Water pH and active ingredient concentration are two of the most important variables to consider in the manufacturing process of fungicides. If these variables do not meet the required standards, the quality of the product may be compromised and lead to poor fungicide performance when water is used as the application carrier, which is in most cases. Given the correlation between the variables, these kinds of manufacturing processes must be analyzed in multivariate settings. Thus, this paper analyzes the variables involved in the process using the multivariate control chart |S| introduced by J. A. Vargas. In the original chart, the arithmetic mean is used as the mean vector estimator. However, in this investigation the arithmetic mean was replaced by the Winsorized Mean for the purpose of evaluating the chart performance with a robust estimator. The results show that using the new estimator, the control chart is able to detect shifts in the variation of the mean vector that the traditional estimator did not. Furthermore, different subgroup sizes for the data were studied in order to examine the performance of the chart in each case. It was found that the proposed control chart is more sensible to changes when the subgroups consist of less observations, since it is able to better identify the outliers in the sample.
Resumen— El monitoreo global de la calidad de un producto está sujeto a la evaluación simultánea de varias de sus características; es necesario bajo estas condiciones la implementación de las cartas de control tipo multivariadas. La variabilidad, en este caso la matriz de varianza covarianza, es sin duda el más importante de los estadísticos desde la perspectiva multivariada, que puede ser monitoreada con distintas cartas. Entre éstas se encuentran: las cartas Shewhart, CUSUM y EWMA. En este artículo se desarrolla una metodología de implementación de la Media Winsorizada en la carta de control multivariada de varianza efectiva |S|, encontrando una gran utilidad en procesos con valores extremos. El estudio muestra además una comparación entre la carta de control tradicional multivariante y la carta propuesta, que muestra mayor sensibilidad.Abstract— The global quality monitoring of a product is often subject to the simultaneous evaluation of several of its features; under these circumstances it is necessary to implement multivariate control charts. Variability, in this particular case, the variance-covariance matrix is indisputably the most important of the statistics from the multivariate perspective and it can be monitored with different charts, among these: Shewhart, CUSUM and EWMA. This article develops the Winsorized Mean in the effective variance multivariate control |S|-chart implementation methodology and it was demonstrated that the modification was more efficient when the sample hat outliers. This study shows a comparison between the traditional multivariate control chart and a proposed chart which was found to have more sensitivity.
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