A practical two-step procedure for taking into account all available information (prior and current) about influence quantities in measurement uncertainty analysis

This paper considers the problem of computing the combined standard uncertainty of an indirect measurement, in which the measurand is related to multiple influence quantities through a measurement model. In practice, there may be prior information or current information, or both, about the influence quantities. We propose a practical two-step procedure for taking into account all available information (prior and current) about influence quantities in measurement uncertainty analysis. The first step is to combine prior and current information to form the merged information for each influence quantity based on the weighted average method or the law of combination of distributions. The second step deals with the propagation of the merged information to calculate the combined standard uncertainty using the law of propagation of uncertainty or the principle of propagation of distributions. The proposed two-step procedure is based entirely on frequentist statistics. A case study on the calibration of a test weight (mass calibration) is presented to demonstrate the effectiveness of the proposed two-step procedure and compare it with a subjective Bayesian approach.