On the confidence interval of measurement uncertainties

Abstract

Measurement uncertainty is a core term in metrology. It is widely used, but often under assumptions that are valid for a large number of measurements. However, the confidence interval of individual measurement uncertainty evaluations has not been analyzed in such depth. The confidence interval for measurement uncertainties evaluated increases as the number of measurements decreases. The paper addresses this problem, which is also important for calibration measurement capabilities as well as for evaluations of international metrological comparisons. Quantification of uncertainty is also important for new measurement and simulation methods. The paper discusses the bias and confidence interval of evaluated measurement uncertainties for normally distributed measurements and presents proposed formulae for the coverage factor for an improvement of their evaluations. The effect of correlations on measurements is also presented. The correlation estimator indicates a correlation for a small number of measurements, even though the measurements are not correlated. Therefore, a formula for the uncertainty of correlation is also presented for uncorrelated measurements. These formulae allow for an improved estimation of measurement uncertainty.