Abstract—Statistical process control (SPC) is widely used to monitor and improve quality in industrial processes. Cumulative sum (CUSUM) chart is an effective tool in statistical process control for detecting change in a process mean. The main purpose of this paper is to present the numerical integration of Average Run Length (ARL) of CUSUM chart when observations are seasonal autoregressive and moving average of order (P,Q)L denoted by SARMA(P,Q)L process with exponential white noise. In addition, we compare the ARL between Cumulative Sum (CUSUM) and Exponentially Weighted Moving Average (EWMA) charts. The results show that the EWMA chart is superior to the CUSUM control chart in the case of process has small shifts in mean.

Index Terms—Seasonal autoregressive and moving average order (P,Q)L, process, cumulative sum (CUSUM), average run length (ARL).

Suvimol Phanyaem is with Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok, Thailand (email: suvimol.p@sci.kmutnb.ac.th).

Cite: Suvimol Phanyaem, "Numerical Integration Method of Average Run Length for SARMA(P,Q)L Process Base on CUSUM Procedure," International Journal of Applied Physics and Mathematics vol. 6, no. 4, pp. 200-206, 2016.