A replacement policy of deteriorating production systems subject to imperfect repairs

In this paper, we investigated a deteriorating production system subject to random machine breakdowns, imperfect repairs and replacement. The machine produces one type of product and upon each breakdown, an action is chosen between repairs and replace. If the machine is to be repaired, then an imperfect repair is undertaken. If not, the machine is replaced by a new identical one. The decision variables of the system are the repair/replacement and production policies. The objective of the control problem is to find decision variables that minimize the total incurred costs over an infinite planning horizon. A semi-Markov decision process (SMDP), is used to determine the optimal repair/replacement and production policies. A numerical example is given to illustrate the proposed approach and to show the impact of the policies on several failures number.