Enhancing the Performance of CUSUM Schemes for Process Mean Monitoring: A Generalized Fast Initial Response Approach

Control charts have gained increasing attention as a feedback process monitoring technique in recent times. Among them, CUSUM schemes have proven to be effective for monitoring processes with small or moderate sustained mean shifts. However, the detection ability of CUSUM schemes is often slow during the initial process setup due to the constant control limits. To address this limitation, the fast initial response (FIR) or headstart feature has been commonly employed to enhance the scheme's performance at process startup. Additionally, the dynamic nature of real-world challenges calls for a more sensitive CUSUM scheme capable of rapidly identifying small disturbances in a process. In this paper, we propose the utilization of a generalized FIR feature to improve the performance of CUSUM schemes for monitoring process means. By incorporating the generalized FIR feature, we enhance the control limits of the CUSUM scheme, thereby improving its sensitivity to smaller sustained shifts in a process. We assess the efficiency of the proposed system by comparing how well it performs against existing alternatives, using the average run length (ARL), median run length (MDRL), and standard deviation average run length (SDRL) measures. The ARL performance comparison results indicate that the suggested approach shows faster detection of small to moderate sustained alterations in a particular process. Therefore, this method is especially useful for monitoring processes that have observations collected at widely spaced time intervals, such as hourly, daily, or weekly measures, where it is believed that any changes over time will be minor or moderate. To validate the practical viability of our proposed scheme, we showcase its successful implementation in real-world scenarios, utilizing data sets acquired from a beverage bottling company and a petroleum refinery laboratory.