Allan Variance Analysis of Josephson Voltage Standard Comparison for Data Taken at Unequal Time Intervals

Stochastic serial correlations are often ignored in the statistical uncertainty (Type A) analysis of measurement values. For repeated measurements, the standard deviation of the mean is often used to specify Type-A uncertainty, but it is frequently underestimated by assuming that it is given by the standard deviation divided by the square root of the number of measurements. Methods of time-series analysis such as the Allan variance (Avar) formalism give realistic estimates of Type-A uncertainty, but they require equal time intervals between successive measurements. This requirement is difficult to satisfy in comparisons of Josephson voltage standards (JVSs) because of the instability of the voltage steps and the small number of repeated measurements. A JVS comparison was made using a completely automatic compact JVS. The time intervals were uneven; thus, we studied the effect of their irregularity on the Avar by simulating data having the same noise model and uneven time intervals as the measured data. We found that, for this JVS comparison, the Avar is only slightly affected by uneven intervals. The noise was found to be a mixture of white and 1/ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> noise. The latter limits the Allan deviation to 0.64 nV after 14.3 h of measurement. The method of simulating data this way should be applicable to other complex measurement situations.