ON THE FAILURE RATE FUNCTION OF A SYSTEM UNDER THE δ-SHOCK MODEL

An interesting type of shock model in reliability theory is the delta-shock model, which is defined based on the length of time between successive shocks. Whenever this length is less than or equal to a prefixed threshold called delta, the system will fail. In this paper, the failure rate function of a system subjected to random shocks under the delta-shock model is discussed. To be more precise, a simple approximate formula for the failure rate function is established. Numerical studies are performed under the assumption that the arrival of shocks follows a Poisson process. Based on the numerical results, the accuracy of the approximation is evaluated, and it is also shown that reducing the mean of inter-arrival times between successive shocks leads to an increase in the failure rate of the system. Conclusions are presented at the end.