Error-in-variables models in calibration

In many calibration operations, the stimuli applied to the measuring system or instrument under test are derived from measurement standards whose values may be considered to be perfectly known. In that case, it is assumed that calibration uncertainty arises solely from inexact measurement of the responses, from imperfect control of the calibration process and from the possible inaccuracy of the calibration model. However, the premise that the stimuli are completely known is never strictly fulfilled and in some instances it may be grossly inadequate. Then, error-in-variables (EIV) regression models have to be employed. In metrology, these models have been approached mostly from the frequentist perspective. In contrast, not much guidance is available on their Bayesian analysis. In this paper, we first present a brief summary of the conventional statistical techniques that have been developed to deal with EIV models in calibration. We then proceed to discuss the alternative Bayesian framework under some simplifying assumptions. Through a detailed example about the calibration of an instrument for measuring flow rates, we provide advice on how the user of the calibration function should employ the latter framework for inferring the stimulus acting on the calibrated device when, in use, a certain response is measured.