Maintenance of multi-state production systems deteriorated by random shocks and production

We consider the preventive maintenance of a production system that is deteriorated by random shocks and the production process itself. The degree of deterioration is modeled by discrete and finite states. Shocks arrive according to a Poisson process and deteriorate the system by random amounts. The system may deteriorate whenever it produces an item. The system is continuously monitored and repaired if the system state is at or above a predetermined level for maintenance. We analyze the lifetime, product quantity, average cost, and average profit considering revenue from the product and cost due to setup, operation, and repair. Assuming a structure of system parameters and costs, using numerical examples, we investigate the impact of production and shock arrivals on the average profit and the optimal maintenance level that maximizes the average profit. The proposed model is applicable to manufacturing tasks in which machines wear due to production, for example, press processes, milling, turning, punching, and drilling.