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Predicting the remaining useful life for operational devices plays a critical role in prognostics and health management. As the models based on the stochastic processes are widely used for characterizing the degradation trajectory, an adaptive skew-Wiener model, which is much more flexible than traditional stochastic process models, is proposed to model the degradation drift of industrial devices. To make full use of the prior knowledge and the historical information, an on-line filtering algorithm is proposed for state estimation, a two-stage algorithm is adopted to estimate unknown parameters as well. For remaining useful life prediction, a novel result is presented with an explicit form based on the closed skew normal distribution. Finally, sufficient Monte Carlo simulations and an application for ball bearings in rotating electrical machines are used to validate our approach. [ABSTRACT FROM AUTHOR]