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. This paper proposes a heuristic method based on adjusted weighted standard deviation for constructing R chart for skewed process distributions. The asymmetric control limits of the chart arc established with no assumption to the process distribution. If the process distribution is symmetric those control limits are equivalent to those of Shewhart R chart. The proposed control limits are compared with weighted variance R chart and skewness correction R chart by Monte Carlo simulation. When the process distribution is Weibull or gamma, simulation results show that the proposed R chart performs better than both weighted variance and skewness correction R chart as the skewness and the sample size increase. For the case where the process distribution is exponential with known mean the Type I risk and Type II risk of the proposed R chart are closer to those of the exact R chart than those of the weighted variance and skewness correction R charts.
Brazilian Journal of Probability and Statistics 18(2), pp.151-162