This paper establishes two stochastic monotonicity results concerning the run length of an upper one?sided Exponentially Weighted Moving Average (EWMA) control chart, based on the logarithm of the sample variance, for monitoring a process standard deviation. These properties cast interesting light on the control chart performance, and their extension to other one?sided EWMA and CUSUM control charts is straightforward.

CEMAT - Center for Computational and Stochastic Mathematics