With the development of scalability and application of multiprocessor system, the components of the system possibly become faulty. It is desirable to know the reliability of the system. However, the exact reliability of a complicated network system is usually difficult to determine. A typical approach is to decompose the system into smaller ones based on a graph-theory model in which nodes are assumed to fail independently with known probabilities to measure the subsystem-based reliability, which is defined as the probability that a fault-free subsystem of a specific size is still available when the system has faults. In this paper, we use the probability fault model to establish upper and lower bounds on the subsystem-based reliability of k-ary n-cube networks, by taking into account the intersection of no more than five or four subgraphs. In addition, some numerical simulations of the subsystem-based reliability of k-ary n-cube networks are conducted.

随着可伸缩性的发展和多处理器系统的应用，系统的组件可能会出现故障。希望知道系统的可靠性。但是，通常很难确定复杂网络系统的确切可靠性。一种典型的方法是基于图论模型将系统分解为较小的系统，在该模型中，假定节点以已知的概率独立发生故障，以测量基于子系统的可靠性，该概率被定义为以下情况的概率：当系统出现故障时，特定大小仍然可用。在本文中，我们使用的概率故障模型来建立上和下限上的基于子系统可靠性ķ进制Ñ-cube网络，考虑到不超过五个或四个子图的交集。此外，的基于子系统可靠性一些数值模拟ķ进制Ñ -cube网络进行。