Diseño del gráfico de control no paramétrico basado en la distancia de Mahalanobis generalizada para datos funcionales.

Abstract

In this paper, we propose a Mahalanobis distance-based control chart with functional data for monitoring processes presenting features that can be viewed as smooth functions. In current literature, multivariate parametric graphs have been proposed in order to monitor such processes. However, in the present work we design a nonparametric control chart which is based on the Mahalanobis distance besides nonparametric control charts based on standardized L1 and standardized L2 statistics. All control charts were designed using bootstrap methods, permutations and depth measurements. Additionally, we present a simulation study where control chart performance comparisons are made using different sample sizes and threshold determining methods which detect atypical curves. Finally, the methodology developed in this work is used to analyze the effect of a medical procedure on patients with high and low risk of brain aneurysm. In particular, our method is used to monitor the time derivative of the radius of aneurysms along the internal carotid artery.