The notion of imperfect maintenance has spawned a large body of literature, and many imperfect maintenance models have been developed. However, there is very little work on developing suitable imperfect maintenance models for systems outfitted with sensors. Motivated by the practical need of such imperfect maintenance models, the broad objective of this paper is to propose an imperfect maintenance model that is applicable to systems whose sensor information can be modeled by stochastic processes. The proposed imperfect maintenance model is founded on the intuition that maintenance actions will change the rate of deterioration of a system, and that each maintenance action should have a different degree of impact on the rate of deterioration. The corresponding parameter-estimation problem can be divided into two parts: the estimation of fixed model parameters and the estimation of the impact of each maintenance action on the rate of deterioration. The quasi-Monte Carlo method is utilized for estimating fixed model parameters, and the filtering technique is utilized for dynamically estimating the impact from each maintenance action. The competence and robustness of the developed methods are evidenced via simulated data, and the utility of the proposed imperfect maintenance model is revealed via a real data set. 
Degradation-based maintenance decision using stochastic filtering for systems under imperfect maintenance