Analysis of smearing-out in contribution plot based fault isolation for Statistical Process Control

This paper studies the smearing effect encountered in contribution plot based fault isolation, i.e., the influence of faulty variables on the contributions of non-faulty variables. Since the generation of contribution plots requires no a priori information about the detected disturbance (e.g., historical faulty data), it is a popular fault isolation technique in Statistical Process Control (SPC). However, Westerhuis al. (2000) demonstrated that contributions suffer from fault smearing. As a consequence, variables unaffected by the fault may be highlighted and faulty variables obscured during the contribution analysis. This paper presents a thorough analysis of the smearing effect for three general contribution computation methods: complete decomposition, partial decomposition and reconstruction-based contributions. The analysis shows that (i) smearing is present in all three methods, (ii) smearing depends on the chosen number of principal components of the underlying PCA or PLS model and (iii) the extent of smearing increases for variables correlated in the training data for a well-chosen model order. The effect of smearing on the isolation performance of single and multiple sensor faults of various magnitudes is studied and illustrated using a simulation case study. The results indicate that correct isolation with contribution plots is not guaranteed for multiple sensor faults. Furthermore, contribution plots only outperform univariate fault isolation for single sensor faults with small magnitudes. For multiple sensor faults, univariate fault isolation exhibits a significantly larger correct fault isolation rate. Based on the smearing analysis and the specific results for sensor faults, the authors advise to use contributions only if a sound physical interpretation of the principal components is available. Otherwise multivariate detection followed by univariate fault isolation is recommended. (C) 2013 Published by Elsevier Ltd.