Quality issue in forecasting problem of production and maintenance policy for production unit

In this study, we consider an unreliable deteriorating production system that produces conforming and non-conforming products to satisfy a random demand under a given service level and during a finite horizon. The production system is subjected to a failure-prone machine. The quality of the produced products is affected by the machine deterioration since the rate of defectives increases as the deterioration increases. Preventive maintenance actions can be piloted on the production system to reduce the influence of deterioration and the defective rate. A joint control policy is based on a stochastic production and maintenance planning problem with goals to determine, firstly, the economic plan of production and secondly, the optimal maintenance strategy. The proposed jointly optimisation minimises the total cost of production, inventory, maintenance and defectives. A failure rate and quality relationship are defined to show the influence of the production rates variation on the failures rate as well as on the defective rate. A numerical example and an industrial case study are adopted to illustrate the proposed approach and a sensitivity analysis to validate the jointly optimisation.