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Multi-state weighted k-out-of-n systems are widely applied in various scenarios, such as multiple line (power/oil transmission line) transmission systems where the capability of fault tolerance is desirable. However, the complex operating environment and the dynamic features of load demands influence the evaluation of system reliability. In this paper, a stochastic multiple-valued (SMV) approach is proposed to efficiently predict the reliability of two models of systems with non-repairable components and dynamically repairable components. The weights/performances and reliabilities of multi-state components (MSCs) are represented by stochastic sequences consisting of a fixed number of multi-state values with the positions being randomly permutated. Using stochastic sequences with L multiple values, linear computational complexities with parameters n and L are required by the SMV approach to compute the reliability of different multi-state k-out-of-n systems at a reasonable accuracy, compared to the complexities of universal generating functions (UGF) and fuzzy universal generating functions (FUGF) that increase exponentially with the value of n. The analysis of two benchmarks shows that the proposed SMV approach is more efficient than the analysis using UGF or FUGF

Approximate Analysis of Multi-State Weighted k-Out-of-n Systems Applied to Transmission Lines