A stochastic approach for the reliability evaluation of multi-state systems with dependent components

A multi-state system (MSS) employs more than two discrete states to indicate different performance rates. Methods using a universal generating function (UGF) and Monte Carlo (MC) simulation are primary approaches for the reliability analysis of an MSS. However, these approaches incur a large computational overhead because the number of system states increases significantly with the number of components in an MSS. In this paper, stochastic multi-valued (SMV) models are proposed for evaluating the reliability of an MSS with dependent multi-state components (MSCs). The performance rates and their corresponding probabilities of the MSCs are simultaneously encoded in multi-valued non-Bernoulli sequences using permutations of fixed numbers of 1 s and 0 s. The sequences are then processed by logic gates. The effectiveness of the proposed approach is demonstrated via a comparative evaluation of a multi-state system consisting of dependent components with steady and time-varying state probabilities.