  Investigating the problem of setting control limits in the case of parameter
uncertainty is more accessible when monitoring the variance because only one
parameter has to be estimated. Simply ignoring the induced uncertainty
frequently leads to control charts with poor false alarm performances.
Adjusting the unconditional in-control (IC) average run length (ARL) makes the
situation even worse. Guaranteeing a minimum conditional IC ARL with some given
probability is another very popular approach to solving these difficulties.
However, it is very conservative as well as more complex and more difficult to
communicate. We utilize the probability of a false alarm within the planned
number of points to be plotted on the control chart. It turns out that
adjusting this probability produces notably different limit adjustments
compared to controlling the unconditional IC ARL. We then develop numerical
algorithms to determine the respective modifications of the upper and two-sided
exponentially weighted moving average (EWMA) charts based on the sample
variance for normally distributed data. These algorithms are made available
within an R package. Finally, the impacts of the EWMA smoothing constant and
the size of the preliminary sample on the control chart design and its
performance are studied.
