A mixture probabilistic PCA model for multivariate processes monitoring

A mixture probabilistic principal component analysis (PCA) model is proposed as a multivariate process monitoring tool in this paper. High dimensional measurement data could be aggregated into some clusters based on the mixture distribution model, where the number of these clusters is automatically determined by the maximum likelihood estimation procedure. The multivariate statistical process monitoring mechanism is developed first with the learning of a finite mixture model for describing the local statistical patterns in each cluster, followed by the construction of the statistical process confidence intervals for the identified regions or nodes from T2 and Q charts. The abnormal input measurement would fall out of the acceptance region set by the confidence control limits and probabilistic PCA model. The experimental studies have illustrated that the mixture probabilistic PCA model conforms to the multivariate data well in the experiments involving Gaussian mixtures, and helps identify the underlying root causes of variation patterns in complicated multivariate manufacturing processes.