On Designing of Extended EWMA Control Chart for Detecting Mean Shifts and Its Application

Abstract

Extended exponentially weighted moving average (Extended EWMA) control chart is one of the control charts for efficient monitoring and detecting changes in the process mean. The average run length (ARL) is a metric commonly used to evaluate and quantify the performance of control charts. This study aims to propose the explicit formulas of ARL on the extended EWMA control chart for moving average with exogenous variables model (MAX(q,r)) with exponential white noise. The accuracy of the solution from the extended EWMA control chart was compared with that from the numerical integral equation (NIE) method.  The results show that the ARLs obtained from the explicit formula and the NIE method are not different. After obtaining the ARL values from the explicit formula method of the extended EWMA control chart, it was compared with the exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) control charts. In this research, the standard deviation run length (SDRL) and median run length (MRL) values are also presented which are the important performance metrics used for evaluating the effectiveness of control charts in detecting out-of-control conditions. Both MRL and SDRL were calculated in addition to the ARL values to assess the performance of control charts. The results show that the performance of the extended EWMA control chart is better than the EWMA and CUSUM control charts in all scenarios. In addition, this explicit formula of the ARL is demonstrated to be used in practical applications.