一般\delta\,-冲击模型中无失效数据的Bayes统计推断
Bayes Statistical Inference on General \xd-Shock Model with Zero-Failure Data
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摘要: 在这篇文章中, 我们针对一般冲击模型, 研究Bayes方法处理无失效数据的问题. 所谓一般\delta\,-冲击模型是指系统受到强度为\lambda的Poisson冲击, 当两个连续冲击之间时间间隔的长度不属于某个固定的区间\delta_1,\delta_2时, 系统将失效. 我们分别选择均匀分布和Beta分布作为先验分布, 用Bayes方法和多层Bayes方法得到了参数\delta_1和\delta_2的估计.Abstract: In this paper, we use Bayesian method to study the estimation problem of the parameters \xd_1 and \xd_2 of the \xd-shock model associated with a Poisson process with intensity \xl under zero-failure data, where the system fails when the length of an interval between two success shocks does not fall in a prespecified interval \xd_1, \xd_2. By choosing U(0,1) and a Beta distribution as the prior distribution of the parameters respectively, we obtain the Bayesian and hierarchical Bayesian estimators of threshold level \xd_1 and \xd_2.