Abstract—The paper propose the method for analyze the explicit formula of Average Run Length (ARL) of Exponentially Weighted Moving Average (EWMA) when the random observations are seasonal moving average order q; SMA(Q)L with exponential white noise. The numerical results from explicit formula and the Gauss-Legendre quadrature rule are presented. The results show that ARL from both methods are in good agreement and useful to detect change in process. In addition, this paper show comparison between explicit formulas of ARLs from EWMA and CUSUM charts to monitor the process.

Index Terms—Exponentially weighted moving average (EWMA), cumulative sum chart (CUSUM), seasonal moving average, fredholm integral.

Kanita Petcharat is with Department of Applied Statistics, King Mongkut's University of Technology North Bangkok, Thailand (email: kanita.p@sci.kmutnb.ac.th).

Cite: Kanita Petcharat, "Explicit Formula of ARL for SMA(Q)L with Exponential White Noise on EWMA Chart," International Journal of Applied Physics and Mathematics vol. 6, no. 4, pp. 218-225, 2016.