Comparative study of EWMA control charts using the GMTD model for autocorrelated processes.
Autocorrelation; ARL; EWMA; GMTD; Quality; Simulation.
Statistical quality control is one of the most important knowledge fronts of quality engineering. Its main objective is the systematic reduction of the variability in the characteristics of the product or process. One of the ways to analyze these characteristics is through the control charts, which allows the monitoring of the process. However, some assumptions are necessary for its use, as is the independence between observations. However, in practice, many processes do not fulfill this assumption and end up generating an auto-correlated process. This autocorrelation, if not noticed, can generate an increase in alarm numbers, thus stopping the process several times and leading to an increase in operating costs. Standard control charts, in general, do not involve the calculation of autocorrelation. An ideal graph to monitor small process shifts and even some autocorrelation processes is the exponentially weighted moving average, or simply EWMA. It is also desirable to use a template that allows monitoring, data series, or process, regardless of whether such data is presented linearly or non-linearly. A model that presents itself as an alternative to this situation is Transition Distribution and Gaussian Mixture, GMTD. The objective of this work is to combine the advantages of the EWMA control chart with the GMTD model and compare it with the adjustments found in the academic literature to deal with autocorrelation. Such a comparison will be made by the performance of such graphs, the most usual measure for the comparison of control chart performance is through the mean sequence length, ARL. The data used in the comparison of performance are derived from computational simulation, generated in the R software. At the end of this step, conclusions were drawn which showed the best of the graphs to deal with some autocorrelation scenarios. An alternative to using real databases is also suggested at the end of the paper.