Based on the concept of network analysis, a manufacturing system can be constructed as a stochastic-flow network since the capacity of each machine is stochastic (i.e., multistate) due to the failure, partial failure, and maintenance. Considering reworking action and different yield rates of machines, we measure the probability that the stochastic manufacturing network (SMN) can satisfy demand. Such probability is defined as the system reliability. A decomposition method is firstly proposed to divide the SMN into one general processing path and one reworking path. Subsequently, an algorithm is utilized for generate the lower boundary vector of machine capacity to guarantee that the SMN is able to produce sufficient products fulfilling the demand. The system reliability of the SMN can be derived in terms of such capacity vector afterwards.