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

Abstract 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 et 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.

[1]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[2]  S. Joe Qin,et al.  Subspace approach to multidimensional fault identification and reconstruction , 1998 .

[3]  In-Beum Lee,et al.  A novel multivariate regression approach based on kernel partial least squares with orthogonal signal correction , 2005 .

[4]  ChangKyoo Yoo,et al.  Fault detection of batch processes using multiway kernel principal component analysis , 2004, Comput. Chem. Eng..

[5]  P. Miller,et al.  Contribution plots: a missing link in multivariate quality control , 1998 .

[6]  Julian Morris,et al.  Dynamic model-based batch process monitoring , 2008 .

[7]  Yale Zhang,et al.  Industrial application of multivariate SPC to continuous caster start-up operations for breakout prevention , 2006 .

[8]  Gülnur Birol,et al.  Statistical Process Monitoring , 2003 .

[9]  Theodora Kourti,et al.  Statistical Process Control of Multivariate Processes , 1994 .

[10]  I. Jolliffe.  Principal Component Analysis , 2002 .

[11]  John F. MacGregor,et al.  Process monitoring and diagnosis by multiblock PLS methods , 1994 .

[12]  A. J. Morris,et al.  Monitoring the performance of the paper making process , 1999 .

[13]  Mabel C. Sánchez,et al.  On the variable contributions to the D-statistic , 2007 .

[14]  Elaine B. Martin,et al.  The statistical monitoring of a complex manufacturing process , 2001 .

[15]  Thomas E. Marlin,et al.  Multivariate statistical monitoring of process operating performance , 1991 .

[16]  I. Helland.  Partial Least Squares Regression , 2006 .

[17]  Age K. Smilde,et al.  Generalized contribution plots in multivariate statistical process monitoring , 2000 .

[18]  Si-Zhao Joe Qin,et al.  Reconstruction-based contribution for process monitoring , 2009, Autom..

[19]  Christos Georgakis,et al.  Disturbance detection and isolation by dynamic principal component analysis , 1995 .

[20]  Tao Chen,et al.  A branch and bound method for isolation of faulty variables through missing variable analysis , 2010 .

[21]  M. Ouladsine,et al.  Fault localization using principal component analysis based on a new contribution to the squared prediction error , 2008, 2008 16th Mediterranean Conference on Control and Automation.

[22]  George W. Irwin,et al.  Improved reliability in diagnosing faults using multivariate statistics , 2006, Comput. Chem. Eng..

[23]  Seongkyu Yoon,et al.  Fault diagnosis with multivariate statistical models part I: using steady state fault signatures , 2001 .

[24]  S. Joe Qin,et al.  Reconstruction-Based Fault Identification Using a Combined Index , 2001 .

[25]  Junghui Chen,et al.  On-line batch process monitoring using dynamic PCA and dynamic PLS models , 2002 .

[26]  A. A. Tates,et al.  Monitoring a PVC batch process with multivariate statistical process control charts , 1999 .

[27]  S. Joe Qin,et al.  Statistical process monitoring: basics and beyond , 2003 .

[28]  George W. Irwin,et al.  Improved fault diagnosis in multivariate systems using regression-based reconstruction , 2009 .

[29]  S. Joe Qin,et al.  Analysis and generalization of fault diagnosis methods for process monitoring , 2011 .

[30]  Barry Lennox,et al.  Monitoring a complex refining process using multivariate statistics , 2008 .

[31]  Ilknur Atasoy,et al.  On‐line Statistical Process Monitoring and Fault Diagnosis in Batch Baker's Yeast Fermentation , 2009 .

[32]  A. Ferrer,et al.  Dealing with missing data in MSPC: several methods, different interpretations, some examples , 2002 .

[33]  Yale Zhang,et al.  Online monitoring of steel casting processes using multivariate statistical technologies: From continuous to transitional operations☆ , 2006 .

[34]  C. E. Schlags,et al.  Industrial application of SPC to batch polymerization processes , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[35]  Stella Bezergianni,et al.  Application of Principal Component Analysis for Monitoring and Disturbance Detection of a Hydrotreating Process , 2008 .

[36]  B. Kowalski,et al.  Partial least-squares regression: a tutorial , 1986 .

[37]  John F. MacGregor,et al.  Multi-way partial least squares in monitoring batch processes , 1995 .