Novel Control Charts for Joint Monitoring of the Mean and Variability of Multichannel Profiles

Abstract In recent years, there has been increasing interest in simultaneously monitoring process mean and variability within the realm of statistical process monitoring (SPM). Monitoring and diagnosing faults using profile data remains challenging, especially with multichannel profiles. By jointly monitoring the mean vector and covariance matrix in multivariate processes, practitioners can reduce the inflated false alarm rates that typically arise from using two separate control charts. This paper extends two control charts, namely, the max exponentially weighted moving average (EWMA) control chart and the sum of squares EWMA (SS‐EWMA) control chart, to introduce novel single generally weighted moving average control charts for the combined monitoring of process mean and variability in multichannel profiles in Phase II. This approach integrates the EWMA scheme with multichannel functional principal components analysis to develop charting statistics for monitoring both the mean vector and covariance matrix of multichannel profiles. The performance of the proposed control charts is demonstrated through simulation studies in terms of average run length (ARL) and the standard deviation of run length criteria, as well as an illustrative example. The findings demonstrate the proposed control charts' detection efficiency across various out‐of‐control (OC) scenarios.