Optimal preventive replacement, lot sizing and inspection policy for a deteriorating production system

Considers an economic manufacturing quantity (EMQ) model with an unreliable production facility and a production process subject to random deterioration. Notes that the shift of the process to the “out‐of‐control” state, which may result in producing defective items, is recognized only through inspections; and that the production unit can be replaced preventively or overhauled after finishing a certain number of production runs. Proposes that the objective is to determine the lot size, inspection interval and a preventive replacement time minimizing the expected average cost per unit of time. Obtains the formula for the expected average cost for a generally distributed time to failure. Presents computational results and studies the joint effect of process deterioration and machine breakdowns on the optimal policy.