Reliability analysis for systems subject to mutually dependent degradation and shock processes

This paper studies the reliability problem for systems subject to two types of dependent competing failure processes, that is, soft failure and hard failure processes. A soft failure happens when the total degradation of the system exceeds a given critical level, while a hard failure occurs when the accumulative shock load caused by shocks surpasses the hard failure threshold. These two failure processes are mutually dependent due to the fact that external shocks will bring sudden increments in the degradation of the system, and the total amount of degradation will decrease the hard failure threshold of the system. The system fails whenever either of these two failure modes happens. Assuming that the arrival of shocks follows a Poisson process, the reliability function of the system under cumulative shock model is derived by using some analytical techniques. Some important reliability indices, including the mean lifetime of the system, the expected number of shocks until system failure, the probabilities of soft and hard failures, are calculated explicitly. Moreover, a special case that the hard failure process and soft failure process are mutually independent is also discussed. Monte Carlo method is employed to calculate the multiple integrals existing in the expressions of reliability function and reliability indices. A numerical example of the Reinforced Concrete pier columns on sea bridge is presented to illustrate the proposed model.