In this context "stable" means the thing it means in statistical process control, i.e. the operational definition of no measurements outside of 2.66 times the mean consecutive difference between observations.
It is a problem -- particularly for software -- that SPC tools do not work with subexponential distributions, but it's separate from the observation that when SPC determines that a process is stable, rougly half of measurements will lie above the average.
It is a problem -- particularly for software -- that SPC tools do not work with subexponential distributions, but it's separate from the observation that when SPC determines that a process is stable, rougly half of measurements will lie above the average.