Two-Phase Degradation Process Model With Abrupt Jump at Change Point Governed by Wiener Process

Observations on degradation performance are often used to analyze the underlying degradation process of highly reliable products. From the two-phase degradation path of the bearing performance observations, we observed that there exists an abrupt increase in degradation measurement at a change point. Then, the following degradation process started with the abrupt degradation measurement will degrade in a higher degradation rate. Here, a stochastic process-based degradation model is constructed to interpret the jump at the change point in the degradation process which is governed by the linear Wiener process. Meanwhile, the distribution of the first passage time over a prespecified threshold for the process is discussed. In addition, to get the estimates of the model parameter, the expectation-maximization algorithm is utilized since the change points are unobservable. Furthermore, to demonstrate the model's advantages over estimate, a comparison is made between the proposed and the existing known models from the literature. The results reveal that considering the jump in the degradation process can improve the accuracy of estimations in real applications.