With the development of high-performance computing and the expansion of large-scale multiprocessor systems, it is significant to study the reliability of systems. Probabilistic fault diagnosis is of practical value to the reliability analysis of multiprocessor systems. In this paper, we design a linear time diagnosis algorithm with the multiprocessor system whose threshold is set to 3, where the probability that any node is correctly diagnosed in the discrete state can be calculated. Furthermore, we give the probabilities that all nodes of a d-regular and d-connected graph can be correctly diagnosed in the continuous state under the Weibull fault distribution and the Chi-square fault distribution. We prove that they approach to 1, which implies that our diagnosis algorithm can correctly diagnose almost all nodes of the graph.

随着高性能计算的发展和大规模多处理器系统的扩展，研究系统的可靠性具有重要意义。概率故障诊断对于多处理器系统的可靠性分析具有实用价值。本文针对多处理器系统设计了一种线性时间诊断算法，阈值设置为3，可以计算任意节点在离散状态下被正确诊断的概率。此外，我们还给出了在威布尔断层分布和卡方断层分布下，d正则图和d连通图的所有节点在连续状态下都能被正确诊断的概率。我们证明它们接近 1，这意味着我们的诊断算法可以正确诊断图中的几乎所有节点。