Semantic analysis of compound terms in metrology. Part 2: Risk in measurement and calculations

Prior to the requirement for testing and calibration laboratories to take into account the risk of statistical assumptions, false accept, and false reject, the methodology of the Guide to the Expression of Uncertainty in Measurement relying on the Bayesian and Monte Carlo approaches was stated by international documents to be inapplicable to calculating probabilistic risk characteristics. The revision draft of the Guide attempted to shift the interpretation of measurement uncertainty from the scattering parameter to the probability distribution. An attempt to address the problem of definitional uncertainty in the International Vocabulary of Metrology-Basic and General Concepts and Associated Terms was unsuccessful. The revised version of General Statistical Terms and Terms Used in Probability excluded the term "measurement uncertainty," with one of the notes stating that the probabilistic properties of outcome uncertainty are fully described by the probability distribution. However, due to the new requirements for risk calculations, international documents were promptly put into effect without radical assessments of the inapplicability of the Bayesian approach and the Monte Carlo method; the drawbacks were redefined as limitations; however, no specific guidelines on risk calculations were provided. Drawing on the composition-based approach to accuracy assessment, the author recommends a procedure relying on the convolution of probability distributions in the form of a modified inversion formula, which provides a means to factor in definitional uncertainty in the moment-based approach. It was found that a way to factor in definitional uncertainty through the convolution of uniform distributions is indicated in the Guide but not applied.