The Allan variance and the rms time error

Abstract

Abstract The traditional plot of a clock's time error versus time is far superior to the Allan variance for showing a pendulum clock's time performance. The Allan variance is admittedly a universal and statistically more accurate measure of a clock or oscillator's random frequency and time variations (that is, variance), because it is averaged over multiples of each time interval. However, it is a whole curve on a graph instead of being just a single memorable number, and its value is drastically reduced by the short time span it is able to cover. The variance, however, can be used to generate an oscillator's ‘root mean square (rms) time error versus time’ curve, a curve that is much easier to understand. But the rms time error's equally short time span also drastically limits its value to the clockmaker.