Joint production, maintenance and quality control chart optimization for a degrading manufacturing–reworking system with assignable causes

This paper presents a new joint production, maintenance and quality control chart for a manufacturing system subject to random failure and produces both conforming and non-conforming products. The degradation of the manufacturing unit increases with the production rate and the time of its use, which affects its reliability and the product quality. The purposed joint policy aims to establish, firstly, the optimal plan of production during finite horizon that satisfies random demand under a given service level. and secondly, to determine simultaneously the optimal number of imperfect preventive maintenance actions at each production cycle, and the optimal control chart parameters for appropriate quality monitoring in the presence of assignable causes. Furthermore, rework activity is proposed for a fraction of the non-conforming products, which are detected in the presence of assignable causes, in order to improve their quality and sold as a second-rate product. The proposed optimization model minimises the average total costs including production, reworking, storage, rejection, quality and maintenance. Numerical examples and sensitivity analyses are presented to show the effectiveness of the proposed joint approach.