Modification of ARL for detecting changes on the double EWMA chart in time series data with the autoregressive model

Abstract

This research aims to derive the average run length (ARL) evaluation of the double exponentially weighted moving average (double EWMA) control chart for observation data that follows exponential white noise in a time series model with an autoregressive model. Since most real-world data is automatically correlated, autoregressive models are available. Comparisons were made between the ARLs obtained using the explicit formula and the numerical integral equation (NIE) approach. The results showed that the explicit formula's use of the ARL outperformed the NIE approach in terms of computation time. After that, the efficacy of the exponentially weighted moving average (EWMA) and double EWMA charts is then compared using the suggested explicit ARL formula. The ARL of the double EWMA chart was found to perform better than the ARL of the EWMA chart in all situations. It also uses natural gas and diesel prices on stock exchanges around the world as cases studies. The results show that the double EWMA chart has better detection sensitivity than the EWMA chart, and the results are consistent with the experimental results. As a result, the sensitivity of the double EWMA chart in detecting changes makes it a good alternative for monitoring processes with real-world data.

KEYWORDS:

• Average run length
• autoregressive model
• double EWMA control chart
• EWMA control chart
• explicit formulas
• numerical integral equation

Acknowledgements

The authors would like to express our gratitude to National Research Council of Thailand (NRCT) and King Mongkut’s University of Technology North Bangkok for supporting the research fund with contact no. N42A650318.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This project was supported by National Research Council of Thailand (NRCT) and King Mongkut’s University of Technology North Bangkok [grant number N42A650318].