双定时混合截尾下Lomax部件的可靠性分析  

Reliability Analysis of Lomax Components Under Double Type-I Hybrid Censoring

作　　者：龙兵[1] 张忠占[2] LONG Bing;ZHANG Zhongzhan(School of Mathematics and Physics,Jingchu University of Technology,Jingmen 448000,China;Faculty of Science,Beijing University of Technology,Beijing 100124,China)

机构地区：[1]荆楚理工学院数理学院,湖北荆门448000 [2]北京工业大学理学部,北京100124

出　　处：《应用数学》2024年第4期1004-1013,共10页Mathematica Applicata

基　　金：国家自然科学基金(12271014);荆楚理工学院科研项目(QN202426)。

摘　　要：在双定时混合截尾数据下,利用极大似然法得到Lomax分布的未知参数、可靠度函数和危险函数的极大似然估计.基于连续型和离散型的混合先验分布在三类损失函数下得到了模型参数、可靠度及危险函数的Bayes估计.分别利用经典方法和Bayes方法得到了被截尾样品未来失效时刻的预测值和预测区间.利用极大似然法对先验分布中的超参数进行了估计,并证明了估计值的唯一性.为了考察估计量的性质,用蒙特卡洛模拟计算出了均方误差,结果表明Bayes估计优于极大似然估计.通过对一个数值例子进行分析,得出了未知参数及可靠性指标的估计.Under double Type-I hybrid censored data,the maximum likelihood method is used to obtain the maximum likelihood estimates of the unknown parameters,reliability function and hazard function for Lomax distribution.Based on a mixture of continuous and discrete prior distributions,the Bayesian estimates of the model parameters,reliability and hazard rate are considered under three types of loss functions.The predictive values and predictive intervals of the future failure times for the censored samples are obtained by using the classical method and Bayesian method,respectively.The maximum likelihood method is used to estimate the hyperparameters in the prior distributions,and the uniqueness of the estimated values is proved.In order to investigate the properties of the estimators,the mean square errors are computed by the Monte Carlo simulation,and the results show that the Bayesian estimates are superior to maximum likelihood estimates.By analyzing a numerical example,the estimates of the unknown parameters and reliability indexes are obtained.

关 键 词：Lomax分布 双定时混合截尾 BAYES估计 BAYES预测 

分 类 号：O213.2[理学—概率论与数理统计]