A model for residual life prediction based on Brownian motion with an adaptive drift

A degradation model is presented in this paper for the prediction of the residual life using an adapted Brownian motion-based approach with a drifting parameter. This model differs from other Brownian motion-based approaches in that the drifting parameter of the degradation process is adapted to the history of monitored information. This adaptation is performed by Kalman filtering. We also use a threshold distribution instead of the usual single threshold line which is sometime difficult to obtain in practice. We demonstrate the model using some examples and show that the model performs reasonably well and has a better prediction ability than the standard Brownian motion-based model. The model is then fitted to the data generated from a simulator using the expectation-maximization algorithm. We also fit a standard Brownian motion-based model to the same data to compare the difference and performance. The result shows that the adapted model performs better in terms of certain test statistics and the total mean square errors.