Simulation of the FPT for Multi-Dimensional Wiener Process with Dynamic Thresholds

Abstract

Reliability modeling and analysis has becoming an essential issue in complex system management. Degradation system reliability modeling is an important part of the reliability field due to that the failure data is more and more difficult to obtain. Degradation data can well describe the failure process of a system or product. In the stochastic process, the Wiener process has been widely used in literature due to its good properties. Multidimensional diffusion Wiener process describes the multidimensional degradation process of products. First passage time is the lifetime of a system to reach a threshold value. In this paper, a generalized model is developed for evaluating the reliability of the multidimensional degradation process. Meanwhile, we use the Monte Carlo method for the solution of the FPT with dynamic threshold value. The comparisons show that the results of the proposed model agree well with the Monte Carlo results. The research can support decision making in the reliability improving.