The monitoring of dynamic processes using multivariate time series

The monitoring of the performance of dynamic processes is proposed through the development of multivariate time series models, in particular Vector Autoregressive (VAR) models, based on the model prediction errors. In the presence of non-stationary variables, cointegration can be used to enhance the identification and estimation of VAR models. A performance monitoring scheme based on a simulation of a Continuous Stirred Tank Reactor where variables exhibit non-stationary behaviour, is used to illustrate the methodology. A fault was introduced into the simulation. By monitoring the prediction errors of the VAR model when cointegration was not taken into the account, the fault was not detected. This was in contrast to the situation where cointegration was included in the development of the VAR model, in this case diagnosis of the fault was possible. The underlying reasons are discussed alongside the implications of cointegration in dynamic multivariate statistical process control.