Real-time Reliability Evaluation with a General Wiener Process-based Degradation Model

The aim of this paper is to investigate the issue of real‐time reliability evaluation based on a general Wiener process‐based degradation model. With its mathematical tractability, the Wiener process with a linear drift has been widely used in the literature, to characterize the dynamics of the degradation process or its transformation. However, the nonlinear degradation process, which can't be properly linearized, exists in practice. The dynamics of such a degradation process can't be accurately captured by linear models. Here, a general Wiener process‐based degradation model is proposed, which covers a variety of Wiener process‐based models as its limiting cases. A two‐stage method is presented to estimate the unknown parameters. Two real‐time reliability evaluation procedures are presented for different conditions: one is the analytical evaluation procedure, and the other is the simulated evaluation procedure. It is shown that when new degradation information is available, the evaluation results can be adaptively updated. Moreover, to check out the proposed degradation model, a graphical method is provided. Finally, the validity of the proposed evaluation method is illustrated by a numerical example and two real‐world examples.