Abstract: A periodic maintenance policy for a degenerate production system in which the products are sold with free minimal repair warranty is considered. The degenerate process of the system is characterized by three states: in-control state, out-of control state and failure state. The amount of time that the process stays in in-control state and out-of-control state are both assumed to be exponentially distributed. The production system is overhauled at fixed time t or at failure, whichever occurs first. The optimal periodic overhaul time minimizing the expected cost per item per cycle is analytically discussed, and three special cases show the property of the optimal value . In addition, sensitivity analysis and numerical examples concerning model parameters are carried out to illuminate the effects of the model parameters on the optimal periodic overhaul policy.