Integrated model of preventive maintenance, quality control and buffer sizing for unreliable and imperfect production systems

In this paper, we develop a joint quality control and preventive maintenance policy for a randomly failing production system producing conforming and non-conforming units. The considered system consists of one machine designed to fulfil a constant demand. According to the proportion l of non-conforming units observed on each lot and compared to a threshold value lm, one decides to undertake or not maintenance actions on the system. In order to palliate perturbations caused by the stopping of the machine to undergo preventive maintenance or an overhaul, a buffer stock h is built up to ensure the continuous supply of the subsequent production line. A mathematical model is developed and combined with simulation in order to determine simultaneously the optimal rate, l^*m and the optimal size h^* which minimize the expected total cost per time unit including the average costs related to maintenance, quality and inventory.