Bayesian evaluation of the standard uncertainty and coverage probability in a simple measurement model

Bayesian analysis is used to evaluate the standard uncertainty and coverage probability corresponding to a measurand Z modelled as the sum of two quantities X and Y . It is assumed that the information about X is cast in the form of Gaussian or rectangular probability density functions, whereas that about Y consists of a series of independently measured values. Prior information about Z is also taken into account. Results are compared with those obtained using the procedure recommended in the ISO Guide to the Expression of Uncertainty in Measurement. It is shown that the application of Bayes' theorem leads to an improved method for evaluation of uncertainty, particularly in the case of the coverage probability.