Abstract

OLMOS-ZEPEDA, José Rodolfo  and  RAMIREZ-VALVERDE, Gustavo. Evaluation of a multivariate control chart based on data depth for non-normal observations in the presence of autocorrelation. Ing. invest. y tecnol. [online]. 2020, vol.21, n.3, 00003.  Epub Dec 02, 2020. ISSN 2594-0732.  https://doi.org/10.22201/fi.25940732e.2020.21.3.023.

The Hotelling Τ2 control chart is widely used to simultaneously monitor two or more continuous quality features. For its use to be valid, the data to be monitored is required to met two assumptions: multivariate normality and independence between observations, however, both assumptions are difficult to sustain in a real process and, consequently, the performance of the control chart it deteriorates. Liu (1995) developed a class of multivariate nonparametric or free distribution control charts based on the concept of data depth. The only assumption to use these graphs is that the observations are independent. In this work, the behavior of the control chart based on depth measurements is studied via simulation, when the assumption of multivariate normality is relaxed in the presence of autocorrelation, its behavior is compared with that of the graph Τ2. It was found that the non-parametric control chart is less affected in most of the cases studied than the parametric method.

Keywords : Control chart; Hotelling Τ² control chart; data depth; Mahalanobis depth; autocorrelation; r-chart.