Modeling the varying effects of shocks for a multi-stage degradation process

In real-world applications, engineering systems at different degradation stages have distinguishing abilities to resist random shocks, which can be embodied by the varying consequences of shocks. In this paper, we model the consequences of random shocks on the degradation process by dividing the system's entire life into four stages, namely the normal stage, slow degradation stage, fast degradation stage and failed stage, which is motivated by practical observations that the plant state is often classified by a three color scheme before failure. At each stage, the consequences caused by random shocks can be classified into different categories. To distinguish the shocks, we use adjustment coefficients to express the cumulative damage of shocks toward the degradation rate. In addition, we developed a hybrid degradation and shock model to represent both the cumulative damage and degradation rate acceleration received from random shocks. The closed-form reliability function is obtained, and an illustrative example of microelectromechanical system (MEMS) is presented to describe the engineering motivation and application. The sensitivity analysis of the reliability on the thresholds and adjustable coefficients in the model is conducted. The results show that the proposed model can characterize the influence of shocks in different degradation stages and reasonably estimate the reliability.