Monitoreo del proceso de pesaje multicabezal con carta de control CUSUM con aprendizaje cauteloso

Control charts, particularly the cumulative sum (CUSUM), are essential tools for monitoring production processes and detecting changes in product quality. The CUSUM chart is highly effective in detecting small shifts in the process mean due to its optimality property. In this article, a CUSUM chart adapted for the Gamma distribution, commonly used for modeling waiting times and product lifetimes, is utilized for monitoring the multihead weighing process. However, implementing this chart presents challenges due to the need to estimate the parameters of the Gamma distribution, which is crucial for the chart’s performance. The uncertainty in this estimation affects the performance of the charts, as investigated in recent studies. To address this uncertainty, a cautious learning methodology is proposed, which updates parameter estimates as more data are collected, minimizing the risk of contamination by out-of-control observations [1–3]. This approach maintains the sensitivity of the CUSUM chart to detect shifts in the process mean while minimizing false alarms. The objective of this work is to extend the proposed methodology by examining the impacts of delays in updating estimates while monitoring processes that follow a Gamma distribution. We utilize an optimized design of the CUSUM chart, inspired by previous studies on monitoring Gamma processes, to ensure robust in-control performance [4].