Towards a general condition based maintenance model for a stochastic dynamic system

This paper considers a stochastic dynamic system subject to random deterioration, with regular condition monitoring and preventive maintenance. A model is presented to advise at a monitoring check what maintenance action to take based upon the condition monitoring and preventive maintenance information obtained to date. A general assumption adopted in the paper is that the performance of the system concerned can not be described directly by the monitored information, but is correlated with it stochastically. The model is relevant to a large class of condition monitoring techniques currently employed in industry including vibration and oil analysis. The model is constructed under fairly general conditions and includes two novel developments. Firstly, the concept of the conditional residual time is used to measure the condition of the monitored system at the time of a monitoring check, and secondly, contrary to previous practice, the monitored observation is now assumed to be a function of the system condition. Relationships between the observed history of condition monitoring, preventive maintenance actions, and the condition of the system are established. Methods for estimating model parameters are discussed. Since the model presented is generally beyond the scope for an analytical solution, a numerical approximation method is also proposed. Finally, a case example is presented to illustrate the modelling concepts in the case of non-maintained plant.