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A Theoretical Basis for the use of Principal Component Models for Monitoring Multivariate Processes

Although principal components analysis (PCA) has shown some utility as a multivariate statistical process control (MSPC) tool, a theoretical basis for its use with dynamic process data has been lacking. It is shown here that, for processes with more measurements than states, proper application of PCA can facilitate the process monitoring and fault detection problem. When the PCA model is accurate, variations in the process states appear primarily as variations in PCA scores, while noise mainly affects the residuals. This allows one to consider on the the noise properties when deriving error-detection limits for the PCA residuals. In particular, the process dynamics need not be considered explicitly. We also show how an arbitrary stat-space model can be transformed so that its states are directly related to the PCA scores.