Integrated optimization for X-bar control chart, preventive maintenance and production rate

There are close relationships among statistical process control, maintenance, and production that have not fully explored in existing studies. In this study, we propose an economic model for jointly optimizing the X-bar control chart, preventive maintenance, and production rate. Unlike conventional studies relying on known failure rate functions, we employ a Gamma process to describe the system's deterioration. This approach allows us to consider not only the relationship between the production rate and the deterioration rate but also a broad range of deterioration scenarios and failure modes in the integrated optimization. After calculating the failure probability at each time point, we propose a recursive method to derive the production revenue, process control costs, and quality losses. This approach explores the close inner relationship between the production rate, deterioration, process monitoring and maintenance. Subsequently, we establish an optimization model aimed at maximizing the profit rate within a renewal cycle. The decision variables of this model include the production rate, control chart coefficient, sample size, length of the first sampling interval, and number of sampling intervals. Finally, we use a case study to illustrate the effectiveness and validity of our proposed model by identifying and explaining the interactions between production rate, deterioration, process control and maintenance.