A real-life manufacturing system can be constructed as a stochastic-flow network. Considering multiple reworking actions and different machine yield rates in a manufacturing network, the input flow (raw materials/WIP) processed by each machine might be defective and therefore the output flow (WIP/products) would be less than the input amount. To evaluate the capability of the manufacturing system, we measure the probability that the manufacturing network can satisfy demand. Such probability is defined as the system reliability. A decomposition method is firstly proposed to divide the manufacturing network into one general processing path and several reworking paths. Algorithms are utilized for the network model to generate the lower boundary vector of machine capacity to guarantee that the manufacturing network is able to produce sufficient products fulfilling the demand. The system reliability of manufacturing network is derived in terms of such capacity vector afterwards.