An Efficiency of DMEWMA Control Chart to Monitor Changes in Process Mean on First Order Moving Average Model with Application to Daily Natural Gas Data

Julalak  Neammai; Yupaporn Areepong Areepong; Saowanit  Sukparungsee

Authors

Julalak Neammai Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok, Thailand
Yupaporn Areepong Areepong Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok, Thailand
Saowanit Sukparungsee Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok, Thailand

Keywords:

Double MEWMA control chart, moving average process, average run length, numerical integer equations, exact formula

Abstract

The double modified exponentially weighted moving average (DMEWMA) control chart is a mixture of two modified exponentially weighted moving average (MEWMA) control chart for monitoring shifts in the process mean. The average run length (ARL) is important for evaluating the performance of control charts. The purpose of this research is to derive the exact formula for ARL on the DMEWMA Control Chart for moving average process order one in one-sided. The absolute percentage relative error (APRE) was used to compare the accuracy of the exact formula to four quadrature distinct numerical integral equation approaches (NIE). Following that, Banach's fixed point theorem is applied to ensure its existence and uniqueness. Furthermore, the effectiveness of the DMEWMA control chart is compared to that of the EWMA and MEWMA control charts. The ARL, the Standard Deviation Run Length (SDRL), and the relative mean index (RMI) are measurement tools used to assess a control chart's capacity to detect process mean. The results demonstrate that the ARL generated by the exact formula and the NIE approach are almost the same, but the exact formula can assist reduce computational (CPU) time. This is further expanded to provide performance comparisons with the EWMA and MEWMA control charts. For almost all scenarios, the DMEWMA control chart outperforms the EWMA control chart and the MEWMA control chart. Finally, the ARL analytical solution gets utilized on real-world data.

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