Analytical method of average run length for trend exponential AR(1) processes in EWMA procedure

The Exponentially Weighted Moving Average (EWMA) procedure are used for monitoring and detecting small shifts in the process mean which performs quicker than the Shewhart control chart. Usually, the common assumption of the Statistical Process Control (SPC) is the observations are independent and identically distributed (IID). In practice, however, the observed data are from industry and finance is serially correlated with trend. In this paper, we extend to use CUSUM procedure to compare with EWMA procedure. The performance of latter is superior to the former when the magnitudes of shift are small to moderate. It is shown that EWMA procedure performs better than the CUSUM procedure for the case of trend exponential AR(1) processes.