System reliability of stochastic networks with multiple reworks

An important performance measure for stochastic networks is so-called “network-system reliability”, defined as the probability that the production output meets a pre-determined demand for stochastic networks consisting of many workstations. Specifically, the random factors of stochastic networks include the capacity of each workstation and numbers of the conforming parts produced in each workstation. Previous work has studied analytical methods to determine network-system reliability, however a great deal of archive publications incorrectly analyzed network-system reliability. The error is caused by assuming continuous network flow, despite the model's flow being discrete and indivisible.The most recent work, named the Song rule in system reliability [16], provided a rigorous analytical approach of network-system reliability, but it is computationally inefficient and is restricted to one rework. The proposed analytical rule in this paper improves the Song rule in terms of the computation time and applications including multiple reworks. Specifically, the proposed rule accomplishes an computation-time-reduction of above 90% for networks with more than two workstations. All analytical results presented in this paper are verified via discrete-event simulation approaches.