We consider a production system that has to satisfy a random demand during a finite planning horizon under a required service level. This study consists in developing an analytical model in order to determine a near-optimal integrated maintenance-production plan which takes into consideration the influence of the production rate on the system's failure rate while attempting in the same time to smooth the production plan through the production rate control between periods of the planning horizon. A numerical example is presented in order to illustrate the contribution of the proposed modelling approach and discuss the different trade-offs that are considered.