Comparison of three approaches for computing measurement uncertainties

This paper compares three approaches for computing measurement uncertainties: GUM’s confidence interval (CI) based approach, Bayesian approach, and probability interval (PI) based approach in a recently proposed unified theory of measurement errors and uncertainties. The key concepts underlying the three approaches are discussed. The similarities of and differences between the three approaches are explored. We focus on a simple problem that is often encountered in practice: Type A and Type B evaluation of uncertainty with a small number of observations. The logical frameworks of the three approaches for the problem considered are discussed. Some misinterpretations of and confusion about several statistical concepts involved in uncertainty analysis are clarified. We conclude that the PI-based approach is superior to both the GUM’s CI-based approach and Bayesian approach. The revision of the GUM should adopt the PI-based approach for computing measurement uncertainties.