Phase II monitoring of process variability in multichannel profiles

Abstract

Monitoring process variability utilizing profile data remains a significant challenge in statistical process monitoring (SPM), especially in the context of multichannel profiles. Detecting shifts in the covariance matrix of a multivariate normal process is crucial for this purpose. The complexity increases notably in high-dimensional processes because of the large number of variables and limited sample sizes. Typically, monitoring changes in the covariance matrix assumes that only a few elements deviate simultaneously from their in-control values. This study introduces a new approach for monitoring the covariance matrix in Phase II for multichannel data. The suggested approach incorporates exponentially weighted moving average (EWMA) control chart with multichannel functional principal components analysis (MFPCA) to derive proposed statistics. Simulation results represent the effectiveness and performance of the suggested approach, highlighting its superior performance in average run length under various shift patterns.