Components of measurement uncertainty from a measurement model with two stages involving two output quantities

Abstract

The GUM uncertainty framework and the Monte Carlo Method can be extended to include multistage measurement models and measurement models having more than one output quantity. A typical multistage measurement model, that also includes a measurement stage with more than one output quantity is the calculation of the coefficients of a calibration curve, constructed by means of least squares regression and the subsequent use this calibration curve for the estimation of a quantity value. In the present work the Monte Carlo Method was used to evaluate the component of measurement uncertainty from a calibration curve used for the determination of the total nitrogen found in a gasoline sample. The slope and the intercept of the calibration curve were treated as a vector output quantity characterized by a joint probability distribution (bivariate Gaussian) and two types of coverage regions were estimated (rectangular and ellipsoid). The Monte Carlo Method algorithm employing fixed number of trials (106) gave a predicted value of 2.09mgL−1, a standard measurement uncertainty of 0.04mgL−1 and a 95% symmetrical coverage interval [2.01–2.17] mgL−1. The standard measurement uncertainty obtained by MCM agrees well with the outcome of the equation giving the standard error of the estimate.