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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。
The reliability of the analysis phase task system (PMS) is an important task. In order to facilitate the analysis of most of the existing analysis methods assume that the duration of the stage is determined or the process in the stage is a homogeneous Markov process, these methods can not analyze the actual number of general PMS. To this end, this paper studies the reliability analysis of a general PMS with a stochastic distribution of stage durations and stages within the process of Markov regeneration (MRGP). Due to the introduction of MRGP, the activities of the general PMS in the phase can be exponential, deterministic or other general distribution. In this paper, a practical and effective 5-tuple model framework is presented to describe the dynamic behavior of this type of PMS. Then, the existing MRGP analysis method is used to illustrate the calculation method of the conditional probability state possession probability matrix in the phase. In order to avoid constructing a huge MRGP for the whole PMS, an efficient method of system reliability calculation is given under the assumption that the memory loss in the phase boundary is allowed. This method is a two-step partitioning method. Firstly, Phase MRGP analysis, and then use the results of the analysis by matrix multiplication to obtain the reliability of the system. The method given in this paper can effectively analyze the reliability of general PMS.