The aim of this paper is to propose a maintenance model for a deteriorating system. The system considered begins to deteriorate with a slow deterioration rate and at an unknown time the system's deterioration rate changes and the new deterioration rate is a time dependent function. To deal with the change of mode of deterioration in the framework of the maintenance decision rule an adequate on-line change detection algorithm is used. The maintenance decision rule is chosen in order to minimise the global maintenance cost.