Degradation-Based Maintenance Using Stochastic Filtering for Systems under Imperfect Maintenance

The stationaryWiener process is widely used in modeling degradation processes, mainly due to the existence of an analytical expression of the first hitting time distribution. However, it is only appropriate for modelling linearly drifted stochastic processes. This paper investigates a maintenance policy in which a family of non-stationary Wiener processes is used to simulate degradation phenomena. An approximation to the first hitting time distribution is invoked. A novel technique to treat imperfect maintenance is initiated by extending the improvement-factor method to the degradation rate function. A recursive filter is utilized to dynamically update the estimate of the degradation rate function. An algorithm, using the Laplace approximation, is developed for estimating model parameters. The applications of the proposed methods are demonstrated via both real-world and numerical examples