Gráficos de Controle Multivariados de Somas Acumuladas (MCUSUM) e de Média Móvel Exponencialmente Ponderada (MEWMA)

Abstract

Statistical process control provides several tools for monitoring quality characteristics, including control. With the need to simultaneously monitoring two or more quality characteristics, control charts have extended to multivariate cases. In the monitoring of multivariate processes, in several situations, it is necessary to detect small and moderate changes. For these occasions it is recommended to use memory control plots, such as the Multivariate Cumulative Sum (MCUSUM) and Multivariate Exponentially Weighted Moving Average (MEWMA) plots. The principal component analysis (PCA) is presented as a great ally of control charts in order to reduce the size of the data and facilitate the understanding of the analysis, once a considerable number of variables is present. This paper proposes to apply the multivariate EWMA and CUSUM control charts, composed of eight variables, using the PCA. Thus, the application of PCA to the data reduces the number of variables to be analyzed for only two components. This work also presents a comparison of the Hotelling T² with MCUSUM and MEWMA considering the application of Principal Components Analysis.