Adaptive multivariate statistical process control for monitoring time-varying processes

Abstract

An adaptive multivariate statistical process monitoring (MSPC) approach is described for the monitoring of a process with incurs operating condition changes. Samplewise and blockwise recursive formulas for updating a weighted mean and covariance matrix are derived. By utilizing these updated mean and covariance structures and the current model, a new model is derived recursively. On the basis of the updated principal component analysis (PCA) representation, two monitoring metrics, Hotelling's T-2 and the Q-statistic, are calculated and their control limits are updated. For more efficient model updating, forgetting factors, which change with time, for the updating of the mean and covariance are considered. Furthermore, the updating scheme proposed is robust in that it not only reduces the false alarm rate in the monitoring charts but also makes the model insensitive to outliers. The adaptive MSPC approach developed is applied to a multivariate static system and a continuous stirred tank reactor process, and the results are compared to static MSPC. The revised approach is shown to be effective for the monitoring of processes where changes are either fast or slow.