Degradation Data Analysis based on Wiener Process with a Nonlinear Drift and a Stochastic Volatility

Considering the dynamic diffusion in degradation process, we propose an integrated Wiener process with a nonlinear drift and a stochastic volatility for degradation modelling. In our model, the drift and stochastic volatility are estimated nonparametrically to avoid the model misspecification issue. The key innovation of this study is the estimation of stochastic volatility which adopts the functional principal component analysis method and applies it to bipower variance. This estimation approach is able to effectively capture both cross-unit variations and time-varying features within the diffusion process. Also, the proposed model can reduce the estimation bias caused by jump points, which are common phenomenon in degradation process. Furthermore, the distribution of remaining useful life and the mean time to failure are both obtained in explicit forms. Finally, the proposed model and the nonparametric estimation method are illustrated by two simulation experiments and two real cases.