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 quan tities X and Y. It is assumed that the information about X is cast in the f orm of Gaussian or rectangular probability density functions, whereas that about Y consists of a series of independently measured values. Prior inform ation about Z is also taken into account. Results are compared with those o btained using the procedure recommended in the ISO Guide to the Expression of Uncertainty in Measurement. It is shown that the application of Bayes' t heorem leads to an improved method for evaluation of uncertainty, particula rly in the case of the coverage probability.