Residual useful life estimation for products with two performance characteristics based on a bivariate Wiener process

Residual useful life estimation plays an important role in the field of prognostics and health management, and condition-based maintenance. This article concerns the issue of residual useful life estimation for degraded components with two performance characteristics. A bivariate Wiener process with random effects is used to model the evolution of two performance characteristics, which are dependent on each other. A bootstrap method is used to estimate the initial parameters with history of degradation data. Once the new degradation information for an individual component is available, the hyper-parameters of the random effects in the model are first updated by the Bayesian theorem. And then, we use a Monte Carlo simulation method to estimate the posterior distribution of residual useful life approximately. Via a simulation study and a case study on Lithium-ion batteries, the effectiveness and validity of the proposed approach are demonstrated.