Reliability analysis of dependent competing failure processes with time-varying δ shock model

The dependent competing failure process model has received increasing research attention in recent years due to its essential role in describing system reliability. For the o shock model, as a main type of shock in dependent competing failure process, the system fails if the interval of time between two sequential shocks is less than a threshold o. As the operation of systems, the aging effect will gradually increase. Thus, systems affected by shocks need more time to recover from damages. In the time-varying o shock model, if damage shocks occur, the degradation rate and o value will change multiple times simultaneously. Three failure processes consisting of a soft process induced by a degradation process and two sudden failure processes due to random shocks. Sudden failure processes include fatal shocks and damaged shocks. Damaged shocks affect systems in three different ways: (1) impacting systems by causing the degradation increment, (2) increasing the degradation rate of systems, and (3) impairing systems' performance by increasing the o value. A real-world example of a microelectromechanical system is presented to show the applicability of the reliability model. Sensitivity analysis is evaluated to demonstrate how parameters affect reliability.