walls, L.A., Quigley, J.L., 2001. Bayesian belief nets for managing expert judgement and modelling reliability. Quality and Reliability Engineering International, 17(3), 181–190. 14th Advances in Reliability Technology Symposium, Manchester, England, December 2000.
13. Spiegelhalter, D.J., 1998. Bayesian graphical modeling: a case-study in monitoring health outcomes. Journal of the Royal Statistical Society: Series C (Applied Statistics), 47, 115–133.
14. Troffaes, M.C.M., Coolen, F.P.A., 2008. Applying the imprecise Dirichlet model in cases with partial observation and dependencies in failure data. International Journal of Approximate Reasoning.
15. Utkin, L.V., Augustin, T., 2007. Decision making under incomplete data using the imprecise Dirichlet model. International Journal of Approximate Reasoning, 44(3), 322–338.
16. Utkin, L.V., 2005. Extensions of belief functions and possibility distributions by using the imprecise Dirichlet model. Fuzzy Sets and Systems, 154(3), 413–431.
17. Utkin, L.V., Kozine, I.O., 2005. Computing system reliability given interval-valued characteristics of the components. Reliable Computing, 11, 19–34.
18. Walley, P., 1991. Statistical Reasoning with Imprecise Probabilities. Chapman & Hall, London.
19. Walley, P., 1996. Inferences from multinomial data: Learning about a bag of marbles. Journal of the Royal Statistical Society B, 58(1), 3–34.
20. Walley, P., Gurrin, L., Burton, P., 1996. Analysis of clinical data using imprecise prior probabilities. Statistician, 45(4), 457–485.
21. Wasserman, L.A., 1990. Belief functions and statistical inference. The Canadian Journal of Statistics, 18, 183–196.
22. Wilson, A.G., Huzurbazar, A.V., 2007. Bayesian networks for multilevel system reliability. Reliabilty Engineering & Systems Safety, 92(10), 1413–1420.
23. Wilson, A.G., McNamara, L.A., Wilson, G.D., 2007. Information integration for complex systems. Reliabilty Engineering & Systems Safety, 92(1), 121–130.
24. Zaffalon, M., 2002. Exactcredal treatment of missing data. Journal of Statistical Planning and Inference, 105(1), 105–122.