Controle multivariado de processos em batelada com duração variável
Multivariate statistical control of unsynchronized batch processes
Fogliatto, Flavio Sanson; Niang, Ndéye
http://dx.doi.org/10.1590/S0103-65132008000200004
Prod, vol.18, n2, p.240-259, 2008
Resumo
Processos em batelada são utilizados em diversos setores industriais (por exemplo, na manufatura de alimentos e fármacos). Nesses processos, matérias-primas são carregadas em uma unidade de processamento e submetidas a uma série de transformações até a obtenção do produto final. O desempenho do processo é descrito por variáveis, monitoradas ao longo da batelada. Dados resultantes desses processos tendem a apresentar uma estrutura de correlação e autocorrelação significativa, sendo usualmente monitorados usando cartas de controle baseadas na análise de componentes principais (CCPs). Neste artigo, investiga-se o caso especial, bastante freqüente na prática, de bateladas com duração variável, as quais não podem ser diretamente monitoradas através das CCPs. Para tanto, propõe-se uma nova estratégia de controle multivariado da qualidade. No procedimento proposto, bateladas não são alinhadas ou time warped relativamente a suas trajetórias, mas completadas utilizando um esquema de fácil implementação prática. Desta forma, preserva-se toda a informação sobre a variabilidade ao longo do eixo do tempo nos perfis das variáveis de processo. O conjunto de dados completados é analisado utilizando o método Statis e o monitoramento do desempenho da batelada é realizado diretamente nos gráficos de planos fatoriais, a partir dos quais cartas de controle não-paramétricas são derivadas. Um exemplo utilizando dados simulados ilustra a proposta metodológica.
Palavras-chave
Bateladas não-sincronizadas, CEP multivariado, método Statis
Abstract
Batch processes are widely used in several industrial sectors, such as food and pharmaceutical manufacturing. In a typical batch, raw materials are loaded in the processing unit and submitted to a series of transformations, yielding the final product. Process performance is described by variables which are monitored as the batch progresses. Data arising from such processes are likely to display a strong correlation-autocorrelation structure, and are usually monitored using control charts based on multiway principal components analysis (MPCA charts). In this paper we investigate the special (and rather frequent) case of batches with varying duration, which cannot be directly monitored using MPCA charts. We propose a new quality control strategy for monitoring such batches. In our proposition, batches are not aligned or time warped with respect to their trajectories, but are rather completed using a straightforward scheme. Thus all information on the variability in batch profiles along the time axis is preserved. The data set completed is reduced using the Statis method and monitoring of batch performance is accomplished directly on principal plane graphs, from which non-parametric control charts are derived. A simulated example illustrates the proposed method.
Keywords
Unsynchronized batches, Multivariate quality control, Statis method
References
CASTAGLIOLA, P.; ROSA, A. F. P. Monitoring of Batch Processes with Varying Durations Based on the Hausdorff Distance. International Journal of Reliability, Quality and Safety Engineering, Vol. 13, p. 213-236, 2006.
ESCOUFIER, Y. Le traitement des variables vectorielles. Biometrics, v. 29, p. 751-760, 1973.
_________. Three-mode data anlysis: the STATIS method. In Methods for multidimensional data analysis, ECAS, Fichet B.; Lauro N. C. (eds.), p. 259-272, 1987.
FLORES-CERRILLO, J.; MACGREGOR, J.F. Control of particle size distribution in emulsion semibatch polymerization using mid-course correction policies. Industrial & Engineering Chemistry Research, v. 41, p. 1805-1814, 2002.
HARRIS, T. C.; SEPPALA, C. T.; DESBOROUGH, L. D. A review of performance monitoring and assessment techniques for univariate and multivariate control systems. Journal of Process Control, v. 9, p. 1-17, 1999.
HASTIE, T.; TIBSHIRANI, R.; FRIEDMAN, J. The elements of statistical learning - Data mining, inference, and prediction. Springer Science: New York, 2001.
JACKSON, J. E. A User's Guide to Principal Components. Wiley: New York, 1991.
JACKSON, J. E.; MUDHOLKAR, G. S. Control Procedures for Residuals Associated with Principal Component Analysis. Technometrics, v. 21, p. 341-34, 1979.
JOLLIFFE, I. T. Principal component analysis. 2. ed. Springer Science: New York, 2004.
KAISTHA, N.; MOORE, C. F.; LEITNAKER, M. G. A statistical process control framework for the characterization of variation in batch profiles. Technometrics, v. 46, p. 53-68, 2004.
KASSIDAS, A.; MACGREGOR, J. F.; TAYLOR, P. A. Synchronization of batch trajectories using dynamic time warping. AIChE Journal, v. 44, p. 864-875, 1998.
KOURTI, T. Multivariate dynamic data modeling for analysis and statistical process control of batch processes, start-ups and grade transitions. Journal of Chemometrics, v. 17, p. 93-109, 2003.
KOURTI, T.; MACGREGOR, J. F. Multivariate SPC Methods for Process and Product Monitoring. Journal of Quality Technology, v. 28, p. 409-428, 1996.
KOURTI, T.; LEE, J.; MACGREGOR, J. F. Experiences with industrial applications of projection methods for multivariate statistical process control. Computers and Chemical Engineering, v. 20, S745-S750, 1996.
LAVIT, C.; ESCOUFIER, Y.; SABATIER, R.; TRAISSAC, P. The ACT (STATIS method). Computational Statistics & Data Analysis, v. 18, p. 97-119, 1994.
LOWRY, C. A.; MONTGOMERY, D. C. A review of multivariate control charts. IIE Transactions, v. 27, p. 800-810, 1995.
MACGREGOR, J. F. Using on-line process data to improve quality: challenges for statisticians. International Statistical Review, v. 65, p. 309-323, 1997.
MINGOTI, S. A. Análise de dados através de métodos de estatística multivariada - uma abordagem aplicada. Editora UFMG: Belo Horizonte, 2005.
MONTGOMERY, D. C. Introduction to Statistical Quality Control. 4. ed. Wiley: New York, 2001.
NEOGI, D.; SCHLAGS, C. E. Multivariate statistical analysis of an emulsion batch process. Industrial & Engineering Chemistry Research, v. 37, p. 3971-3979, 1998.
NOMIKOS, P. Statistical process control of batch processes. Ph.D. Thesis, McMaster University, Hamilton (Canada), 1995.
NOMIKOS, P.; MACGREGOR, J. F. Multivariate SPC charts for monitoring batch processes. Technometrics, v. 37, p. 41-59, 1995.
ROSA, A. F. P. Maîtrise statistique de procédés par lots à temps variable. Thèse de Doctorat de l'Université de Nantes, Nantes (França), 2005.
SCEPI, G. Parametric and non parametric multivariate quality control charts. In Multivariate Total Quality Control, Physica-Verlag, Lauro C. et al. (eds.), p. 163-189, 2002.
WIERDA, S. J. Multivariate statistical process control - Recent results and directions for future research. Statistica Neerlandica, v. 48, p. 147-168, 1994.
ZANI, S.; RIANI, M.; CORBELLINI, A. Robust bivariate boxplots and multiple outlier detection. Computational Statistics & Data Analysis, v. 28, p. 257-270, 1998.
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