Análise de desempenho do gráfico de Shewhart para o processo POMINAR(1)

Abstract

Since the industrial revolution to the present day it is in the industry's interest to monitor the quality of their products. That way, the techniques of statistical process control (SPC), especially control charts, are used to monitor certain quality characteristics. Nowadays, because of the nature of many processes, it is common to model such data through models that capture the autocorrelation among. Thus, time series models of integer values together with modified control charts are being widely used in order to better monitor processes with presence of autocorrelation and that the monitored variable has a measure expressed by integers values. Based on all these features, this study has the main purpose of constructing the appropriate Shewhart chart, or $\overline{X}$ Chart, to monitor data from a POMINAR(1) process and to evaluate its performance in some scenarios. Both the construction of the chart and the performance evaluation will be performed through computational studies using the Monte Carlo method in the generation of the control limit and in the performance evaluation of the chart. We will analyze the proposed control chart based on the in-control average run length ($ARL_0$) and out-control average run length ( $ARL_1$) in 50 different scenarios. The modified Shewhart chart presented a good performance in relation to $ARL_0$ wich was around 240 and 400 samples, in relation to detection of mean deviations the chart present $ARL_1$ around 20 and 3 samples. But as the deviation from the mean increases the $ARL_1$ decreases to 3 samples.

Autocorrelation Process. Statistical Process Control. Time Series of Integer Values. X Chart.