Gráficos de controle para o monitoramento de dados simétricos e log-simétricos

Abstract

Since the industrial revolution until to the present day it is in the industry’s interest to monitor the quality of their products, aiming at good quality product, good operation on the production line and a profitable production. In this context, control charts are the main tools used for monitoring a particular quality characteristic. Usually the monitored characteristic is the process mean and the most used control chart for such monitoring are: X of Shewhart, CUSUM and EWMA, which are based on two assumptions: independence between the monitored samples and that the monitored variable follows a normal distribution. However, breaking any of these assumptions implies in a poor control chart performance. Considering this, the present work proposes a control chart, for the monitoring of the mean, based on the bootstrap method for data that follows a distribution that belongs to the symmetric class of distributions. In addition, a monitoring method was proposed for the monitoring of the median (which in case of asymmetric data is more informative than the mean) for data that belong to the log-symmetric class of distributions, based on the empirical distribution of three new median estimators proposed by Balakrishnan et al. (2017). Additionally, simulation studies were performed for both proposed methods, in order to evaluate the in-control and the out-control average run length (ARL), to evaluate the behavior of the control limits and to compare the proposed method with the traditional methods for each situation. As result, the simulation study indicates that the proposed approaches presents better ARL0 than the usual methods. Regarding to the power of detection, the proposed methods present good performance, being comparable to traditional methods, but with the advantage of better ARL0. In addition, the work presents an application for each of the two proposed methods in order to illustrate their applicability in a real situation.