Applying State Space to SPC: Monitoring Multivariate Time Series

Monitoring cross-sectional and serially interdependent processes has become a new issue in statistical process control (SPC). In up-to-date SPC literature, Kalman filtering was reported to monitor univariate autocorrelated processes. This paper applies a Kalman filter or state-space method for SPC to monitoring multivariate time series. We use Aoki's approach to estimate the parameter matrices of a state-space model. Multivariate Hotelling T ² control charts are employed to monitor the residuals of the state-space. Examples of this approach are illustrated.