Assessment of measurement uncertainty via observation equations
Antonio M. Possolo, Blaza Toman
According to the Guide to the Expression of Uncertainty in Measurement, measurement uncertainty is assessed by computational propagation of error based on a measurement equation that expresses the measurand as a known function of input variables. However, in measurement situations where some of these input variables in turn depend on the measurand, this approach is circuitous and ultimately impracticable. An alternative approach to measurement uncertainty that starts from the observation equation or, more generally, from a statistical model that relates the observations to the measurand, allows a uniform treatment of all relevant cases, including those where the measurement equation suffices. In particular, this approach facilitates the exploitation of pre-existing information about the measurand, and the updating of such information by incorporation of the information that fresh experimental data may provide about the measurand. And when all that is known about some of the data is that their values are above or below certain bounds (for example, when some observations are censored), then it makes best use of all relevant information, albeit incomplete. The widest applicability of the statistical approach, and the uniform treatment of diverse metrological problems that it allows, especially within the context of Bayesian inference, is illustrated with detailed examples concerning the lifetime of mechanical parts, the measurement of mass, the calibration of a non-linear model in biochemistry, and the estimation of a consensus value for arsenic concentration in a sample measured by multiple laboratories.