Residual life estimation based on bivariate Wiener degradation process with time-scale transformations

The issue of residual life (RL) estimation plays an important role for products while they are in use, especially for expensive and reliability-critical products. For many products, they may have two or more performance characteristics (PCs). Here, an adaptive method of RL estimation based on bivariate Wiener degradation process with time-scale transformations is presented. It is assumed that a product has two PCs, and that each PC is governed by a Wiener process with a time-scale transformation. The dependency of PCs is characterized by the Frank copula function. Parameters are estimated by using the Bayesian Markov chain Monte Carlo method. Once new degradation information is available, the RL is re-estimated in an adaptive manner. A numerical example about fatigue cracks is given to demonstrate the usefulness and validity of the proposed method.