Inference on the high-reliability lifetime estimation based on the three-parameter Weibull distribution基于三参数 Weibull 分布的高可靠性寿命估计推断
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Yang XY, Xie LY, Wang BW, Chen JP, Zhao BF, 2024. Inference on the high-reliability lifetime estimation based on the three-parameter Weibull distribution. Probabilistic Engineering Mechanics, 77: 103665.DOI: 10.1016/j.probengmech.2024.103665
吊耳的高可靠性寿命估计至关重要，因为它是航空炸弹中最关键的部件。本文针对吊耳疲劳数据，基于三参数 Weibull 分布对其高可靠性寿命进行了研究。本文提出了一种新方法，根据广义信赖推断生成可靠性寿命估计值，其先验通过失效数据计算。基于 Bayes 理论得到后验分布，使用蒙特卡罗 Markov 链方法计算广义信赖推断的可靠性寿命点估计和置信区间。随后，将该方法与非信息先验 Bayes 推断进行对比。蒙特卡罗模拟表明，所提方法优于非信息先验 Bayes 推断，广义信赖推断的可靠寿命较低置信限具有令人满意的覆盖概率。最后，对 18 个吊耳在可变荷载下进行疲劳测试，估计了高可靠性寿命的点估计和较低置信限，展示了所提方法的适用性。关键词: 三参数 Weibull 分布, 可靠性寿命, 广义信赖推断, Bayes 推断, 蒙特卡洛 Markov 链方法The high-reliability lifetime estimation of the lifting lug is of significant importance, as it is the most crucial component of the aerial bomb. This paper focuses on the high-reliability lifetime of the three-parameter Weibull distribution for lifting lug fatigue data. A novel method is developed to generate estimates of reliability lifetime according to the generalized fiducial inference, whose prior is calculated by the failure data. A posterior distribution is obtained based on Bayesian theory to compute the point estimate and the confidence interval of the generalized fiducial inference for reliability lifetime using the Monte Carlo Markov chain method. Subsequently, it is compared with the non-informative prior Bayesian inference. A Monte Carlo simulation demonstrates that the proposed method outperforms the non-informative prior Bayesian inference. The lower confidence limit of the generalized fiducial inference for the reliability lifetime exhibis satisfactory coverage probabilities. Finally, fatigue tests are performed on 18 lifting lugs under variable loads. The point estimate and the lower confidence limit of the high-reliability lifetime are estimated, which can illustrate the applicability of the proposed method.
Keywords: Three-parameter Weibull distribution; Reliability lifetime; Generalized fiducial inference; Bayes inference; Monte Carlo Markov chain method.![]()
图 1: 分布参数与可靠性寿命的 Markov 链蒙特卡罗样本迹线图Fig. 1. Trace plots of the MCMC sample for β^, η^, γ^, and t^_R (R = 0.99)
图 2: 分布参数与可靠性寿命的 Markov 链蒙特卡罗样本概率密度函数Fig. 2. Probability density functions of the MCMC sample for β^, η^, γ^, and t^_R (R = 0.99)
图 3: 分布参数与可靠性寿命的 Markov 链蒙特卡罗样本运动均值图Fig. 3. Running mean plots of the MCMC sample for β^, η^, γ^, and t^_R (R = 0.99)
图 4: 分布参数与可靠性寿命的 Markov 链蒙特卡罗样本自相关图Fig. 4. Autocorrelation plots of the MCMC sample for β^, η^, γ^, and t^_R (R = 0.99)
图 5: 广义信赖推断置信下限与 Bayes 置信下限的对比Fig. 5. Comparisons between the GFI LCL and Bayes LCL
图 6: 广义信赖推断置信下限的平均下限与真实值之比Fig. 6. Ratios of the average lower limit to the true value for GFI LCL
图 7: 吊耳疲劳试验: (a) SHIMADZU 疲劳试验机; (b) 夹具与吊耳组装; (c) 吊耳与航弹分段模型组装; (d) 吊耳Fig. 7. Lifting lug fatigue test: (a) SHIMADZU fatigue testing machine; (b) Assembly of fixture and lifting lug; (c) Assembly of lifting lug and aerial bomb section model; (d) Lifting lug
图 8: 基于吊耳失效寿命数据的两类方法下高可靠性寿命估计Fig. 8. High-reliability lifetime estimated by the two methods for failure lifetime data of the lifting lugs
作者信息 | Authors
东北大学 (Northeastern University) 机械工程与自动化学院
谢里阳 Li-Yang Xie, 通讯作者 (Corresp.)东北大学 (Northeastern University) 机械工程与自动化学院Email: lyxie@mail.neu.edu.cn
北京动力机械研究所 (Beijing Power Machinery Institute)
东北大学 (Northeastern University) 机械工程与自动化学院
东北大学 (Northeastern University) 机械工程与自动化学院
律梦泽 M.Z. Lyu | 编辑 (Ed)
P.D. Spanos | 审校 (Rev)
陈建兵 J.B. Chen | 审校 (Rev)
彭勇波 Y.B. Peng | 审校 (Rev)
