On-line multivariate statistical monitoring of batch processes using Gaussian mixture model

This paper considers multivariate statistical monitoring of batch manufacturing processes. It is known that conventional monitoring approaches, e.g. principal component analysis (PCA), are not applicable when the normal operating conditions of the process cannot be sufficiently represented by a multivariate Gaussian distribution. To address this issue, Gaussian mixture model (GMM) has been proposed to estimate the probability density function (pdf ) of the process nominal data, with improved monitoring results having been reported for continuous processes. This paper extends the application of GMM to on-line monitoring of batch processes. Furthermore, a method of contribution analysis is presented to identify the variables that are responsible for the onset of process fault. The proposed method is demonstrated through its application to a batch semiconductor etch process.