Identificação de variáveis fora de controle em processos produtivos multivariados
Identification of out-of-control variables in a multivariate productive process
Souza, Adriano Mendonça; Rigão, Maria Helena
http://dx.doi.org/10.1590/S0103-65132005000100007
Prod, vol.15, n1, p.74-86, 2005
Resumo
A maioria dos processos produtivos, envolvendo múltiplas variáveis, geram grande quantidade de dados, nos quais o monitoramento simultâneo se faz necessário. Assim, o objetivo principal deste trabalho é mostrar, por meio de um exemplo, um procedimento de identificação de variáveis responsáveis pela instabilidade do processo. Ele considera variáveis fraca e fortemente correlacionadas. O comportamento destas variáveis é analisado, inicialmente, por meio do gráfico de controle T2 de Hotelling, para a verificação da estabilidade do processo. Quando o processo é considerado fora de controle, uma investigação adicional é realizada. Para as variáveis fracamente correlacionadas o gráfico X-barra, com limites de Bonferroni, é utilizado. Para as variáveis com forte correlação, os dados são decompostos em componentes principais e estas são analisadas pelo gráfico de controle X-barra. Em ambos os casos, as técnicas utilizadas identificaram corretamente a variável responsável pela instabilidade do processo, bem como o período do distúrbio.
Palavras-chave
Controle estatístico de processos, Gráfico de controle T2 de Hotelling, Gráfico X-barra com limites de Bonferroni, Análise de componentes principais
Abstract
Most productive processes are affected by multiple variables and generate a great amount of data and simultaneous monitoring becomes necessary. Thus, the main purpose of this work is to show, by means of an example, procedures of identification of variables responsible for process instability. It considers weakly and strongly correlated variables. The behavior of these variables is analyzed, initially by means of a Hotteling`s T2 chart for the verification of the process stability. When the process is considered to be out-of-control, another investigation is carried out. For variables of weak correlation an X-bar chart with Bonferroni limits is used. For variables of strong correlation, the data are decomposed in principal components and analyzed by means of a X-bar control chart. In both cases, the techniques used can correctly identify the variable responsible for the process instability, as well as the period of disturbance.
Keywords
Statistical process control, Hotelling's T2 chart, X-bar chart with Bonferroni limits, Principal components analysis
References
APARISE, F. Sampling plans for the multivariate T2 control chart. Quality Enginering, v. 10, n. 1, p.141-147, 1997.
BLAND, J.M. & ALTMAN, D.G. Multiple significances test: the Bonferroni method. British Medical Journal, n. 310:170, 21, jan. 1995.
CATTEL, R.B. The screen test for the number of factors. Multivariate Behavior Research, v.1, p. 245-276, 1966.
DEWEY, M.E. Bonferroni e le diduguaglianze. Disponível em:
GNANADESIKAN, R & KETTEREING, J. R. Robust estimates, residual and outlier detection with multiresponse data. Biometrics, v. 28, p. 81-124, 1972.
HAWKINS, D.M & FATTI, L.P. Exploring multivariate data using minor principal components. The Statistician, v. 33, p. 325-338, 1984.
HOTELLING, H. Multivariate quality control. Techniques of statistical analysis. New York: Mc Graw Hill, p. 111-184, 1947.
JACKSON, J. EDWARD. Quality control methods. Industrial Quality Control, p. 4-8, Jan. 1956.
JACKSON, J. EDWARD. Quality control methods for several related variables. Technometrics, p. 359-377, nov. 1959.
JACKSON, J.E. & MORRIS, R.H. An application of multivariate quality control to photographic processing. Journal of the American Statistical Association, v. 52, p. 186-199, 1957.
JOHNSON, R.A. & WICHERN, D.W. Applied multivariate statistical analysis. 3. ed. New Jersey : Prentice-Hall, 1992.
KHATTREE, R. & NAIK, D.N. Multivariate data reduction and discrimination. Cary, USA: SAS Institute Inc., 558 p., 2000.
KOURTI, T. & MACGREGOR, J.F. Multivariate SPC methods for process and product monitoring. Journal of Quality Technology, v. 28, n. 4, p. 409-428, Oct. 1996.
LOWRY, C.A. & MONTGOMERY, D.C.A review of multivarate control chart. IIE Transaction, v. 27, p. 800-810, 1995.
MARDIA, K.V. et al. Multivariate analysis. London : Academic, 1979.
MASON, Robert L. & YOUNG, John C. Multivariate statistical process control with industrial applications. Philadelphia: Society for Industrial and Applied Mathematics, 263 p., 2002.
MEYER, P. L. Probabilidade: aplicações à estatística. 2. ed. Rio de Janeiro: Livros Técnicos e Científicos, 426 p., 1983
MONTGOMERY, D.C. Introduction to statistical quality control. 2. ed. New York: Jonhn Wiley & Sons, 674 p., 1991.
PERNEGER, T. V. What's wrong whith Bonferroni adjustment. British Medical Journal, n. 316, p. 1236-1238, 18 Apr., 1998.
PFEIFFER, P.E. Concepts of probability theory. 2. ed. New York: Dover Publications, 403 p., 1978.
RYAN, T.P. Statistical methods for quality improvement. New York: John Wiley D& Sons, Inc, 1989.
TRACY, N.D. et al. Multivariate Control Charts for Individual Observations. Journal of Quality Technology, v. 24, p. 88-95, 1992.
TRACY, N.D. et al. A bivariate control chart for paired measurements. Journal of Quality Technology, v. 27, p. 370-376, 1995.