Abstract
The goal of this thesis is to obtain the so-called “system reliability”, defined as the probability that the production output meets a predetermined demand for a stochastic system with many workstations, each of which has random capacity following a discrete probability distribution. Moreover, with positive probability, a workstation successfully passes an input unit to the next node in the network. The “system reliability” is an important performance measure in stochastic systems. The application of stochastic systems are manufacturing system, network system and logistics system. According to the latest literature [19], we have found that eighteen papers have actually incorrectly calculated the system reliability. Paper [19] presents a correct version of analytical approach, named Song Rule, limited to one production line with one rework system. Motivated by the problem that the Song rule is computational inefficient, this thesis proposes an extended Song rule to improve the efficiency of computation. Moreover, this thesis extends the Song rule to present a general analytical theory for networks with multiple reworks. The proposed method is more computational efficient than the Song rule. Specifically, the proposed extended Song rule accomplishes an computation-time-reduction of above 90% for networks with more than 2 workstations. Moreover, all analytical results presented in this paper are validated via simulation approaches including C and Flexsim.