The routing algorithms for parallel computers, on-chip networks, multi-core processors, and multiprocessors system-on-chip (MP-SoCs) exhibit router failures must be able to handle interconnect router failures that render a symmetrical mesh non-symmetrically. When developing a routing methodology, the time complexity of calculation should be minimal, and thus complicated routing strategies to introduce profitable paths may not be appropriate. Several reports have been released in the literature on using the concept of fault rings to provide detour paths to messages blocked by faults and to route messages around the fault regions. In order to analyze the performance of such algorithms, it is required to investigate the characteristics of fault rings. In this paper, we introduce a novel performance index of network reliability presenting the probability of message facing fault rings, and evaluating the performance-related reliability of adaptive routing schemes in n-D mesh-based interconnection networks with a variety of common cause fault patterns. Sufficient simulation results of Monte-Carlo method are conducted to demonstrate the correctness of the proposed analytical model.