Optimal maintenance and EMQ policy for a deteriorating production system

We consider a production facility subject to deterioration and condition monitoring (CM) which is performed at the end of each production run. The production facility deterioration is described by a continuous-time Markov process using proportional hazards model (PHM). The hazard rate is updated at each sampling epoch when new observation becomes available. When the hazard rate crosses a control limit, the preventive maintenance (PM) is performed. Production will resume when all available inventory is depleted. The stochastic demand process is described by a homogeneous Poisson process. The shortage and set-up costs are considered in the model along with the maintenance, inventory holding, and lost production costs. The objective is to minimize the long-run expected average cost per unit time. The problem is formulated and solved in the semi-Markov decision process (SMDP) framework. The optimal policy is found and a numerical example is presented to illustrate the whole procedure.