Non parametric on-line control of batch processes based on STATIS and clustering
[Contrôle non paramétrique de procédés par lots basé sur STATIS et la classification]
Journal de la société française de statistique, Méthodes statistiques en agronomie, Tome 154 (2013) no. 3, pp. 124-142.

Les procédés par lots sont largement utilisés dans le secteur industriel notamment dans l’industrie agroalimentaire, chimique ou pharmaceutique. Le suivi de tels procédés est effectué à travers un ensemble de variables caractéristiques du procédé prélevées par un échantillonnage en ligne au fur et à mesure de son déroulement. Le procédé est contrôlé à travers des cartes multivariées basées sur une analyse en composantes principales particulière (multiway principal component analysis). Nous proposons une approche du contrôle de qualité des procédés par lots basée sur la méthode STATIS et des régions de contrôles non paramétriques obtenues à partir d’enveloppes convexes. Cette approche générale peut être utilisée pour le contrôle en fin de fabrication des procédés par lots ainsi que pour le contrôle en cours de fabrication après une étape de classification sous contrainte basée sur une extension multivariée de l’algorithme de W.D. Fisher. La méthode proposée est illustrée sur des données réelles issues d’un procédé par lots à temps fixe.

Batch processes are widely used in several industrial sectors, e.g. food and pharmaceutical manufacturing. Process performance is described by variables which are monitored as the batch progresses. Data arising from such processes are usually monitored using control charts based on multiway principal components analysis. In this paper we propose a non parametric quality control strategy for monitoring batch processes with fixed as well as variable duration. In our proposition, data sets associated to batches are reduced using the STATIS method. Monitoring of batch performance is accomplished directly on principal plane graphs, from which non-parametric control regions are derived through convex hull peeling. This general approach allows off-line monitoring of batch processes as well as on-line monitoring after a constrained clustering step based on multivariate extension of W.D. Fisher’s algorithm is carried out. A real example of batch process with fixed duration illustrates the proposed method.

Keywords: Batch process, Clustering, Multivariate quality control, STATIS method
Mot clés : Procédés par lots, Classification, Contrôle de qualité multivarié, Méthode STATIS 
@article{JSFS_2013__154_3_124_0,
     author = {Niang, Nd\`eye and Fogliatto, Flavio S. and Saporta, Gilbert},
     title = {Non parametric on-line control of batch processes based on {STATIS} and clustering},
     journal = {Journal de la soci\'et\'e fran\c{c}aise de statistique},
     pages = {124--142},
     publisher = {Soci\'et\'e fran\c{c}aise de statistique},
     volume = {154},
     number = {3},
     year = {2013},
     language = {en},
     url = {http://archive.numdam.org/item/JSFS_2013__154_3_124_0/}
}
TY  - JOUR
AU  - Niang, Ndèye
AU  - Fogliatto, Flavio S.
AU  - Saporta, Gilbert
TI  - Non parametric on-line control of batch processes based on STATIS and clustering
JO  - Journal de la société française de statistique
PY  - 2013
SP  - 124
EP  - 142
VL  - 154
IS  - 3
PB  - Société française de statistique
UR  - http://archive.numdam.org/item/JSFS_2013__154_3_124_0/
LA  - en
ID  - JSFS_2013__154_3_124_0
ER  - 
%0 Journal Article
%A Niang, Ndèye
%A Fogliatto, Flavio S.
%A Saporta, Gilbert
%T Non parametric on-line control of batch processes based on STATIS and clustering
%J Journal de la société française de statistique
%D 2013
%P 124-142
%V 154
%N 3
%I Société française de statistique
%U http://archive.numdam.org/item/JSFS_2013__154_3_124_0/
%G en
%F JSFS_2013__154_3_124_0
Niang, Ndèye; Fogliatto, Flavio S.; Saporta, Gilbert. Non parametric on-line control of batch processes based on STATIS and clustering. Journal de la société française de statistique, Méthodes statistiques en agronomie, Tome 154 (2013) no. 3, pp. 124-142. http://archive.numdam.org/item/JSFS_2013__154_3_124_0/

[1] Abdi, H.; Williams, L. J.; Valentin, D.; Bennani-Dosse, M. STATIS and DISTATIS: optimum multitable principal component analysis and three way metric multidimensional scaling, Wiley Interdisciplinary Reviews: Computational Statistics, Volume 4 (2012) no. 2, pp. 124-167

[2] Bellman, R. On the approximation of curves by line segments using dynamic programming, Communications of the ACM, Volume 4 (1961) no. 6, p. 284-284 | Zbl

[3] Castagliola, P.; Ferreira, A. Monitoring of Batch Processes with Varying Durations Based on the Hausdorff Distance., International Journal of Reliability, Quality and Safety Engineering, Volume 13 (2006) no. 3, pp. 213-236

[4] des Plantes, H. L’hermier Structuration des Tableaux à Trois Indices de la Statistique, Université de Montpellier, Montpellier (France) (1976) (Ph. D. Thesis)

[5] Doan, X.; Srinivasan, R. Online monitoring of multi-phase batch processes using phase-based multivariate statistical process control, Computers and Chemical Engineering, Volume 32 (2008), pp. 230-243

[6] Eriksson, L.; Johansson, E.; Kettaneh-Wold, N.; Wold, S. Multi-and Megavariate Data Analysis, Umetrics, 2001

[7] Escoufier, Y. Three-mode data analysis: the STATIS method, Methods for multidimensional data analysis (B., Fichet; N.C., Lauro, eds.), ECAS, 1987, pp. 259-272

[8] Flores-Cerrillo, J.; MacGregor, J.F. Control of particle size distribution in emulsion semibatch polymerization using mid-course correction policies, Industrial & Engineering Chemistry Research, Volume 41 (2002), pp. 1805-1814

[9] Fisher, W.D. On grouping for maximum homogeneity, Journal of the American Statistical Association, Volume 53 (1958) no. 284, pp. 789-798 | Zbl

[10] Harris T.J., Desborough L.D. Seppala C.T. A review of performance monitoring and assessment techniques for univariate and multivariate control systems, Journal of Process Control, Volume 9 (1999), pp. 1-17

[11] Hébrail, G.; Hugueney, B.; Lechevallier, Y.; Rossi, F. Exploratory analysis of functional data via clustering and optimal segmentation, Neurocomputing, Volume 73 (2010) no. 7, pp. 1125-1141

[12] Hastie, T.; Tibshirani, R.; Friedman The elements of statistical learning: data mining, inference and prediction, Springer, 2001 | Zbl

[13] Jackson, J.E. A User’s Guide to Principal Components, Wiley, 1991 | Zbl

[14] Jain, A. K. Data clustering: 50 years beyond K-means, Pattern Recognition Letters, Volume 31 (2010) no. 8, pp. 651-666

[15] Jackson, J. E.; Mudholkar, G. S. Control Procedures for Residuals Associated With Principal Component Analysis, Technometrics, Volume 21 (1979) no. 3, pp. 341-349 | Zbl

[16] Kourti, T.; MacGregor, J. F. Multivariate SPC Methods for Process and Product Monitoring, Journal of Quality Technology, Volume 28 (1996) no. 0, pp. 409-428

[17] Kaistha, N.; Moore, C. F.; Leitnaker, M. G. A Statistical Process Control Framework for the Characterization of Variation in Batch Profiles, Technometrics, Volume 46 (2004) no. 1, pp. 53-68

[18] Kassidas, A.; MacGregor, J. F.; Taylor, P. A. Synchronization of batch trajectories using dynamic time warping, AIChE Journal, Volume 44 (1998) no. 4, pp. 864-875

[19] Kourti, T. Multivariate dynamic data modeling for analysis and statistical process control of batch processes, start-ups and grade transitions, Journal of Chemometrics, Volume 17 (2003) no. 1, pp. 93-109

[20] Lechevallier, Y. Recherche d’une partition optimale sous contrainte d’ordre total (1990) no. RR-1247 (Rapport de recherche INRIA)

[21] Lavit, C.; Escoufier, Y.; Sabatier, R.; Traissac, P. The ACT (STATIS method), Computational Statistics & Data Analysis, Volume 18 (1994) no. 1, pp. 97-119 | Zbl

[22] Liu, R. Y. Control charts for multivariate processes, Journal of the American Statistical Association, Volume 90 (1995) no. 432, pp. 1380-1387 | Zbl

[23] Lowry, C.A.; Montgomery, D.C. A review of multivariate control charts, Computational Statistics & Data Analysis, Volume 27 (1995) no. 1, pp. 800-810

[24] Liu, R. Y.; Tang, J. Control charts for dependent and independent measurements based on bootstrap methods, Journal of the American Statistical Association, Volume 91 (1996) no. 436, pp. 1694-1700 | Zbl

[25] Lombardo, R.; Vanacore, A.; Durand, J.F. Non Parametric Control Chart by Multivariate Additive Partial Least Squares via Spline, Data Analysis, Machine Learning and Applications (Preisach, C.; Burkhardt, H.; Schmidt-Thieme, L.; Decker, R., eds.), Springer, 2008, pp. 201-208

[26] MacGregor, J. F. Using On-Line Process Data to Improve Quality: Challenges for Statisticians, International Statistical Review, Volume 65 (1997) no. 3, pp. 309-323 | Zbl

[27] Montgomery, D.C. Introduction to Statistical Quality Control, John Wiley & Sons, 2001, pp. 309-323 | Zbl

[28] Niang, N.; Fogliatto, F.S.; Saporta, G. Batch Process Monitoring by Three-way Data Analysis Approach, The XIIIth International Conference Applied Stochastic Models and Data Analysis ASMDA-2009 (2009), pp. 463-468

[29] Nomikos, P.; MacGregor, J.F. Multivariate SPC charts for monitoring batch processes, Technometrics, Volume 37 (1995), pp. 41-59 | Zbl

[30] Rosa, A.F.P. Maîtrise statistique de procédés par lots à temps variable, Université de Nantes, Nantes (France) (2005) (Ph. D. Thesis)

[31] Scepi, G. Parametric and Non Parametric Multivariate Quality Control Charts, Multivariate Total Quality Control (C., Lauro; J., Antoch; V., Esposito; G., Saporta, eds.), Physica-Verlag, 2002, pp. 163-189 | Zbl

[32] Wierda, S.J. Multivariate statistical process control - Recent results and directions for future research, Statistica Neerlandica, Volume 48 (1994), pp. 147-168 | Zbl

[33] Zani, S.; Riani, M.; Corbellini, A. Robust bivariate boxplots and multiple outlier detection, Computational Statistics & Data Analysis, Volume 28 (1998) no. 3, pp. 257-270 | Zbl