Published

2016-07-01

Robustificación de la carta de control multivariada √(|S|) en la fase I de control

Robustification of multivariate control chart √|S| in control phase I

DOI:

https://doi.org/10.15446/rev.fac.cienc.v5n2.50666

Keywords:

Control estadístico multivariado, estimación robusta, fase I de control, matriz de covarianzas (es)
Multivariate statistical control, robust estimation, phase I control, covariance matrix (en)

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En este artículo se estudia la robustificación de la carta basada en la raiz cuadrada de la varianza muestral generalizada √|S| para el control de la variabilidad de un proceso normal bivariado, en la etapa 1 de la Fase I de control, construida con observaciones sobre subgrupos racionales y utilizando los estimadores robustos MVE, MCD, estimador S. Estas cartas se comparan con la carta usual basada en el estimador insesgado muestral S de la matriz de covarianza ∑_0, en presencia de outliers provenientes de esquemas de perturbación del tipo contaminación con inflación de ∑_0 y contaminación perturbando sólo la correlación. Como medida de desempeño se usa el error cuadrático medio en la estimación de ∑_0 y el sesgo absoluto en la estimación de √(|∑_0 | ), sobre los estimadores insesgados para cada uno de estos parámetros, respectivamente, construidos con los subgrupos racionales que quedan después del proceso de depuración realizado en la Fase I y que se consideran como el conjunto de datos que representa el estado de variación estable del proceso.
This article, chart robustification based on the square root of the sample generalized variance √|S|, is studied to control the variability of a bivariate normal process in stage 1 of Phase I control, built with observations for rational subgroups, and using the robust estimators, MVE, MCD and estimator S. These charts, are being compared with the usual chart, based on unbiased sample estimator, S, of the covariance matrix, ∑_0, in the presence of outliers from perturbation schemes such as, ∑_0 inflation contamination, and contamination affecting only the correlation. We use as performance measure, the mean squared error in estimating ∑_0, and absolute bias in the estimate, used √(|∑_0 | ), about the unbiased estimators for each one of the parameters respectively    built with the rational subgroups that remain after the purification process undertaken in Phase 1 and are consider as the data group that represent the stage of the stable variation process.

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How to Cite

APA

Dugarte Peña, E. and González Álvarez, N. G. (2016). Robustificación de la carta de control multivariada √(|S|) en la fase I de control. Revista de la Facultad de Ciencias, 5(2), 12–37. https://doi.org/10.15446/rev.fac.cienc.v5n2.50666

ACM

[1]
Dugarte Peña, E. and González Álvarez, N.G. 2016. Robustificación de la carta de control multivariada √(|S|) en la fase I de control. Revista de la Facultad de Ciencias. 5, 2 (Jul. 2016), 12–37. DOI:https://doi.org/10.15446/rev.fac.cienc.v5n2.50666.

ACS

(1)
Dugarte Peña, E.; González Álvarez, N. G. Robustificación de la carta de control multivariada √(|S|) en la fase I de control. Rev. Fac. Cienc. 2016, 5, 12-37.

ABNT

DUGARTE PEÑA, E.; GONZÁLEZ ÁLVAREZ, N. G. Robustificación de la carta de control multivariada √(|S|) en la fase I de control. Revista de la Facultad de Ciencias, [S. l.], v. 5, n. 2, p. 12–37, 2016. DOI: 10.15446/rev.fac.cienc.v5n2.50666. Disponível em: https://revistas.unal.edu.co/index.php/rfc/article/view/50666. Acesso em: 29 jan. 2025.

Chicago

Dugarte Peña, Edwin, and Nelfi Gertrudis González Álvarez. 2016. “Robustificación de la carta de control multivariada √(|S|) en la fase I de control”. Revista De La Facultad De Ciencias 5 (2):12-37. https://doi.org/10.15446/rev.fac.cienc.v5n2.50666.

Harvard

Dugarte Peña, E. and González Álvarez, N. G. (2016) “Robustificación de la carta de control multivariada √(|S|) en la fase I de control”, Revista de la Facultad de Ciencias, 5(2), pp. 12–37. doi: 10.15446/rev.fac.cienc.v5n2.50666.

IEEE

[1]
E. Dugarte Peña and N. G. González Álvarez, “Robustificación de la carta de control multivariada √(|S|) en la fase I de control”, Rev. Fac. Cienc., vol. 5, no. 2, pp. 12–37, Jul. 2016.

MLA

Dugarte Peña, E., and N. G. González Álvarez. “Robustificación de la carta de control multivariada √(|S|) en la fase I de control”. Revista de la Facultad de Ciencias, vol. 5, no. 2, July 2016, pp. 12-37, doi:10.15446/rev.fac.cienc.v5n2.50666.

Turabian

Dugarte Peña, Edwin, and Nelfi Gertrudis González Álvarez. “Robustificación de la carta de control multivariada √(|S|) en la fase I de control”. Revista de la Facultad de Ciencias 5, no. 2 (July 1, 2016): 12–37. Accessed January 29, 2025. https://revistas.unal.edu.co/index.php/rfc/article/view/50666.

Vancouver

1.
Dugarte Peña E, González Álvarez NG. Robustificación de la carta de control multivariada √(|S|) en la fase I de control. Rev. Fac. Cienc. [Internet]. 2016 Jul. 1 [cited 2025 Jan. 29];5(2):12-37. Available from: https://revistas.unal.edu.co/index.php/rfc/article/view/50666

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