基于有限混合逆xgamma分布的应力-强度模型可靠度估计  

Reliability Estimation of Stress-strength Model Based on Finite Mixed Inverse xgamma Distribution

作　　者：马雄 黄介武 MA Xiong;HUANG Jiewu(School of Data Science and Information Engineering,Guizhou Minzu University,Guiyang 550025,China)

机构地区：[1]贵州民族大学数据科学与信息工程学院,贵阳550025

出　　处：《西安文理学院学报(自然科学版)》2025年第1期13-20,共8页Journal of Xi’an University(Natural Science Edition)

基　　金：贵州省教育厅自然科学研究项目(黔教技[2022]015号)

摘　　要：假设应力和强度变量相互独立,均服从有限混合逆xgamma分布,研究应力-强度模型的可靠度估计.首先,利用EM算法结合牛顿迭代法推导了模型可靠度的极大似然估计,利用Bootstrap方法得到了模型可靠度的95%置信区间.其次,利用Metropolis-Hastings算法,得到了模型可靠度的贝叶斯估计和均方损失函数下95%的最高后验密度可信区间.同时,利用R软件里的changepoint包,检验了数据的同质性.最后,为了比较有限混合模型和单一模型可靠度估计的准确性,运用上述方法进行了Monto Carlo模拟和一个关于发射器修复时间的实例来说明.结果显示,在偏差意义下,有限混合逆xgamma分布的可靠度比单一逆xgamma分布的估计效果更优,且随着样本量的增大,有限混合逆xgamma分布逐渐接近真实值.Assuming that the stress and strength variables are independent of each other and both obey the finite mixed inverse xgamma distribution,the reliability estimation of the stressstrength model is studied.Firstly,the maximum likelihood estimation of the model reliability is derived by using the EM algorithm combined with Newton iteration method,and the 95%confidence interval of the model reliability is obtained by using the Bootstrap method.Secondly,the Bayesian estimation of the model reliability and the 95%confidence interval of the highest posterior density under the mean square loss function are obtained by using the Metropolis-Hastings algorithm.At the same time,the changepoint package in R software is used to test the homogeneity of the data.Finally,in order to compare the accuracy of the reliability estimations between the finite mixture model and the single model,the Monto Carlo simulation and an example about the repair time of the launcher are carried out by using the above methods.The results show that,in the sense of bias,the reliability of the finite mixed inverse xgamma distribution is better than that of the single inverse xgamma distribution.Furthermore,with increase of the sample size,the finite mixed inverse xgamma distribution gradually approaches the true value.

关 键 词：应力-强度模型 可靠度估计 EM算法 BOOTSTRAP方法 Metropolis-Hastings算法 

分 类 号：TB114.3[理学—概率论与数理统计]