逐步Ⅰ型混合截尾下指数-威布尔分布竞争失效模型的统计分析

摘要

In this paper,we investigate a competing risks model based on exponentiated Weibull distribution under Type-Ⅰ progressively hybrid censoring scheme.To estimate the unknown parameters and reliability function,the maximum likelihood estimators and asymptotic confidence intervals are derived.Since Bayesian posterior density functions cannot be given in closed forms,we adopt Markov chain Monte Carlo method to calculate approximate Bayes estimators and highest posterior density credible intervals.To illustrate the estimation methods,a simulation study is carried out with numerical results.It is concluded that the maximum likelihood estimation and Bayesian estimation can be used for statistical inference in competing risks model under Type-Ⅰ progressively hybrid censoring scheme.%本文基于指数-威布尔分布研究逐步Ⅰ型混合截尾竞争失效模型的统计推断问题.根据模型假设和竞争失效数据,推导出未知参数和产品可靠度的极大似然估计;考虑极大似然估计的渐近正态性质,计算出观测Fisher信息阵,从而获得未知参数和可靠度的渐近置信区间.由于贝叶斯后验密度函数不具有封闭形式,利用MCMC方法给出未知参数和可靠度的近似贝叶斯估计以及最大后验密度可信区间.最后通过模拟研究对估计方法作出解释并给出数值结果.结果表明极大似然方法和贝叶斯方法可以对逐步Ⅰ型混合截尾竞争失效模型进行统计推断.