Approximate reliability of multi-state two-terminal networks by stochastic analysis

Reliability is an important feature in the design and maintenance of a large-scale system. Usually, for a two-terminal network reliability is a measure for the connectivity between the source and sink nodes. Various approaches have been presented to evaluate system reliability; however, they become cumbersome or prohibitive due to the large computational complexity, especially when multiple states are considered for nodes. In this study, a stochastic approach is presented for estimating corresponding reliability. Randomly permuted sequences with fixed numbers of multiple values are generalized from non-Bernoulli binary sequences to model the multi-state property. State probabilities are represented by randomly permuted sequences to improve both computational efficiency and accuracy. Stochastic models are then constructed for arcs and nodes with different capacities. The proposed stochastic analysis is capable of predicting reliability at high accuracy and without a need for constructing the commonly-used but complex multi-state minimal cut vectors. Non-exponential distributions and correlated signals are readily handled by the stochastic approach for a general network. Results obtained through the stochastic analysis are compared with exact values and those found by Monte Carlo simulation. The accuracy, efficiency and scalability of the stochastic approach are assessed by evaluating several case studies.