Probabilistic Contribution Analysis for Statistical Process Monitoring: A Missing Variable Approach

Probabilistic models, including probabilistic principal component analysis (PPCA) and PPCA mixture models, have been successfully applied to statistical process monitoring. This paper reviews these two models and discusses some implementation issues that provide alternative perspective on their application to process monitoring. Then a probabilistic contribution analysis method, based on the concept of missing variable, is proposed to facilitate the diagnosis of the source behind the detected process faults. The contribution analysis technique is demonstrated through its application to both PPCA and PPCA mixture models for the monitoring of two industrial processes. The results suggest that the proposed method in conjunction with PPCA model can reduce the ambiguity with regard to identifying the process variables that contribute to process faults. More importantly it provides a fault identification approach for PPCA mixture model where conventional contribution analysis is not applicable.