Abstract
Reliability analysis of a system based on probability theory has been widely studied and used. Nevertheless, it sometimes meets with one problem that the components of a system may have only few or even no samples, so that we cannot estimate their probability distributions via statistics. Then reliability analysis of a system based on uncertainty theory has been proposed. However, in a general system, some components of the system may have enough samples while some others may have no samples, so the reliability of the system cannot be analyzed simply based on probability theory or uncertainty theory. In order to deal with this type systems, this paper proposes a method of reliability analysis based on chance theory which is a generalization of both probability theory and uncertainty theory. In order to illustrate the method, some common systems are considered such as series system, parallel system, k-out-of-n system and bridge system.
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References
Cornell, C. A. (1969). A probability-based structural code. Journal of American Concrete Institute, 66, 975–985.
Freudethal, A. M. (1947). The safety of structures. Transactions of the American Society of Civil Engineers, 112(1), 125–159.
Ke, H., Su, T., & Ni, Y. (2014). Uncertain random multilevel programming with application to production control problem. Soft Computing, 19(6), 1739–1746.
Liu, B. (2007). Uncertainty theory (2nd ed.). Berlin: Springer.
Liu, B. (2009a). Some research problems in uncertainty theory. Journal of Uncertain Systems, 3(1), 3–10.
Liu, B. (2009b). Theory and practice of uncertain programming (2nd ed.). Berlin: Springer.
Liu, B. (2010a). Uncertainty theory: A branch of mathematics for modeling human uncertainty. Berlin: Springer.
Liu, B. (2010b). Uncertain risk analysis and uncertain reliability analysis. Journal of Uncertain Systems, 4(3), 163–170.
Liu, B. (2012). Why is there a need for uncertainty theory? Journal of Uncertain Systems, 6(1), 3–10.
Liu, Y. H. (2013a). Uncertain random variables: A mixture of uncertainty and randomness. Soft Computing, 17(4), 625–634.
Liu, Y. H. (2013b). Uncertain random programming with applications. Fuzzy Optimization and Decision Making, 12(2), 153–169.
Liu, B. (2014). Uncertain random graph and uncertain random network. Journal of Uncertain Systems, 8(1), 3–12.
Liu, B. (2015). Uncertainty theory (4th ed.). Berlin: Springer.
Liu, Y. H., & Ha, M. H. (2010). Expected value of function of uncertain variables. Journal of uncertain Systems, 13, 181–186.
Liu, Y. H., & Ralescu, D. A. (2014). Risk index in uncertain random risk analysis. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 22(4), 491–504.
Liu, Y. H., & Ralescu, D. A. (2016). Value-at-risk in uncertain random risk analysis, Applied Soft Computing, to be published.
Sheng, Y., & Gao, J. (2014). Chance distribution of the maximum flow of uncertain random network, Journal of Uncertainty Analysis and Applications. 2, Article 15. doi:10.1186/s40467-014-0015-3.
Zhou, J., Yang, F., & Wang, K. (2014). Multi-objective optimization in uncertain random environments. Fuzzy Optimization and Decision Making, 13(4), 397–413.
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This work was supported by National Natural Science Foundation of China (Nos.71201005, 61573043).
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Wen, M., Kang, R. Reliability analysis in uncertain random system. Fuzzy Optim Decis Making 15, 491–506 (2016). https://doi.org/10.1007/s10700-016-9235-y
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DOI: https://doi.org/10.1007/s10700-016-9235-y