Application of robust multivariate control chart with Winsorized Mean: a case study

Abstract

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.