In practice, the observations are usually autocorrelated. The autocorrelation between successive observations has a large impact on control charts with the assumption of independence. It can decrease the in-control average run length which leads to a higher false alarm rate than in the case of independent process. This paper considers the problem of monitoring the mean of AR(1) process with a random error and provides a conditional maximum likelihood estimation method to improve the control chart performance when the sample size is small. Numerical result shows that the standard estimation method is very unstable when the sample size is small, and there is a large probability that the standard estimation method breaks down if the level of correlation between successive means is small-to-moderate. The new method given here overcomes this difficulty.
Brazilian Journal of Probability and Statistics 18(2), pp.151-162