The objective of this paper is to show an explicit formulas of the Average Run Length (ARL) for Exponentially Weighted Moving Average (EWMA) chart when observations are described by Moving Average order q (MA(q)) processes with exponential white noise. The ARL is a traditional measurement of control chart’s performance, the expected number of observations taken from an in-control process until the control chart falsely signals out-of-control is denoted by ARL0. An ARL0 will be regarded as acceptable if it is large enough to keep the level of false alarms at an acceptable level. A second common characteristic is the expected number of observations taken from an out-of-control process until the control chart signals that the process is out-of-control is denoted by ARL1. In particular, the explicit analytical formulas for evaluating ARL0 and ARL1 be able to get a set of optimal parameters which depend on a smoothing parameter ( ) and width of control limit ( ) for designing EWMA chart with minimum of ARL1.