Simulation approach for assessing the performance of the γEWMA control chart
i) Purpose: The purpose of this paper is to evaluate the performance of a modified EWMA control chart ($\gamma$EWMA control chart), which considers data distribution and incorporate its correlation structure, simulating in-control and out-of-control processes and to select an adequate value for smoothing parameter with these conditions. ii) Design/methodology/approach: This paper is based on a simulation approach using the methodology for evaluating statistical methods proposed by Morris et al. (2019). Data were generated from a simulation considering two factors that associated with data: (1) quality variable distribution skewness as an indicator of quality variable distribution; (2) the autocorrelation structure for type of relationship between the observations and modeled by AR(1). In addition, one factor associated with the process was considered, (1) the shift in the process mean. In the following step, when the chart control is modeled, the fourth factor intervenes. This factor is a smoothing parameter. Finally, three indicators defined from the Run Length are used to evaluate γEWMA control chart performance this factors and their interactions. iii) Findings: Interaction analysis for four factor evidence that the modeling and selection of parameters is different for out-of-control and in-control processes therefore the considerations and parameters selected for each case must be carefully analyzed. For out-of-control processes, it is better to preserve the original features of the distribution (mean and variance) for the calculation of the control limits. It makes sense that highly autocorrelated observations require smaller smoothing parameter since the correlation structure enables the preservation of relevant information in past data. iv) Originality/value: The $\gamma$EWMA control chart there has advantages because it gathers, in single chart control: the process and modelling characteristics, and data structure process. Although there are other proposals for modified EWMA, none of them simultaneously analyze the four factors nor their interactions. The proposed $\gamma$EWMA allows setting the appropriate smoothing parameter when these three factors are considered.