Reliability estimation and optimisation of multistate flow networks using a conditional Monte Carlo method - Zhou, Yifan; Liu, Libo; Li, Hao (Reliability engineering & system safety, 2022)
•A conditional MC method is proposed to evaluate the reliability of MSFNs.•A recursive conditional sampling method is developed using matrix operations.•d-MPs and d-MCs are selected recursively for narrow gaps between reliability bounds.•GA embedding the conditional MC method is developed for reliability optimisation. The Monte Carlo (MC) method is a practical approach to estimating the reliability of large multistate flow networks (MSFNs) in reality, e.g. transportation systems and computer networks. However, deriving an accurate reliability estimate using the crude MC method is computational expensive. This research proposes a conditional MC method to estimate the reliability of a MSFN using the minimal path vectors to level d (d-MPs) and minimal cut vectors to level d (d-MCs). A recursive method is developed to select d-MPs and d-MCs that incur a narrow gap between upper and lower reliability bounds. Then, state vectors are conditionally sampled in a recursive manner using matrix operations. The conditional MC method is embedded in the genetic algorithm (GA) to optimise system reliability. A ranking and selection procedure is used in GA to allocate simulation efforts to different solutions. Numerical studies validate that the proposed conditional MC method can obtain a more accurate reliability estimate than the crude MC method within the same computation time. The improved GA that includes the conditional MC method also outperforms the original GA in reliability optimisation.