{"references": ["W.A. Shewhart, Economic Control of Quality of Manufactured Product, Van Nostrand, New York, 1931.", "E.S. Page, \"Continuous inspection schemes\", Biometrika, vol.41, pp. 100-114, 1954.", "S.W. Roberts, \"Control chart tests based on geometric moving average\", Technometrics, 1, 239-250, 1959.", "W.C. Smiley and T. Keoagile, \"Max-CUSUM chart for autocorrelated processes\", Statistica Sinica, 15, 527-546, 2005.", "D. Brook, D.A. Evans, \"An approach to the probability distribution of CUSUM run length\", biometrika, 59, 539-548, 1972.", "M.S. Srivastava, Y. Wu, \"Evaluation of optimum weights and average run lengths in EWMA control schemes\", Communications in Statistics: Theory and Methods, 26, 1253 \u2013 1267, 1997.", "S.V. Crowder, \"A simple method for studying run length distributions of exponentially weighted moving average charts\", Technometrics, 29, 401-407, 1978.", "D. G. Wardell, H. Moskowitz and R.D. Plante, \"Control Charts in the Presence of Data Correlation\", Management Science, 38, 1084-1105, 1992.", "NF. Zhang, \"A statistical control chart for stationary process data\", Technometrics, 40, 24\u201338. 1998. \n[10]\tC.W. Lu, M.R. Reynolds, \"EWMA control charts for monitoring the mean of autocorrelated process\", Journal of Quality Technology, 31,166\u2013188, 1999.\n[11]\tW. Suriyakat, Y. Areepong, S. Sukparungsee, G. Mititelu., \"An analytical approach to EWMA control chart for trend stationary exponential AR(1) process\", In Proceeding for World Congress on Engineering (WCE 2012), London.\n[12]\tS. Phanyaem, Y. Areepong, S. Sukparungsee S. and G. Mititelu, \"Explicit Formulas of Average Run Length for ARMA(1,1)\", International Journal of Applied Mathematics and Statistics, 43, 392-405, 2013.\n[13]\tP. Paichit, Y.Areepong and S.Sukparungsee, \"Exact solution of Average Run Length for SARMA(P, Q)L Processes\" (Submitted)."]}

The main goal of this paper is to study Statistical Process Control (SPC) with Exponentially Weighted Moving Average (EWMA) control chart when observations are serially-correlated. The characteristic of control chart is Average Run Length (ARL) which is the average number of samples taken before an action signal is given. Ideally, an acceptable ARL of in-control process should be enough large, so-called (ARL0). Otherwise it should be small when the process is out-of-control, so-called Average of Delay Time (ARL1) or a mean of true alarm. We find explicit formulas of ARL for EWMA control chart for Seasonal Autoregressive and Moving Average processes (SARMA) with Exponential white noise. The results of ARL obtained from explicit formula and Integral equation are in good agreement. In particular, this formulas for evaluating (ARL0) and (ARL1) be able to get a set of optimal parameters which depend on smoothing parameter (λ) and width of control limit (H) for designing EWMA chart with minimum of (ARL1).