Treatment of uncertainties in precision measurements

A procedure is proposed for expressing and handling uncertainties in precision measurements. It is based on the least squares method and conforms with the German standard DIN 1319 Part 4 for the treatment of uncertainties in the evaluation of measurements. The procedure is applicable to most of the arising evaluation tasks, is quite simple on the level of differential and matrix calculus, and is well-suited for computer-aided measurements and estimations. Its consistency allows successive evaluations to be made. All physical quantities in question, e.g., measured and influence quantities, as well as the result quantities of ultimate interest and the parameters to be estimated, are regarded as random variables. The covariance matrix of the estimation of their true (expectation) values serves as a measure of the uncertainty.