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

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