基于随机截尾数据非参化Nelson-Aalen可靠性评估模型  

Nonparametric Nelson-Aalen reliability evaluation model based on random censored data

作　　者：刘新玲 唐家银[1,2] 王劲博 吴怡 LIU Xinling;TANG Jiayin;WANG Jinbo;WU Yi(School of Mathematics,Southwest Jiaotong University,Chengdu 611756,China;National Engineering Laboratory of Integrated Transportation Big Data Application Technology,Southwest Jiaotong University,Chengdu 611756,China)

机构地区：[1]西南交通大学数学学院,成都611756 [2]西南交通大学综合交通大数据应用技术国家工程实验室,成都611756

出　　处：《航空动力学报》2025年第1期359-369,共11页Journal of Aerospace Power

基　　金：国家社会科学基金一般项目(23BTJ010)。

摘　　要：针对可靠性工程试验中的随机截尾数据,从累积失效率函数的分析角度出发,基于NelsonAalen(NA)估计理论,实现了对产品的非参数化可靠性评估。基于所获离散样本,给出累积失效率在连续和离散形式下的非参数极大似然估计,并推导出随机截尾样本下累积失效率函数的NA估计形式;由NA估计所得的可靠度衍生完全非参数化置信评估模型;构建广义加权滑动平均模型,实现了对样本最大观测时间之后的可靠度估计。算例分析表明:在对寿命分布信息完全未知时,NA模型实现了基于随机截尾受测型寿命数据对产品可靠性的有效置信评估,估计相对偏差率控制在0.9787%以下,且估计精度随着样本量的增加和截尾比例的减小而显著提高。结果验证了NA可靠性计算的有效性和评估精准性。For the random censored data in the reliability engineering test,a nonparametric reliability evaluation of the product was realized based on the Nelson-Aalen(NA)estimation theory from the perspective of the analysis of cumulative failure rate function.The nonparametric maximum likelihood estimation of the cumulative failure rate in continuous and discrete forms was given by using the obtained discrete samples,and the NA estimation form of the cumulative failure rate function under the random censored samples was derived.A completely nonparametric confidence evaluation model was derived from the reliability by NA estimation.A generalized weighted moving average model was constructed to estimate the reliability after the maximum observation time of the sample.Finally,example analysis showed that when the life distribution information was completely unknown,the NA model realized the effective confidence evaluation of product reliability based on random censored life data,and the estimated relative bias rate was controlled below 0.9787%,and the estimation accuracy was improved significantly with the increase of sample size and the decrease of censoring ratio.The results verified the validity and evaluation accuracy of NA reliability calculation.

关 键 词：Nelson-Aalen估计 随机截尾数据 非参数极大似然估计 置信评估 可靠性分析 

分 类 号：V438.4[航空宇航科学与技术—航空宇航推进理论与工程] TB114.3[理学—概率论与数理统计]