Joint production, control-chart design and maintenance optimization for a multivariate production system considering timely replenishment

This paper proposes an integrated design scheme that jointly optimizes production scheduling (PS), multivariate quality control (QC), and equipment maintenance (EM). A non-uniform dynamic sampling strategy is employed, where samples are collected at variable time intervals to monitor the process in real time. Hotelling’s T^2 A control chart is utilized to detect shifts in multiple correlated quality characteristics simultaneously. Unlike most existing studies, which assume that buffer stocking takes place at the beginning of a production run and can result in excessive inventory holding costs, this work adopts a more realistic strategy. Replenishment is initiated only after the sampling instant that immediately precedes the preventive maintenance (PM), thereby aligning inventory decisions with the evolving process condition. Furthermore, this study models maintenance times as random variables following a Weibull distribution, moving beyond the common deterministic assumption in the literature and capturing the inherent variability in repair activities. Based on an economic-statistical design approach, the optimal integrated policy is derived by minimizing the expected total cost per unit time, using a developed genetic algorithm for solution search. In the numerical analysis section, a practical production example demonstrates the application of the integrated strategy. Finally, through benchmarking against alternative approaches and sensitivity testing across key parameters, the effectiveness and superiority of the proposed integrated scheme are demonstrated.