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.