Reliability Assessment for Very Few Failure Data and Zero-failure Data

doi:10.3901/JME.2016.02.182

Abstract

Abstract: For zero-failure data and very few failure data, the current methods fail to obtain both the estimate and confidence interval of parameters. If the estimate and confidence interval of parameters are obtained based on different methods, the results seem to be unconvincing. In this case, the match distribution curve (MDC) method is analyzed and improved to be able to compute both the estimate and confidence interval of parameters for Weibull distribution. And the improved method could make the results more convincing. After calculation for three examples, the estimate and confidence interval of parameters based on the proposed method are better than the results by other methods. It demonstrates the effectiveness and rationality of this method.

Key words: the match distribution curve method, very few failure data, Weibull distribution, zero-failure data

CLC Number:

TB114

JIA Xiang, WANG Xiaolin, GUO Bo. Reliability Assessment for Very Few Failure Data and Zero-failure Data[J]. Journal of Mechanical Engineering, 2016, 52(2): 182-188.

References

[1] 陈家鼎, 孙万龙, 李补喜. 关于无失效数据情形下的置信限[J]. 应用数学学报, 1995, 18(1)：90-100. CHEN Jiading, SUN Wanlong, LI Buxi. On the confidence limits in the case of no failure data[J]. Acta Mathe-maticae Applicatae Sinica, 1995, 18(1)：90-100.
[2] 韩明. Weibull分布可靠性参数的置信限[J]. 机械强度, 2009, 31(1)：59-62. HAN Ming. Confidence limits of reliability parameters for Weibull distributionJournal[J]. Journal of Mechanical Strength, 2009, 31(1)：59-62.
[3] 王凭惠, 范本尧, 傅惠民. 卫星推力器可靠性评估和寿命预测[J]. 航空动力学报, 2004, 19(6)：745-748. WANG Pinghui, FAN Benyao, FU Huimin. Reliability assessment and life prediction for satellite engine[J]. Journal of Aerospace Power, 2004, 19(6)：745-748.
[4] 韩明. 无失效数据下液体火箭发动机的E-Bayes可靠性分析[J]. 航空学报, 2011, 32(12)：2213-2219. HAN Ming. E-Bayes reliability analysis for liquid rocket engine with zero-faiure data[J]. Acta Aeronauticaet Astronautica Sinica, 2011, 32(12)：2213-2219.
[5] 峁诗松, 罗朝斌. 无失效数据的可靠性分析[J]. 数理统计与应用概率, 1989, 4(4)：489-506. MAO Shisong, LUO Chaobin. The reliability analysis for zero-failure data[J]. Mathematical Statistics And Applied Probability, 1989, 4(4)：489-506.
[6] 茆诗松, 夏剑锋, 管文琪. 轴承寿命试验中无失效数据的处理[J]. 应用概率统计, 1993, 9(3)：326-331. MAO Shisong, XIA Jianfeng, GUAN Wenqi. The reliability analysis of zero-failure data for bearing life test[J]. Chinese Journey of Applied Probability and Statistics, 1993, 9(3)：326-331.
[7] 茆诗松, 汤银才, 王玲玲. 可靠性统计 [M]. 北京：高等教育出版社, 2008. MAO Shisong, TANG Yincai, WANG Lingling. Reliability statistics [M]. Beijing：High Eucation Press, 2008.
[8] 傅惠民, 岳晓蕊, 张勇波. 极少失效数据的可靠性评估和寿命预测[J]. 航空动力学报, 2010, 25(8)：1855-1859. FU Huimin, YUE Xiaorui, ZHANG Yongbo. Reliability assessment and life prediction for very few failure data[J]. Journal of Aerospace Power, 2010, 25(8)：1855-1859.
[9] 张志华. 正态分布场合下只有一个失效数据的统计分析[J]. 应用概率统计, 1998, 14(2)：185-190. ZHANG Zhihua. Satistical analysis of data only one failure under normal case[J]. Chinese Journal of Applied Probability and Statistics, 1998, 14(2)：185-190.
[10] 陈文华, 崔杰, 樊晓燕. 单失效数据的可靠性统计分析[J]. 机械工程学报, 2003, 39(9)：44-48. CHEN Wenhua, CUI Jie, FAN Xiaoyan. Reliability statistical analysis of data only one failure[J]. Chinese Journal of Mechanical Engineering, 2003, 39(9)：44-48.
[11] 宁江凡. 液体火箭发动机无失效条件下的可靠性评估方法研究 [D]. 长沙：国防科学技术大学, 2005. NING Jiangfan. Study on reliability assessment method for liquid rocket engine in the case of zero-failure data [D]. Changsha：National University of Defense Technology, 2005.
[12] 贾祥, 蒋平, 郭波. 威布尔分布场合无失效数据的失效概率估计方法[J]. 机械强度, 2015, 37(2)：288-294. JIA Xiang, JIANG Ping, GUO Bo. The estimation to failure probability for zero-failure data in Weibull distribution[J]. Journal of Mechanical Strength, 2015, 37(2)：288-294.

[1]	YANG Xiaoyu, XIE Liyang, YANG Yifeng, ZHAO Bingfeng. Comparison of Three-parameter Weibull Shape Parameter Estimation Methods and Its Recommended Values [J]. Journal of Mechanical Engineering, 2024, 60(16): 367-376.
[2]	CAI Shurao, GAO Ziwei, JI Minzun, YAO Jiachi, LI Pengxin, MIN Daomin, LI Shengtao, WU Qingzhou. Simulation of Carrier Transport and Energy Accumulation Modulated DC Breakdown Weibull Distribution in Polypropylene [J]. Journal of Electrical Engineering, 2021, 16(2): 50-59.
[3]	WANG Yashun, ZHANG Shufeng, CHEN Xun. Study on the Design of Statistical Schemes for Reliability Demonstration Test of Electromechanical Equipment [J]. Journal of Mechanical Engineering, 2021, 57(12): 247-257.
[4]	LI Haiyang, XIE Liyang, LIU Jie, YUAN Yankai, YAO Changhui, JIANG Chunlong. Reliability Evaluation of Bearings in theIntelligent Robot for Changing the Hobwithout Failure Data [J]. Journal of Mechanical Engineering, 2019, 55(2): 186-194.
[5]	NAN Donglei, JIA Zhixin, LI Wei. Parametric Interval Estimation for Doubly-Truncated Weibull#br# Distribution Based on Likelihood Ratio Test [J]. Journal of Mechanical Engineering, 2017, 53(6): 203-212.
[6]	LI Zhen, WANG Minjie, CAI Yujun, LI Guohe, PAN Xin. Research on Wire Net Reliability Assessing Method in Multi-wire Sawing [J]. Journal of Mechanical Engineering, 2017, 53(23): 174-181.
[7]	YANG Xiucong, DONG Tianshun, LI Guolu, WANG Haidou, KANG Jiajie. Rolling Contact Fatigue Life of Supersonic Plasma Sprayed Ni60A Coatings [J]. Journal of Mechanical Engineering, 2016, 52(20): 38-43.
[8]	ZHAO Yongxiang, LIANG Hongqin. Modeling of the Probabilistic Fatigue S-N Curves Using the Two Parameter Weibull Distribution [J]. Journal of Mechanical Engineering, 2015, 51(20): 208-212.
[9]	LI Lingling, MA Dongjuan, LI Zhigang. Performance Assessment Based on Condition Monitoring Data of Electrical Contact of Electrical Products [J]. Journal of Mechanical Engineering, 2015, 51(18): 198-203.
[10]	SUN Yongquan;REN He;GUO Jianying;YUAN Huijuan;LIU Xin. Availability Assessment for Passenger Aircraft Subsystem with Different Lifetime and Repair-time Distribution [J]. , 2014, 50(16): 54-61.
[11]	ZHANG Xiangpo;SHANG Jianzhong;CHEN Xun;ZHANG Chunhua. Statistical Inference of Varying-stress Accelerated Life Test with Competing Failures Based on Three-parameter Weibull Distribution [J]. , 2014, 50(14): 42-49.
[12]	XUE Guangjin;LI Qiang;WANG Binjie;PAN Wu;LI Kai. Estimation of Distribution for Rail Vehicle Dynamic Stress [J]. , 2013, 49(4): 102-105.
[13]	YANG Jianguo;WANG Zhiming;WANG Guoqiang;ZHANG Genbao. Likelihood Ratio Test Interval Estimation of Reliability Indices for Numerical Control Machine Tools [J]. , 2012, 48(2): 9-15.
[14]	LI Guolu;WANG Shaoyun;WANG Haidou;LIU Jinhai;PIAO Zhongyu. Study on the Residual Stress of Plasma Sprayed NiCrBSi Coating in Contact Fatigue Process [J]. , 2012, 48(10): 23-27.
[15]	CUI Weimin;XUE Hongjun;YU Tianxiang;SONG Bifeng. Determination of Sample Size for Weibull Distribution in Structural Reliability Tests [J]. , 2008, 44(1): 51-55.