A new cumulative shock model with damage and inter-arrival time dependency

In this paper, a system is considered that fails when the cumulative damage due to shocks exceeds the handling capacity of the system. It is also supposed that if the time between two consecutive shocks is not large enough, the system lacks the time necessary for recovering to receive subsequent shocks; hence, larger damages might be inflicted upon the system. In other words, shocks occurring at short intervals are more fatal and cause larger damages to the system. Based on these assumptions, a new model is developed for evaluating system reliability that takes into account the likely dependencies between inter-arrival times and random shock magnitudes. The proposed model is then validated through a method based on phase-type distributions that enables the model to be efficiently and easily evaluated. Approximation of its reliability function and estimation of model parameters are also investigated. Finally, an illustrative example is provided to demonstrate the efficiency of the proposed model.