Process monitoring based on probabilistic PCA

Abstract

This paper proposes a multivariate process monitoring method based on probabilistic principal component analysis (PPCA). First we will summarize several well-known statistical process monitoring methods, e.g. univariate/multivariate Shewhart charts, and the PCA-based method, i.e. Q and Hotelling's T-2 charts. And then the probabilistic method will be proposed and compared to the existing methods. In essence, the univariate Shewhart chart, multivariate Shewhart chart, Q chart, and T-2 chart are unified to the probabilistic method. The PPCA model is calibrated by the expectation and maximization (EM) algorithm similar to PCA by NIPALS algorithm; EM algorithm will be explained briefly in the article. Finally, through an illustrative example, we will show how the probabilistic method works and is applied to the process monitoring. (C) 2003 Elsevier Science B.V. All rights reserved.