Estimation of the percentile maximum time interval error of Gaussian white phase noise

The MTIE is historically one of the main time-domain quantities considered for the specification of clock stability requirements in telecommunications standards. In this paper, MTIE is first introduced according to its classical definition and as a percentile quantity. Then, the percentile MTIE is estimated under the assumption of time error (TE) affected by Gaussian white phase modulation noise, by deriving the probability distribution, of the TE spanned range as a function of the noise standard deviation σ. The formulas herein derived may allow to interpret common Allan-variance factory specifications in terms of percentile MTIE as well. In order to support the theory with sound experimental evidence, some results measured on state-of-the-art telecommunications clocks are eventually provided