This paper addresses the system reliability evaluation for a manufacturing system with multiple production lines in parallel, where the system reliability is the possibility that a manufacturing system can satisfy demand. In the manufacturing system, the capacity of each machine is stochastic (i.e., multi-state) due to failure, partial failure, or maintenance. Thus, the manufacturing system can be constructed as a manufacturing network in terms of stochastic-flow network model. With considering reworking actions, we propose a graphical-based methodology to transform the manufacturing system into a manufacturing network. Thereafter, the manufacturing network is decomposed into general manufacturing paths and reworking paths. A simple algorithm is subsequently developed to generate the minimal capacity vectors that machines should provide to satisfy demand. The system reliability is derived in terms of such capacity vectors afterwards.