A Research on Mechanical Reliability Assessment Based on Small Sample Failure Data

doi:10.3969/j.issn.1007-7375.e17-4099

Abstract

Abstract: “Higher reliability, less failure” features of mechanical products or system make reliability assessment more difficult. To address this problem, an evaluation method of small sample of three parameter Weibull distribution is proposed based on the data of failure of mechanical reliability. Based on the determination of life distribution model, the failure data of small sample is estimated by using the grey estimation method, and the goodness of fit test is carried out, then Bayes prior distribution obtained by Monte Carlo sample as a parameter. On this basis, the three- parameter posterior distribution can be calculated by Bayes formula, and then the system reliability, failure rate and so on are derived, to evaluate the mechanical reliability of small sample failure data more accurately. The effectiveness of the method is verified by a practical example.

Key words: small sample failure data, Weibull distribution, Bayesian Monte-Carlo, mechanical reliability

CLC Number:

TH21

SONG Mingshun, LU Wei, FANG Xinghua. A Research on Mechanical Reliability Assessment Based on Small Sample Failure Data[J]. Industrial Engineering Journal , 2017, 20(5): 87-93.

References

[1] 杨玉恭, 窦秋芳. 威布尔分布形状参数b对试验特征寿命Nn及可靠性寿命N95的影响研究[J]. 结构强度研究, 2012(1): 11-14.
YANG Yugong, DOU Qiufang. The research on Shape parameter b of Weibull distribution influence on test characteristics life Nn and reliability life N95/5[J]. Structural Strength Study, 2012 (1): 11-14.
[2] ABBASI B, JAHROMI A E. Estimating the parameters of Weibull distribution using simulated annealing algorithm[J]. Applied Mathematics & Computation, 2006, 183(1): 85-93.
[3] TOUW A E. Bayesian estimation of mixed Weibull distributions[J]. Reliability Engineering & System Safety, 2009, 94(2): 463-473.
[4] NELSON W. Weibull analysis of reliability data with few or no failures[J]. Journal of Quality Technology, 1985, 17(3): 140-146.
[5] 刘海涛, 张志华. 威布尔分布无失效数据的Bayes可靠性分析[J]. 系统工程理论与实践, 2008, 28(11): 103-108.
LIU Haitao, ZHANG Zhihua. Bayes reliability analysis of zero failure data for Weibull distribution. [J]. Systems Engineering-Theory & Practice, 2008, 28 (11): 103-108.
[6] 汤银才, 侯道燕. 三参数Weibull分布参数的Bayes估计[J]. 系统科学与数学, 2009, 29(1): 109-115.
TANG Yincai, HOU Daoyan. Bayes estimation of the parameters of the three parameter Weibull distribution [J]. systems science and mathematics, 2009, 29 (1): 109-115.
[7] WAIS P. Two and three-parameter Weibull distribution in available wind power analysis[J]. Renewable Energy, 2017, 103: 15-29.
[8] BUTTON K S, IOANNIDIS J P, MOKRYSZ C, et al. Power failure: why small sample size undermines the reliability of neuroscience. [J]. Nature Reviews Neuroscience, 2013, 14(5): 365-76.
[9] NAGATSUKA H, Balakrishnan N. An efficient method of parameter and quantile estimation for the three-parameter weibull distribution based on statistics invariant to unknown location parameter[J]. Journal of Statistical Computation & Simulation, 2015, 142(7): 1-19.
[10] 刘飞, 张为华. 三参数威布尔分布的Bayes参数估计方法研究[C]//中国航空学会航空动力分会火箭发动机专业委员会2006年学术年会. 2006.
[11] 邓聚龙. 灰色系统理论教程[M]. 武汉: 华中理工大学出版社, 1990.
[12] 李芷筠, 戴志辉, 焦彦军. 小样本失效数据下保护可靠性的贝叶斯-蒙特卡罗评估方法[J]. 电力系统及其自动化学报, 2016, 28(5): 23-27.
LI Zhiyun, DAI Zhihui, JIAO Yanjun. Bayesian Monte Carlo evaluation method for protection reliability under small sample failure data [J]. proceedings of the Chinese society of power systems and automation, 2016, 28 (5): 23-27.
[13] RAJABALINEJAD M. Bayesian Monte Carlo method[J]. Reliability Engineering & System Safety, 2010, 95(10): 1050-1060.
[14] 贾现召, 张涛, 赵海莲, 等. 截尾时间下数控机床可靠性分析的灰色模型法[J]. 河南科技大学学报: 自然科学版, 2013, 34(4): 12-16.
JIA Xianzhao, ZHANG Tao, ZHAO Hailian, et al. The grey model method to analysis the reliability of CNC machine tool of the censored time[J]. Journal of Henan University of Science and Technology: Natural Science Edition, 2013, 34 (4): 12-16.
[15] 郑荣跃, 严剑松. 威布尔分布参数估计新方法研究[J]. 机械强度, 2002, 24(4): 599-601.
ZHENG Rongyue, YAN Jiansong. Study on a new method for parameter estimation of Weibull distribution [J]. Mechanical Strength, 2002, 24 (4): 599-601.
[16] DAI Z, WANG Z, JIAO Y. Bayes Monte-Carlo assessment method of protection systems reliability based on small failure sample data[J]. IEEE Transactions on Power Delivery, 2014, 29(4): 1841-1848.
[17] 刘方亮. 核电站小样本数据贝叶斯处理方法研究[D]. 北京: 清华大学, 2010.
LIU Fangliang. Study on Bayesian method for small sample data processing of nuclear power plant [D]. Tsinghua University, 2010.
[18] 郑锐. 三参数威布尔分布参数估计及在可靠性分析中的应用[J]. 振动与冲击, 2015(5): 78-81.
ZHENG Rui. Parameter estimation of three parameter Weibull distribution and its application in reliability analysis [J]. vibration and shock, 2015 (5): 78-81.
[19] 方志强, 高连华. 三参数威布尔分布在寿命分析中的参数估计[J]. 装甲兵工程学院学报, 2001, 15(2): 70-74.
FANG Zhiqiang, GAO Lianhua. Three parameters of Weibull distribution in life analysis of the estimation [J]. Journal of The Academy of Armored Forces Engineering, 2001, 15 (2): 70-74.
[20] 刘爱民, 刘有恒. 关于可修复系统的MTBF和MTTR[J]. 电子学报, 1998, 26(1): 70-72.
LIU Aimin, LIU Youheng. MTBF and MTTR for repairable systems[J], 1998, 26 (1): 70-72.