Análise de desempenho do gráfico de controle por grupos com base em estatística de ordem

Abstract

The use of Shewhart charts is not recommended for monitoring processes with multiple production flows, which can generate samples with items from different populations. This situation can affect the effectiveness of control charts in identifying special causes of variation. A common approach is to use a pair of Shewhart charts for each flow, but this can make monitoring more complex and time-consuming. Another option is to use the Group Control Chart, which allows controlling multiple flows with a single pair of charts. However, both types of charts can be influenced by the presence of correlation between flows, violating the assumption of independence of samples. Therefore, this work proposes a method for estimating the distribution of the maximum and minimum of a Dependent Multivariate Normal, which can handle the dependence between observations and allow the simulation of different scenarios by changing the mean and variance of the process. The method is used to compare the performance of Group Control with the traditional Shewhart chart, showing competitiveness in scenarios with low correlation between data and performing better when the correlation is high. This method is applied to a practical dataset, demonstrating its applicability and illustrating how the group chart is sensitive to changes in the mean or variance of the process, with detections of points outside the control limits becoming faster. Additionally, it was found that the method for obtaining the NMA based on the proposed method in this study was more efficient than the Monte Carlo method, demonstrating greater theoretical robustness.