A multi-phase Wiener process-based degradation model with imperfect maintenance activities

In order to improve the performance and prolong the life of the equipment, it is usually necessary to maintain the equipment in practice. Remaining useful life prediction with imperfect maintenance activities is of great importance to prognostics and health management. In this paper, a multi-phase Wiener process-based degradation model is constructed to characterize the degradation process subjected to imperfect maintenance activities. The beta distribution is introduced to describe the residual degradation coefficient caused by the imperfect maintenance activity. The hyper-parameters of residual degradation coefficient are estimated through the maximum likelihood estimation and Newton iteration method. To reflect the unit heterogeneity, the drift coefficient and diffusion coefficient of each phase are synchronously defined as random variables. Furthermore, the analytical forms of remaining useful life are obtained by the convolution operator. The approximate expression of probability density function is derived by the Monte Carlo simulation approach. In the end, a numerical study and a practical study of gyroscopes are provided to demonstrate the practicality and effectiveness of the proposed method.