Bayesian analysis of repeated measurements affected by a systematic error and its application to conformity assessment

The Bayesian analysis of a series of correlated indications of an unknown quantity is here presented when they are modelled by a joint Gaussian distribution and their covariance is assumed to be the (known) squared uncertainty associated with a systematic effect common to all the indications. An interesting application of the obtained results to the conformity assessment of a series production is also presented. A criterion is derived so that at least a portion p1 of the series production shows to have a characteristic value below a prescribed limit, with a probability not less than p2.