Non parametric on-line control of batch processes based on STATIS and clustering

Niang, Ndèye; Fogliatto, Flavio S.; Saporta, Gilbert

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.

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