Joint optimization of X¯ control chart and preventive maintenance policies: A discrete-time Markov chain approach

Statistical process control and maintenance planning have long been treated as two separate problems. The interdependence between these two activities has not been adequately addressed in the literature, despite their apparent connections. Information obtained in the course of statistical process control signals the need for possible maintenance actions, and thus, affects the preventive maintenance schedules. Preventive maintenance actions can prevent a production process from further deterioration and improve product quality in conjunction with statistical process control. This paper presents an integrated model for the joint optimization of statistical process control and preventive maintenance. The proposed model is developed for a production process that deteriorates according to a discrete-time Markov chain. It is assumed that preventive maintenance is imperfect, and both preventive and corrective maintenance are instantaneous. The formulation of the deterioration process with maintenance interventions, formulated as a Markov chain, provides a breakthrough in designing an efficient solution algorithm and obtaining analytical results. A numerical example is used to illustrate the proposed integrated statistical process control and preventive maintenance policies. Sensitivity analysis is conducted to analyze the impact of model parameters on optimal policies. Sensitivity analysis further indicates the interrelationship between statistical process control and maintenance actions. Numerical results indicate that potential cost savings can be achieved from the proposed integrated policies.