  The traditional variable control charts, such as the X-bar chart, are widely
used to monitor variation in a process. They have been shown to perform well
for monitoring processes under the general assumptions that the observations
are normally distributed without data contamination and that the sample sizes
from the process are all equal. However, these two assumptions may not be met
and satisfied in many practical applications and thus make them potentially
limited for widespread application especially in production processes. In this
paper, we alleviate this limitation by providing a novel method for
constructing the robust X-bar control charts, which can simultaneously deal
with both data contamination and unequal sample sizes. The proposed method for
the process parameters is optimal in a sense of the best linear unbiased
estimation. Numerical results from extensive Monte Carlo simulations and a real
data analysis reveal that traditional control charts seriously underperform for
monitoring process in the presence of data contamination and are extremely
sensitive to even a single contaminated value, while the proposed robust
control charts outperform in a manner that is comparable with the traditional
ones, whereas they are far superior when the data are contaminated by outliers.
