Parametric Interval Estimation for Doubly-Truncated Weibull#br#
Distribution Based on Likelihood Ratio Test

doi:10.3901/JME.2017.06.203

Abstract

Abstract:

Since no analytical solution was found in the process of parametric point estimation as well as solution for the parametric interval estimation for Doubly-Truncated Weibull distribution, an extreme value solution method and Monte Carlo method based parametric point estimation solution method and likelihood ratio test theory based parametric interval estimation method for Doubly-Truncated Weibull distribution model are proposed. During calculation, the multi-step detailed interval conversion iterative numerical solution method for random data interval is put forward further. On the basis of CNC external cylindrical grinding failure data, Doubly-Truncated Weibull distribution is used for analysis and comparison with two-parameter and three-parameter Weibull distribution. According to results, the interval conversion iterative algorithm set and likelihood ratio test theory based parametric interval estimation method are correct and available as a result of good estimation effect.

Key words: likelihood ratio, Monte Carlo, parameters estimation, doubly-truncated Weibull distribution

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.

References

[1] 贾祥，王小林，郭波. 极少失效数据和无失效数据的可靠性评估[J]. 机械工程学报，2016，52(2)：182-188.
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.
[2] 张根保，郭书恒. 基于竞争威布尔模型的加工中心可靠性评估[J]. 计算机集成制造系统，2015，21(1)：180-186.
ZHANG Genbao，GUO Shuheng. Reliability evaluation of machining tool center based on competing weibull model[J]. Computer Integrated Manufacturing System，2015，21(1)：180-186.
[3] BÜTIKOFER L，STAWARCZYK B，ROOS M. Two regression methods for estimation of a two-parameter Weibull distribution for reliability of dental materials[J]. Dental Materials，2015，31(2)：33-50.
[4] PIÑA-MONARREZ M，ORTIZ-YAÑEZ J. Weibull and lognormal taguchi analysis using multiple linear regression[J]. Reliability Engineering & System Safety，2015，144：244-253.
[5] 贾志新，张宏斌，郗安民. 基于径向基函数神经网络的电火花线切割机床可靠性数据模拟生成[J]. 机械工程学报，2010，46(2)：145-149.
JIA Zhixin，ZHANG Hongbin，XI Anmin. Simulating and extending wire electrical discharge machining reliability data by radial basis function neural network[J]. Journal of Mechanical Engineering，2010，46(2)：145-149.
[6] DAS K. A comparative study of exponential distribution vs weibull distribution in machine reliability analysis in a CMS design[J]. Computers & Industrial Engineering，2008，54(1)：12-33.
[7] 赵永翔，梁红琴. 基于两参数Weibull分布的概率疲劳S-N曲线模型[J]. 机械工程学报，2015，51(20)：208-212.
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.
[8] YANG Z，KAN Y，CHEN F，et al. Bayesian reliability modeling and assessment solution for NC machine tools under small-sample data[J]. Chinese Journal of Mechanical Engineering，2015，28(6)：1229-1239.
[9] 杨兆军，杨川贵，陈菲，等. 基于PSO算法和SVR模型的加工中心可靠性模型参数估计[J]. 吉林大学学报，2015，45(3)：829-836.
YANG Zhaojun，YANG Chuangui，CHEN Fei，et al. Parameter estimation of reliability model of machining center based on particle swarm optimization and support vector regression[J]. Journal of Jilin University 2015，45(3)：829-836.
[10] WINGO D. Parametric point estimation for a doubly- truncated weibull distribution[J]. Microelectronics Reliability，1988，28(4)：613-617.
[11] ZHANG T，XIE M. On the upper truncated weibull distribution and its reliability implications[J]. Reliability Engineering & System Safety，2011，96(1)：194-200.
[12] PARK S，NG H，CHAN P. On the Fisher information and design of a flexible progressive censored experiment[J]. Statistics & Probability Letters，2015，97：142-149.
[13] GELMAN A，CARLIN J，STERN H，et al. Bayesian data analysis[M]. New York：Chapman & Hall/CRC，2004.
[14] 杨建国，王智明，王国强，等. 数控机床可靠性指标的似然比检验区间估计[J]. 机械工程学报，2012，48(2)：9-15.
YANG Jianguo，WANG Zhiming，WANG Guoqiang，et al. Likelihood ratio test interval estimation of reliability indices for numerical control machine tools[J]. Journal of Mechanical Engineering，2012，48(2)：9-15.
[15] 齐奥. 可靠性与风险分析蒙特卡罗方法[M]. 北京：国防工业出版社，2014.
ZIO. Monte carlo simulation method for system reliability and risk analysis[M]. Beijing：National Defense Industry Press，2014.

Parametric Interval Estimation for Doubly-Truncated Weibull#br# Distribution Based on Likelihood Ratio Test

PDF

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Recommended Articles

Metrics

Comments

[1]	ZHAO Jingyu, XU Cheng, LI Xiaoyu. Electric Vehicle Energy Consumption Analysis and Prediction Based on Real-world Driving Data [J]. Journal of Mechanical Engineering, 2023, 59(10): 263-274.
[2]	WU Chunling, CHENG Yanqing, XU Xianfeng, MENG Jinhao, XIE Meimei. SOC Estimation of Lithium Battery Based on Monte Carlo and SH-AUKF Algorithm [J]. Journal of Electrical Engineering, 2022, 17(3): 66-75.
[3]	Gaohong Xu, Zexin Jia, Wenxiang Zhao, Qian Chen, Guohai Liu. Multi-objective Optimization Design of Inset-surface Permanent Magnet Machine Considering Deterministic and Robust Performances^* [J]. Chinese Journal of Electrical Engineering, 2021, 7(3): 73-87.
[4]	WANG Yiwei, DENG Lei, ZHENG Lianyu, WANG Yahui. A Multi-channel Signal Fusion and Bayesian Theory Based Method for Tool Remaining Useful Life Prediction [J]. Journal of Mechanical Engineering, 2021, 57(13): 214-224.
[5]	ZHANG Zhao, TAN Zhijun, LI Jianyu, YUAN Honglei, LIU Weiwei. Integrated Numerical Simulation of Temperature-recrystallization-precipitate- mechanical Property in Friction Stir Lap Welding of Aluminum Alloy [J]. Journal of Mechanical Engineering, 2020, 56(6): 213-220.
[6]	YING Feixiang,WANG Yuhang,LI Yan,ZHANG Enmu,XU Tianqi,TIAN Hua,HE Min,JIA Jian. Economic Evaluation of Small Power Generation System Containing Wind and Solar Generating Unit Considering Reliability [J]. Journal of Electrical Engineering, 2020, 15(3): 13-21.
[7]	MA Yali, LI Yangyang. Motion Error of Rolling Guide Based on Uncertainty of Geometric Error [J]. Journal of Mechanical Engineering, 2019, 55(5): 11-18.
[8]	ZHAO Zhiyuan, XU Zhenbang, HE Junpei, HE Shuai, XU Ce. Configuration Optimization of Nine Degree of Freedom Super-redundant Serial Manipulator Based on Workspace Analysis [J]. Journal of Mechanical Engineering, 2019, 55(21): 51-63.
[9]	ZHU Daye, DING Xiaohong, WANG Shenlong, WANG Haihua, YU Huijie. Uncertainty Evaluation Method of Complex Nonlinear System Test Based on Support Vector Machine Model [J]. Journal of Mechanical Engineering, 2018, 54(8): 177-184.
[10]	Yanjin Zhao,Qinghai Meng,Peng Chen,Jinji Wang. Reactive Power Optimization for Distribution Network with the Electric Vehicle [J]. Journal of Electrical Engineering, 2017, 12(3): 48-52.
[11]	YAN Xiaoling, DONG Shiyun, XU Binshi. Flaw Diagnosis Technology for Remanufactured Motor Rotor Based on Optimal Wavelet Packet Shannon Entropy [J]. Journal of Mechanical Engineering, 2016, 52(4): 7-12.
[12]	LIU Yu, LI Tianxiang, LIU Kuo, ZHANG Yimin. Chatter Reliability of Turning Processing System Based on Fourth Moment Method [J]. Journal of Mechanical Engineering, 2016, 52(20): 193-200.
[13]	Chen Peng,Meng Qinghai,Zhao Yanjin. The Electric Vehicle Charging Load Calculation Based on the Monte Carlo Method [J]. Journal of Electrical Engineering, 2016, 11(11): 40-46.
[14]	CHEN Hua, LIN Guansheng, TANG Tao, YANG Jia, JIN Sun. A New Approach of Constraints Establishment and Optimization for Matrix Tolerance Model [J]. Journal of Mechanical Engineering, 2016, 52(1): 123-129.
[15]	HONG Huangjie, WANG Hongyan, LI Jianyang, RUI Qiang, ZHANG Fang. Research on Assessment Method of Airbag Cushion System for Airdropping Equipment [J]. Journal of Mechanical Engineering, 2015, 51(4): 148-154.