An Adaptive Regression‐Adjusted CUSUM Chart for Monitoring Covariate‐Driven Processes

Explanatory variables affect the characteristics of processes in most monitoring applications, and the failure to consider them may give misleading signals and performance in detection. Control charts based on regression help to overcome this problem by observing regression‐adjusted residuals, but most of the current schemes depend on a set of given parameters and assume that shift magnitudes are known. The paper suggests a Regression‐based Adaptive CUSUM (RA‐ACUSUM) control chart whose reference parameter is dynamically changed in accordance with the observed residual deviations. Results of the simulation, which has been calibrated to a typical in‐control average run length, indicate that the proposed chart performs better in small to moderate shifts with stable in‐control behavior compared to the benchmark regression‐based CUSUM charts and EWMA charts. The practical usefulness of the proposed method is demonstrated by an application to the agricultural production monitoring.