Reliability Assessment for the Solenoid Valve of a High-Speed Train Braking System under Small Sample Size
Tóm tắt
Reliability assessment of the braking system in a high-speed train under small sample size and zero-failure data is very important for safe operation. Traditional reliability assessment methods are only performed well under conditions of large sample size and complete failure data, which lead to large deviation under conditions of small sample size and zero-failure data. To improve this problem, a new Bayesian method is proposed. Based on the characteristics of the solenoid valve in the braking system of a high-speed train, the modified Weibull distribution is selected to describe the failure rate over the entire lifetime. Based on the assumption of a binomial distribution for the failure probability at censored time, a concave method is employed to obtain the relationships between accumulation failure probabilities. A numerical simulation is performed to compare the results of the proposed method with those obtained from maximum likelihood estimation, and to illustrate that the proposed Bayesian model exhibits a better accuracy for the expectation value when the sample size is less than 12. Finally, the robustness of the model is demonstrated by obtaining the reliability indicators for a numerical case involving the solenoid valve of the braking system, which shows that the change in the reliability and failure rate among the different hyperparameters is small. The method is provided to avoid misleading of subjective information and improve accuracy of reliability assessment under conditions of small sample size and zero-failure data.
Tài liệu tham khảo
C D Lai, M Xia M, D N P Murthy. A modified Weibull distribution. IEEE Transactions on Reliability, 2003, 52(1): 33–37.
H T Liu, Z H Zhang. Bayesian reliability analysis of Weibull zero failure data. Systems Engineering-Theory & Practice, 2008, 28(11): 103–108. (in Chinese)
S Singh, Y M Tripathi. Bayesian estimation and prediction for a hybrid censored lognormal distribution. IEEE Transactions on Reliability, 2015, 65(2): 1–14.
A A Soliman, A H Abd-Ellah, N A Abou-Elheggag, et al. Modified Weibull model: A Bayes study using MCMC approach based on progressive censoring data. Reliability Engineering & System Safety, 2012, 100(6): 48–57.
Z Yang, Y Kan, C Fei, et al. Bayesian reliability modeling and assessment solution for NC machine tools under small-sample data. Chinese Journal of Mechanical Engineering, 2015, 28(6): 1229–1239.
X Xia. Reliability analysis of zero-failure data with poor information. Quality & Reliability Engineering, 2012, 28(8): 981–990.
D Lord, L F Miranda-Moreno. Effects of low sample mean values and small sample size on the estimation of the fixed dispersion parameter of Poisson-gamma models for modeling motor vehicle crashes: A Bayesian perspective. Safety Science, 2008, 46(5): 751–770.
E Fabrizi, C Trivisano. Bayesian conditional mean estimation in Log-Normal linear regression models with finite quadratic expected loss. Scandinavian Journal of Statistics Theory & Applications, 2016, 43(4): 1064–1077.
V Junttila, M Laine. Bayesian principal component regression model with spatial effects for forest inventory variables under small field sample size. Remote Sensing of Environment, 2017, 192: 45–57.
Z P Hao, S K Zeng, J B Guo. Bayesian method for system reliability assessment of overlapping pass/fail data. Journal of Systems Engineering and Electronics, 2015, 26(1): 208–214.
Z Ming, J Tao, X Chen, et al. Bayesian demonstration test method with mixed beta distribution. Chinese Journal of Mechanical Engineering, 2008, 21(3): 116–119.
G Jin. Performance reliability modeling and estimation for space bearing under small sample circumstance. Journal of National University of Defense Technology, 2010, 32(1): 133–137.
H Li, H Zuo, Y Su, et al. Study on segmented distribution for reliability evaluation. Chinese Journal of Aeronautics, 2017, 30(1): 310–329.
X Jia, D Wang, P Jiang, et al. Inference on the reliability of Weibull distribution with multiply Type–I censored data. Reliability Engineering & System Safety, 2016, 150: 171–181.
W Peng, H Z Huang, Y Li, et al. Life cycle reliability assessment of new products—A Bayesian model updating approach. Reliability Engineering & System Safety, 2013, 112(112): 109–119.
W Peng, H Huang, Y Li, et al. Bayesian information fusion method for reliability assessment of milling head. Journal of Mechanical Engineering, 2014, 50(6): 185–191. (in Chinese)
Z Yang, Y Zhu, H Ren, et al. Comprehensive reliability allocation method for CNC lathes based on cubic transformed functions of failure mode and effects analysis. Chinese Journal of Mechanical Engineering, 2015, 28(2): 315–324.
S Salvinder, A Shahrum, N M N Abdullah, et al. Markov chain modelling of reliability analysis and prediction under mixed mode loading. Chinese Journal of Mechanical Engineering, 2015, 28(2): 1–8.
M S Hamada, A G Wilson, C S Reese, et al. Bayesian reliability. New York: Springer, 2008.
H Cai, S F Zhang, J H Zhang. Bayes test analysis and assessment. Changsha: National University of Defence Technology Press, 2004. (in Chinese)
C Yao, D Chen, B Wang, et al. Fuzzy reliability assessment method based on T–S fault tree and Bayesian network. Journal of Mechanical Engineering, 2014, 50(2): 193–201. (in Chinese)
L Meng, Z Liu, L Diao, et al. Reliability evaluation of high–speed train traction transmission system based on Markov model. Journal of the China Railway Society, 2016, 38(8): 23–27.
L Z Wang, Y G Xu, J D Zhang. Research on reliability analysis model for key components and parts of railway equipment and its application. Journal of the China Railway Society, 2008, 30(4): 93–97. (in Chinese)
M L Wu, X Y Wang, C Tian. Reliability of relay valve of brake system for rail vehicles. Journal of Southwest Jiaotong University, 2009, 44(3): 365–369. (in Chinese)
X Y Wang, M L Wu. On the reliability of unit brake for urban rail vehicle. Urban Mass Transit, 2010, 13(11): 52–73. (in Chinese)
Y Tian. Reliability analysis application for structure of beam of C70 railway vehicle under extreme small sample size. Beijing: Beijing Jiaotong University, 2008. (in Chinese)
D X Zhu, H Z Liu. Reliability evaluation of high–speed train bearing with minimum sample. Journal of Central South University (Science and Technology), 2013, 44(3): 963–969. (in Chinese)
J Z Dong. Study on urban rail vehicle brake system reliability modeling and simulation. Shanxi: Taiyuan University of Science and Technology, 2012. (in Chinese)
M Akama. Bayesian analysis for the results of fatigue test using full–scale models to obtain the accurate failure probabilities of the Shinkansen vehicle axle. Reliability Engineering & System Safety, 2002, 75(3): 321–332.
W Chen. Study for frequent faults of brake system of CRH1A EMU. Conference Proceedings: China Railway Society Academic Committee for Trains, Passenger Vehicle, Qingdao: China Railway Society, 2012: 271–275. (in Chinese)
H Zhang, H Jiang. The analysis of brake not releasing for CRH5 EMU. Conference Proceedings: China Railway Society Academic Committee for Trains, Passenger Vehicle, Qingdao: China Railway Society, 2012: 269–270. (in Chinese)