Reliability analysis for [formula omitted]-out-of-[formula omitted](G) systems subject to dependent competing failure processes

Abstract

In this paper, reliability analysis for k-out-of-n(G) systems suffering from interdependent competing failure processes is conducted. The system consisting n different components fails if and only if the number of operating components is less than k. Each component degrades linearly with time. A soft failure happens if the total degradation performance exceeds the soft failure threshold of the corresponding component. All components in the system are influenced by random shocks which arrive according to a homogeneous Poisson process. The hard failure of a component occurs when a single shock with large shock load arrives (extreme shock model), or the accumulated shock load of a sequential shocks surpasses the hard failure threshold of the component (cumulative shock model). A component fails if a hard failure or a soft failure occurs. Since the external shock may cause an abrupt degradation increment to a component, the hard failure and soft failure processes of each component are relevant. Moreover, because a shock has impact on all working components in the system, the failure processes of these components are also relevant. Using multivariate analysis methods and techniques, the closed forms of the reliability functions of the k-out-of-n(G) system under the extreme shock model and the cumulative shock model are obtained. Monte Carlo simulation is used as an auxiliary method to compute the system reliability. As a numerical example, the reliability of the micro-electro-mechanical systems is calculated to illustrate the developed theory.