A Poisson limit theorem for reliability models based on Markov chains

被引：0
作者：
Ledoux, J
机构：
[1] INSA Rennes, Ctr Math, F-35043 Rennes, France
[2] IRMAR, Rennes, France
来源：
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS | 2006年 / 35卷 / 01期
关键词：
compound Poisson approximation; discrete-time multivariate point process; filtering; time inhomogeneous Markov chain;
D O I：
10.1080/03610920500439331
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
In this article, we deal with a class of discrete-time reliability models. The failures are assumed to be generated by an underlying time inhomogeneous Markov chain. The multivariate point process of failures is proved to converge to a Poisson-type process when the failures are rare. As a result, we obtain a Compound Poisson approximation of the cumulative number of failures. A rate of convergence is provided.
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页码：173 / 196
页数：24
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