Performance Measurement of a DMEWMA Control Chart on an AR(p) Model with Exponential White Noise

Abstract

The double-modified exponentially weighted moving average (DMEWMA) control chart running an autoregressive (AR) process is proposed to detect unusual events. The AR equation and the DMEWMA statistic are combined to evaluate the control limit of the exponential residual term to obtain the explicit formula for the average run length (ARL). The ARLs computed using the explicit formula approach and the well-established numerical integral equation method were compared to validate the former. The efficiencies of the original EWMA, MEWMA, and DMEWMA control charts running AR processes based on simulation and real data were compared by using the results of ARL and relative mean index calculations. The results indicate that the explicit formula for the ARL of an AR process running on a double-modified EWMA control chart detected changes more quickly than on either of the other two control charts for small and moderate changes. Finally, real data on COVID-19 is provided to demonstrate the application of this explicit formula.