Abstract: Tree network system is common in pipeline transportation and network communication. It is very important to evaluate its reliability for system design and optimization. For a tree redundant system, under the k-out-of-n failure criterion, the reliability solution method of tree system is studied by using the finite Markov embedding method and its deformation. In this paper, a tree system modeling is defined, and the tree system representation method based on the three parameters of layer parameters, layer node vector and parent-child node matrix is proposed. The reliability solution method under the failure criterion of consecutive k-out-of-n in tree system of deformation finite Markov embedding method is studied. Three numerical examples are given and the operation complexity of the algorithm is analyzed. Finally, this paper compares and discusses the reliability solution methods of the tree system based on the probability generating function method under the k-out-of-n criterion, and considers that the algorithm in this paper has a wider application range and higher efficiency for the system reliability solution under the failure criterion of consecutive k-out-of-n in tree redundant system.

Key words: reliability, tree network system, reliability modeling, finite Markov embedding method

摘要： 树状网络系统在管道运输,网络通信中较为常见,对其进行可靠性评估对系统设计及优化具有重要意义。针对树状冗余系统,在n中连续取k失效准则下,通过有限马尔可夫嵌入法并对其进行变形,研究了树状系统可靠性求解方法。本文对树状系统建模加以定义,提出了基于层数参数,层-节点向量,父-子节点矩阵三元参数的树状系统表示方法,研究了变形有限马尔可夫嵌入法的树状系统n中连续取k失效准则下的可靠性求解方法,给出了三个数值算例应用并分析了算法的运算复杂度。最后,本文对比讨论了基于概率母函数法的树状系统在n中连续取k准则下系统可靠性求解方法的研究,得出结论本文算法针对树状冗余系统n中连续取k失效准则下系统可靠性求解应用范围更广,求解效率较高。

关键词: 可靠度, 树状网络系统, 可靠性建模, 有限马尔可夫嵌入法