Use of the Monte Carlo method for the estimation of measurement uncertainty in chemical analysis systems with intensive mathematical treatment

In recent years, the scientific community has made great efforts to establish procedures for the estimation of uncertainty in various measurement processes in laboratories. In this regard, the Guide to the Expression of Uncertainty in Measurement has been one of the most widely used documents for the estimation of uncertainty values in measurement processes. In spite of its success, the linear propagation method of uncertainties proposed in this guide presents serious deficiencies when trying to estimate uncertainty in measurement or calibration processes where an intensive mathematical treatment is used, particularly when these introduce important sources of variability. An example of this is the quantification of Sn, Sb and Cu in Babbitt metal by energy-dispersive X-ray fluorescence. In this material, Sn and Sb present a strong spectral interference between their different lines, which forces the use of mathematical methods of deconvolution and correction of inter-element effects that introduce sources of variability usually neglected. This work proposes an alternative to the uncertainty quantification based on the Monte Carlo method where the sources of variability resulting from the spectral treatment and matrix effects are included. Methodologies for the establishment of the main practical aspects of the Monte Carlo method and its adaptation to calibration methodologies are also proposed. The influence of disregarding the variability introduced by the spectrum treatment algorithms on the uncertainty estimation is shown.