Uncertainty Calculation for the Ratio of Dependent Measurements

Published

June 1, 2003

Author(s)

C M. Wang, H K. Lyer, J Hannig

Abstract

In this paper we consider the problem of computing an uncertainty interval a ratio with a prescribed confidence level. Although an exact confidence interval procedure, known as the Fieller interval, is available for this problem, practitioners often use various non-exact methods. One such non-exact method is based on the propagation of error approach described in the ISO Guide to the Expression of Uncertainty in Measurement to calculate the standard uncertainty. A confidence interval with presumed confidence level of 95% is obtained by using a coverage factor k = 2. We demonstrate that, using n-1 degrees of freedom for the standard uncertainty, and the corresponding coverage factor of the t table value, leads to uncertainty intervals which are nearly identical to Fieller's exact intervals whenever the measurement relative uncertainties are small. In addition, they are easy to compute and may be recommended for routine use in metrological applications.

Citation

Metrologia

Pub Type

Journals

Keywords

coverage probability, fieller interval, ISO GUM, propagation of error

Citation

Wang, C. , Lyer, H. and Hannig, J. (2003), Uncertainty Calculation for the Ratio of Dependent Measurements, Metrologia (Accessed December 5, 2024)