Dynamic VAR model-based control charts for batch process monitoring

In the field of Statistical Process Control (SPC) there are several different approaches to deal with monitoring of batch processes. Such processes present a three-way data structure (batches×variables×time-instants), so that for each batch a multivariate time series is available. Traditional approaches do not take into account the time series nature of the data. They deal with this kind of data by applying multivariate techniques in a reduced two-way data structure, in order to capture variables dynamics in some way. Recent developments in SPC have proposed the use of the Vector Autoregressive (VAR) time series model considering the original three-way structure. However, they are restricted to control approaches focused on VAR residuals. This paper proposes a new approach to deal with batch processes focusing on VAR coefficients instead of residuals. In short, we estimate VAR coefficients from historical in-control reference batch samples and build two multivariate control charts to monitoring new batches. We showcase the advantages of the proposed methodology for offline and online monitoring in a simulate example comparing it with the residual-based approach.