Abstract—The main purpose of this paper is to present the numerical integration of average run length (ARL) for the Cumulative Sum (CUSUM) control chart. In addition, we compare the ARL between the cumulative sum (CUSUM) and the exponentially weighted moving average (EWMA) control charts for an autoregressive and moving average process, ARMA(p, q) with exponential distribution white noise. The results show that the EWMA control chart is superior to the CUSUM control chart when the process has small shifts in the process mean.

Index Terms—Autoregressive and moving average (ARMA), cumulative sum (CUSUM), exponentially weighted moving average (EWMA), average run length (ARL).

The authors are with the Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok, 10800, Thailand (e-mail: suvimolp@kmutnb.ac.th, yupaporna@kmutnb.ac.th, swns@kmutnb.ac.th; tel.: 662-555-2000; fax: 662-585-6105).

Cite: S. Phanyaem, Y. Areepong, and S. Sukparungsee, "Numerical Integration of Average Run Length of CUSUM Control Chart for ARMA Process," International Journal of Applied Physics and Mathematics vol. 4, no. 4, pp. 232-235, 2014.