Reliability Evaluation For Acyclic Consecutively Connected Networks

This paper studies the reliability of acyclic consecutively connected network, the acyclic consecutively connected network reliability problems can be divided into two categories: acyclic consecutively multistate-node network(ACMNN) and acyclic consecutively multistate-arc Network(ACMAN).The third chapter of this paper,mainly introduces the results of Levitin and Yeh’s studies of ACMNN reliability and the limitations of this studies. In Levitin’s study, he assumes that all the nodes in the ACMNN is perfectly reliable and the arcs have two states:working and failed, establishes a method based on the UGF and recursive method to evaluate the reliability of the network. But the application of the method is very few because in practice the node is unreliable which does not satisfied the assumption. In Yeh’s study, a special node called k-/n node, which can only receive not more than k amount of signals, is newly introduced. Combining with the k/n node,the concept of ACMNN contains k/n node is newly introduced. Yeh improved the UGF to solve reliability evaluation of the ACMNN which contains unreliable nodes-k/n node. However, the improved UGF can only indicate each node receives a signal whether or not,but can not presents the number of signal,thus we need to develop different recursive methods for common nodes, k-jn nodes and k+/n nodes, so that the recursive process is very complex.Because of the limitations which are presented in the IV Chapter of this paper, a special node called [k1,k2] out-of-n node,which can only receive not less than k1 and not more than k2 amount of signals, is newly introduced.In fact, all nodes can be represented as [k1,k2]/n nodes. Then the improved UGF for the [k1,k2]/n node is established, the improved UGF can not only indicates whether the node receives signal but also can indicates the number of signals. A new recursive method based on the improved UGF is suggested by using the characteristics of [k1, k2]/n node and ACMNN.In the V Chapter of this paper, we use the UGF and a recursive method to evaluate the reliability of ACMAN which contains multi-state arcs and two-state nodes.In ACMAN, all signals in the network obey the flow conservation law. Therefore, we need to improve the UGF, the improved UGF can not only indicate the number of signals, but also indicate the states of signals and corresponding strength. Then we summarize the characteristics of ACMAN and establish a method based on the UGF and the simplified recursive method to evaluate the reliability of the ACMAN.