That greatly undersells the accuracy of quartz watches. An individual unit may gain or lose 15 seconds per month (though that level of inaccuracy would be unusual), but that given unit will consistently gain or lose almost the exact same amount of time every month.
After you have measured the relative speed of a given quartz movement, it becomes trivial to obtain the correct time (for, e.g., navigation purposes).
For what itβs worth, the NBS and US Naval Observatory switched from mechanical (pendulum) clocks to quartz during the Great Depression.
It's a pain in the butt. Recalibration means physically trimming the crystal. Which side you trim depends on whether it's too fast or too slow. It's really fiddly though (especially too slow, which requires grinding the ends down instead of the face). Even in the 20s they would have been producing these dozens at a time with a big lapping wheel, so they could just pick a better crystal from the same batch.
It would be possible to make the IC adjustable (e.g. a tiny microcontroller) so that it could compensate for the difference without having to modify the crystal.
After you have measured the relative speed of a given quartz movement, it becomes trivial to obtain the correct time (for, e.g., navigation purposes).
For what itβs worth, the NBS and US Naval Observatory switched from mechanical (pendulum) clocks to quartz during the Great Depression.