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.
Relation:
Brazilian Journal of Probability and Statistics 18(2), pp.151-162