基于马尔科夫再生过程分析阶段任务系统的可靠性

摘要

分析阶段任务系统(PMS)的可靠性是一项重要的工作.为了方便分析大部分已有的分析方法都假设阶段持续时间是确定的或者阶段内过程是齐次马尔科夫过程,这些方法不能够分析实际存在的大量一般的PMS.为此本文研究具有随机分布的阶段持续时间和阶段内过程是马尔科夫再生过程(MRGP)的一般PMS的可靠性分析.由于引入MRGP,一般PMS的阶段内活动可以是指数,确定或者其他一般分布.本文首先给出了一个实际有效的5元组模型框架来刻画该类PMS的动态行为,然后利用已有的MRGP分析方法,说明了阶段内条件瞬时状态占有概率矩阵的计算方法.为了避免为整个PMS构造一个巨大的MRGP,在假设阶段边界允许记忆丢失的条件下,本文给出了一个系统可靠性的有效计算方法,该计算方法是两步的分治方法,首先对每个阶段内的MRGP进行分析,然后利用分析结果通过矩阵乘获得系统的可靠度.通过本文给出的方法可以有效的分析一般PMS的可靠性.%Reliability analysis of phased mission systems (PMS) is important. For the sake of a cost-effective analytical solution, several methods proposed in the literature necessarily need to introduce simplifying assumptions, such as deterministic phase durations and homogeneous Markov intraphase process. To attack the weak points of the state-of-the-art, this paper shows how to analyze reliability of general PMS with random phases duration and Markov regenerative intraphase processes. Thanks to the representative power of Markov regenerative processes (MRGP), the intraphase process of these general PMS may include exponential,deterministic, as well as general transitions. Firstly, these general PMS are modeled under a simple and practical 5-tuple framework. Then by exploiting the techniques available in the literature for the analysis of the MRGP, we show how to compute conditional transient occupation probability matrix for each phase. Then under assumption that memory is lostable at phase boundaries we propose a divide-and-conquer reliability analysis methodology to avoid building a large MRGP for the whole PMS and it has two steps: solve each intraphase process separately and then calculate the reliability of the system by matrix multiplication. With the proposed method, the reliability of general PMS can be efficiently analyzed.