Assembly of PXL Programs : Commercial Timing Devices : Parts and Manufacturing : Stability

Stability
The widely adopted and by far the most simple measure of clock stability is the co called Allan Variance, internationally known as two sample sigma. It is computed as follows: Form the squares of the second differences, add them, divide by 2 times the number of terms and form the square root. This gives 86 / 28 = 3.07; the square root finally gives 1.75ms/day as the measure of stability. Such stability measures are also often expressed in relative terms, i.e., as parts per million, etc. One finds the translation between these two styles by remembering that one day has 86400 s. Therefore 1ms rate change per day corresponds with (1.0E-3) / 8.64E4 = 1.157 parts in 10 to the eight.
Our test clock, therefore, exhibits a frequency instability of 2.02 parts in 10 to the eight from day to day (1.157x1.75).
Remember: A clock error is given in units of time (s, ms, ns), whereas a rate difference is given as a relative number or as ms/day, ns/day, etc.
More information is available in literature upon request. Time Service Dept., U.S. Naval Observatory, Washington, DC

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