Reliability analysis for systems with interactive competing degradation processes and mixed shock effects

In this article, an extended mixed shock model is investigated, in which the system suffers from mutually dependent competing soft failure and hard failure processes. The system studied degrades gradually with time and the number of shocks coming from the environment. A soft failure occurs when the overall degradation amount surpasses the soft failure threshold of the system. The extended mixed shock model is a combination of a system-state-dependent extreme shock model and a system-state-dependent 8 shock model. A hard failure occurs when the magnitude of a single shock exceeds the threshold D(t), or an inter-arrival time between shocks is less than the recovery time threshold Delta(t). The mutual dependency between the soft failure and hard failure processes is reflected in the fact that: (1) the external shock will accelerate the degradation process of the system by causing an abrupt increment of its degradation amount; (2) the system degradation amount determines the thresholds of the extreme shock model and the (5 shock model. The system fails when a hard failure or a soft failure occurs. By using the stochastic process theory, the reliability expression and some reliability indices of the system are obtained. Some special cases of the model are also discussed. Finally, a case study of the pier columns of a sea bridge is presented to illustrate the developed model.