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Advances in data combination, analysis and collection for system reliability assessment. (English) Zbl 1129.62093

Summary: The systems that statisticians are asked to assess, such as nuclear weapons, infrastructure networks, supercomputer codes and munitions, have become increasingly complex. It is often costly to conduct full system tests. As such, we present a review of methodology that has been proposed for addressing system reliability with limited full system testing. The first approaches presented in this paper are concerned with the combination of multiple sources of information to assess the reliability of a single component. The second general set of methodology addresses the combination of multiple levels of data to determine system reliability. We then present developments for complex systems beyond traditional series/parallel representations through the use of Bayesian networks and flowgraph models. We also include methodological contributions to resource allocation considerations for system relability assessment. We illustrate each method with applications primarily encountered at the Los Alamos National Laboratory.

MSC:

62N05 Reliability and life testing
62F15 Bayesian inference

Software:

R
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References:

[1] Anderson-Cook, C. M., Graves, T. L., Hengartner, N. W., Klamann, R., Koehler, A., Wilson, A. G., Anderson, G. and Lopez, G. (2005). Reliability modeling using both system test and quality assurance data. Technical Report LA-UR-05-2252, Los Alamos National Laboratory.
[2] Bedford, T. and Cooke, R. (2001). Probabilistic Risk Analysis : Foundations and Methods . Cambridge Univ. Press. · Zbl 0977.60002 · doi:10.1017/CBO9780511813597
[3] Bennentt, T. R., Booker, J. M., Keller-McNulty, S. A. and Singpurwalla, N. D. (2003). Testing the untestable: Reliability in the 21st century. IEEE Transactions on Reliability 52 118–124.
[4] Farrow, M., Goldstein, M. and Spiropoulos, T. (1997). Developing a Bayes linear decision support system for a brewery. In The Practice of Bayesian Analysis (S. French and J. Q. Smith, eds.) 71–106. Arnold, London.
[5] Gå semyr, J. and Natvig, B. (2001). Bayesian inference based on partial monitoring of components with applications to preventive system maintenance. Naval Res. Logist. 48 551–577. · Zbl 1005.90022 · doi:10.1002/nav.1034
[6] Goldberg, D. E. (1989). Genetic Algorithms in Search , Optimization and Machine Learning . Addison-Wesley, Reading, MA. · Zbl 0721.68056
[7] Graves, T. L. (2003). An introduction to YADAS. Available at yadas.lanl.gov.
[8] Graves, T. L. (2007). Design ideas for Markov chain Monte Carlo software. J. Comput. Graph. Statist. 16 24–43. · doi:10.1198/106186007X179239
[9] Graves, T. L. and Hamada, M. S. (2005). Bayesian methods for assessing system reliability: Models and computation. In Modern Statistical and Mathematical Methods in Reliability (A. G. Wilson, N. Limnios, S. A. Keller-McNulty and Y. M. Armijo, eds.) 41–54. World Scientific, Singapore. · Zbl 1082.62094
[10] Graves, T. L., Hamada, M. S., Booker, J., Decroix, M., Chilcoat, K. and Bowyer, C. (2006). Estimating a proportion using stratified data from both convenience and random samples. Technometrics . · doi:10.1198/004017007000000047
[11] Gutiérrez-Pulido, H., Aguirre-Torres, V. and Christen, J. A. (2005). A practical method for obtaining prior distributions in reliability. IEEE Transactions on Reliability 54 262–269.
[12] Hamada, M. S., Martz, H. F., Reese, C. S., Graves, T. L., Johnson, V. E. and 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 and System Safety 86 297–305.
[13] Huzurbazar, A. V. (2000). Modeling and analysis of engineering systems data using flowgraph models. Technometrics 42 300–306.
[14] Huzurbazar, A. V. (2005). Flowgraph Models for Multistate Time-to-Event Data . Wiley, Hoboken, NJ. · Zbl 1055.62123 · doi:10.1002/0471686565
[15] Jensen, F. (2001). Bayesian Networks and Decision Graphs . Springer, New York. · Zbl 0973.62005
[16] Johnson, V. E., Graves, T. L., Hamada, M. S. and Reese, C. S. (2003). A hierarchical model for estimating the reliability of complex systems (with discussion). In Bayesian Statistics 7 (J. M. Bernardo, A. P. Dawid, J. O. Berger and M. West, eds.) 199–213. Oxford Univ. Press.
[17] Kadane, J. B. and Wolfson, L. J. (1998). Experiences in elicitation. The Statistician 47 3–19.
[18] Keeney, R. L. and von Winterfeldt, D. (1991). Eliciting probabilities from experts in complex technical problems. IEEE Transactions on Engineering Management 38 191–201.
[19] Klamann, R. and Koehler, A. (2005). Large-scale qualitative modeling for system prediction. Technical Report LA-UR-05-2624, Los Alamos National Laboratory.
[20] Laskey, K. B. and Mahoney, S. M. (2000). Network engineering for agile belief network models. IEEE Transactions on Knowledge and Data Engineering 12 487–498.
[21] Lee, B. (2001). Using Bayes belief networks in industrial FMEA modeling and analysis. In Annual Reliability and Maintainability Symposium 7–15. IEEE Press, Piscataway, NJ.
[22] Meilijson, I. (1994). Competing risks on coherent reliability systems: Estimation in the parametric case. J. Amer. Statist. Assoc. 89 1459–1464. JSTOR: · Zbl 0810.62090 · doi:10.2307/2291007
[23] Meyer, M. A. and Booker, J. M. (2001). Eliciting and Analyzing Expert Judgment : A Practical Guide . SIAM, Philadelphia. · Zbl 0969.62075
[24] Mosleh, A. (1991). Common cause failures: An analysis methodology and examples. Reliability Engineering and System Safety 34 249–292.
[25] Neil, M., Fenton, N. and Nielson, L. (2000). Building large-scale Bayesian networks. Knowledge Engineering Review 15 257–284. · Zbl 0988.68187 · doi:10.1017/S0269888900003039
[26] O’Hagan, A. (1998). Eliciting expert beliefs in substantial practical applications. The Statistician 47 21–35.
[27] Parker, J. (1972). Bayesian prior distributions for multi-component systems. Naval Research Logistics Quarterly 19 509–515. · Zbl 0249.62091 · doi:10.1002/nav.3800190311
[28] Pepe, M. S. (1992). Inference using surrogate outcome data and a validation sample. Biometrika 79 355–365. JSTOR: · Zbl 0751.62049 · doi:10.1093/biomet/79.2.355
[29] Percy, D. F. (2002). Subjective reliability analysis using predictive elicitation. In Mathematical and Statistical Methods in Reliability (B. H. Lindqvist and K. A. Doksum, eds.) 57–72. World Scientific, River Edge, NJ.
[30] Portinale, L., Bobbio, A. and Montani, S. (2005). From artificial intelligence to dependability: Modeling and analysis with Bayesian networks. In Modern Statistical and Mathematical Methods in Reliability (A. G. Wilson, N. Limnios, S. A. Keller-McNulty and Y. M. Armijo, eds.) 365–381. World Scientific, Singapore. · Zbl 1082.62099
[31] Prentice, R. L. (1989). Surrogate endpoints in clinical trials: Definition and operational criteria. Statistics in Medicine 8 431–440.
[32] R Development Core Team (2004). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna. Available at www.r-project.org.
[33] Reese, C. S., Hamada, M. and Robinson, D. (2005). Assessing system reliability by combining multilevel data from different test modalities. Qual. Technol. Quant. Manag. 2 177–188.
[34] Ryan, K. J. and Reese, C. S. (2005). Estimating reliability trends for supercomputers. Technical Report TR05-103, Dept. Statistics, Brigham Young Univ.
[35] Santner, T. J., Williams, B. J. and Notz, W. (2003). The Design and Analysis of Computer Experiments . Springer, New York. · Zbl 1041.62068
[36] Seshasai, S. and Gupta, A. (2004). Knowledge-based approach to facilitate engineering design. J. Spacecraft and Rockets 41 29–38.
[37] Sigurdsson, J., Walls, L. and Quigley, J. (2001). Bayesian belief nets for managing expert judgement and modelling reliability. Quality and Reliability Engineering International 17 181–190.
[38] Spiegelhalter, D. (1998). Bayesian graphical modeling: A case-study in monitoring health outcomes. Appl. Statist. 47 115–133.
[39] Wilson, A. G., McNamara, L. A. and Wilson, G. D. (2007). Information integration for complex systems. Reliability Engineering and System Safety 92 121–130.
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