Evaluation of an uncertainty factor due to repeatable measurements by weighted statistics

A formula to evaluate uncertainty due to repeatable measurement, i.e., type A uncertainty, has been discussed for long time to revise the GUM since 2012. The discussion on type A uncertainty has not been very successful from the Bayesian viewpoint. Instead, the frequentist viewpoint has been intensified during the discussion in the literature. Nevertheless, there is one point which has not been focused on in the discussion for revising the type A uncertainty. The weighted statistics is one such point. In this study, some experimental data were examined to discuss potential use of weighted statistics for evaluating the type A uncertainty. Flow velocity signal behind a circular cylinder, and flow rate signal along a turbulent pipe flow were analyzed to get weighting functions by curve fitting histogram distributions. The effective number of measurements is suggested to relate weighted statistics to arithmetic statistics. The effective number of measurements was found to be less than or equal to 3 in this study. This indicates that the standard deviations of time series data could be converted into the type A standard uncertainty of the same quantity by arithmetic statistics with the effective number of measurements less than or equal to 3.