Abstract:The control charts with exponentially weighted moving average (EWMA) had been shown to be effective for detecting small shifts in the mean of the process characteristic. When the data depart from normality or have the presence of outliers, the sample median might be used to provide a fairer representation of centrality of the data. In the present paper, the performances of the EWMA median control charts are evaluated under several distributions. The average run length (ARL) is applied to evaluate the performance of control charts, and the method for calculating ARL of the EWMA median chart is developed using the integral equation approach. Based on our study, the EWMA median chart with a small value of smoothing constant has a low false alarm rate. But as the shift of process mean is large, to maintain the detection ability of the chart, the value of smoothing constant should be increased. In addition, if the data follow a heavy-tailed distribution, it can be shown that the EWMA median chart is always more efficient than the EWMA average chart in detecting the shift of process mean.
Abstract:The control charts with exponentially weighted moving average (EWMA) had been shown to be effective for detecting small shifts in the mean of the process characteristic. When the data depart from normality or have the presence of outliers, the sample median might be used to provide a fairer representation of centrality of the data. In the present paper, the performances of the EWMA median control charts are evaluated under several distributions. The average run length (ARL) is applied to evaluate the performance of control charts, and the method for calculating ARL of the EWMA median chart is developed using the integral equation approach. Based on our study, the EWMA median chart with a small value of smoothing constant has a low false alarm rate. But as the shift of process mean is large, to maintain the detection ability of the chart, the value of smoothing constant should be increased. In addition, if the data follow a heavy-tailed distribution, it can be shown that the EWMA median chart is always more efficient than the EWMA average chart in detecting the shift of process mean.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.