Abstract: These paper, we approximate the average run length
(ARL) for CUSUM chart when observation are an exponential first
order moving average sequence (EMA1). We used Gauss-Legendre
numerical scheme for integral equations (IE) method for approximate
ARL0 and ARL1, where ARL in control and out of control,
respectively. We compared the results from IE method and exact
solution such that the two methods perform good agreement.