Monte Carlo Evaluation of the Uncertainty in a Calibrated Instrument

A Monte Carlo procedure is presented for computing the joint state-of-knowledge probability distribution to be assigned to the parameters of a calibration function. The procedure is fully in line with the approach in Supplement 1 to the Guide to the Expression of Uncertainty in Measurement. It consists of propagating the joint probability distribution of the calibration quantities through the mathematical model of the measurement by which the parameters are defined. Usually this model is derived from a least-squares adjustment procedure. When the instrument is in use, we desire to obtain the probability distribution for the stimulus that corresponds to an indicated response. This goal can be accomplished by propagating the distributions for the parameters of the calibration curve, together with the distribution of the indicated response.