Estimation of Interval-Valued Reliability of Multi-State System in Consideration of Epistemic Uncertainty under the Random Shock

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Journal of Vibration and Shock ›› 2016, Vol. 35 ›› Issue (10) : 29-37.

PAN Gang, SHANG Chao-xuan, LIANG Yu-ying, CAI Jin-yan，MENG Ya-feng

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Abstract

Components may suffer from random shocks under some environments or other conditions. Performance degradation of components consists of normal performance degradation and random shocks. Since it was hard to obtain adequate performance data of high-reliability components within a short time, there were epistemic uncertainties on components and system reliability cannot be accurately estimated. For the purpose of accurate estimation of system reliability, components’ performance damage distribution parameters caused by random shocks were assumed the interval variables, the components’ performance distribution model based on the interval variable was built, the definition of interval-continuous sequences of components’ state performances and a method to calculate the interval-valued state probability were provided, the traditionally universal generating function method was improved, the interval-valued universal generating function and its algorithm were defined, a method to assess multi-state system reliability in consideration of epistemic uncertainty under random shocks was proposed, and verification and illustration were conducted with simulations. This method not only overcomes the inaccuracy of the reliability analysis model, but also has strong versatility and engineering application value.

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random shocks / epistemic uncertainties / interval-continuous sequences / interval-valued universal generating function

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PAN Gang, SHANG Chao-xuan, LIANG Yu-ying, CAI Jin-yan，MENG Ya-feng. Estimation of Interval-Valued Reliability of Multi-State System in Consideration of Epistemic Uncertainty under the Random Shock[J]. Journal of Vibration and Shock, 2016, 35(10): 29-37

References

[1] Nakagawa T. Shock and Damage Models in Reliability Theory[M]. Springer, 2006.
[2] Liu Y, Huang H, Pham H. Reliability Evaluation of Systems with Degradation and Random Shocks, 2008[C].
[3] YAPING W. multi-objective impact for dependent competing system with multiple degradation progress and random shock[D]. the State University of New Jersey, 2012.
[4] A. Lisnianski And G. Levitin. Multi-State System Reliability: Assessment, Optimization and Applications[M]. Singapore: World Scientiﬁc, 2003.
[5] Barton R M, Damon W. Reliability in a multi-state system[C]: Procedings of the Sixth Annual Southeastern Symposium on Systems Theory., Louisiana, 1974[C].
[6] Barton R E, Wu A S. Coherent systems with multi-state components[J]. Mathematica of Operations Research, 1978(3):275-281.
[7] Li Y, Zio E. A multi-state model for the reliability assessment of a distributed generation system via universal generating function[J]. Reliability Engineering and System Safety, 2012(106):28-36.
[8] Billinton R, Y G. Adequacy assessment of composite power generation model for reliability evaluation.[J]. International Journal of Reliability and Safety, 2008,2(1):79-98.
[9] 史新红, 齐先军, 王治国. 基于UGF的发电系统区间可靠性评估及其仿射算法改进[J]. 合肥工业大学学报（自然科学版）, 2014,37(3):286-291.
SHI Xin-hong，QI Xian-jun，WANG Zhi-guo. Interval reliability estimation of power generating system based on UGF method and its modification by using affine arithmetic[J]. Journal of Hefei University of Technology(Natural Science), 2014,37(3):286-291.
[10]尚彦龙, 蔡琦, 赵新文等. 基于UGF和Semi-Markov方法的反应堆泵机组多状态可靠性分析[J]. 核动力工程, 2012(01): 117-123.
SHANG Yan-long, CAI Qi, ZHAO Xin-wen, CHEN Ling .Multi-State Reliability for Pump Group in Nuclear Power System Based on UGF and Semi-Markov Process. Nuclear Power Engineering , 2012(01): 117-123.
[11] Natvig B. Multistate Systems Reliability Theory with Applications[M]. Hoboken, NJ, USA: Wiley: 2010.
[12] Levitin G. The Universal Generating Function in Reliability Analysis and Optimization[M]. London: Springer, 2005.
[13] Ding-Yi M J Z. Fuzzy Multi-State Systems: General Definitions, and Performance Assessment[J]. IEEE Transactions on Reliability, 2008,57(4):589-594.
[14] Ding Y, Lisnianski A. Fuzzy universal generating functions for multi-state system reliability assessment[J]. Fuzzy Sets and Systems, 2008(159):307-324.
[15] 鄢民强, 杨波, 王展. 不完全覆盖的模糊多状态系统可靠性计算方法[J]. 西安交通大学学报, 2011(10):109-114.
Yan Minqiang, Yang Bo, and Wang Zhan. Reliability assessment for multi-state system subject to imperfect fault coverage[J]. Journal of Xi'an Jiao tong University, 2011,45(10): 109-114.
[16] Chun-yang Li X C X Y. Interval-Valued Reliability Analysis of Multi-State Systems[J]. IEEE Transactions on Reliability, 2011,60(1):323-330.
[17] Li W, Pham H. Reliability Modeling of Multi-State Degraded Systems With Multi-Competing Failures and Random Shocks[J]. IEEE Transactions on Reliability, 2005,54(2):297-303.
[18] 邱志平. 非概率集合理论凸方法及其应用[M]. 北京: 国防工业出版社, 2005.
Qiu Zhiping. Convex Method of Non-Probabilistic Set-Theory and Its Application[M]. Beijing: National Defense Industry Press, 2005.