A study of relationship between the maximum time interval error and Allan variance

The maximum time interval error (MTIE) and the Allan variance are commonly used to analyze or evaluate time-frequency signal generation and transmission systems. In some applications, measuring the maximum time interval error is more convenient than measuring Allan variance. To find whether there is a definite statistical relationship between them or whether it is possible to estimate the Allan variance via the maximum time interval error, we performed mathematical analysis and derivation. The results show that while direct conversion between them is impossible, an upper limit of the Allan variance exists for a fixed maximum time interval error, which holds for different sampling times. This relation is verified with the specific data generated by the computer program under five noise patterns in the Power Law Noise Model. Both derivation and data verification show that the upper limit of the Allan variance can be determined according to the maximum time interval error of the sampled data.