Reliability assessment of degradation processes with random shocks considering recoverable shock damages

For the products that are exposed to random shocks in the field use, the continuous degradation processes of the products are often affected by random shocks. There are two types of shock effects typically: (1) a sudden change of the degradation signal; (2) an increment of the degradation rate. For some kinds of the products, such as the material with recovery properties and smart systems with self-recovery properties, the sudden change of degradation signals caused by shocks can be fully or partially recovered after the occurrence of the shocks. Thus, the recoverable shock damage should be considered in the degradation modeling and reliability prediction of such products. In this paper, a degradation model considering recoverable shock damage is established based on a Wiener process. Three transition zones are divided according to different shock effects. The arrival of the random shocks is expressed by a homogeneous Poisson process, and the shock magnitudes are non-negative independent random variables following a normal distribution. The shock effect is described as the cumulative shock damage function consisting of both the effect on the degradation signal which is expressed by an exponential function with/without a residual effect for a partial or full recovery, and on the degradation rate which is proportional to the shock magnitude when the shock magnitude exceeds the critical threshold. Parameter estimation and reliability prediction are discussed. Numerical examples are presented as demonstrations of the applications of the proposed model.