Contribution plots for Statistical Process Control: Analysis of the smearing-out effect

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 et al. reported that contribution plots suffer from fault smearing, i.e., the influence of faulty variables on the contributions of non-faulty variables, which complicates the fault isolation task as variables unaffected by the fault may be highlighted and faulty variables obscured [1]. This paper presents an 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 latent variable 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 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 results for sensor faults, the authors advise to use contributions only if a sound physical interpretation of the principal components is available.