Reliability analysis of multi-state systems with s-dependent components

The assumption of stochastic independence between components is frequently made in studies of system reliability. However, in a specific system, the failure of a component can trigger the failure of other components, or the current health condition of a component may affect the performance of other components. Thus, the state of a component can affect the state and degradation of other components in a multi-component system, that is, stochastic dependence (s-dependence) may exist in real and complex systems. In this paper, reliability analysis of multi-state systems (MSS) with s-dependent components will be considered. The MSS consists of 2 multi-state components in series, with each component possibly operating at different performance levels, varying from perfect functioning to complete failure. When the first component degrades to a lower performance level, it affects the state as well as the degradation of the other component in the system. A combined technique of stochastic process and modified universal generating function is used to evaluate the system reliability. The combined approach is then verified using the Monte Carlo Simulation method. An illustrative example on reliability analysis of MSS with dependent components is also provided.