Standard addition method with cumulative additions: Monte Carlo uncertainty evaluation

The cumulative standard addition method allows the calibration of an instrument affected by matrix effects when a small sample volume is available. Recently, it was developed and validated a metrologically sound procedure to estimate the uncertainty of these measurements based on the modelling of the uncertainty of the extrapolation of the calibration curve by the linear least squares regression model. However, this procedure is only applicable when the uncertainty of cumulative sample dilutions and analyte mass additions are negligible given the uncertainty of the total solution volume (v) times the instrumental signal (I) (i.e. v∙I). This work developed a measurement uncertainty model, not limited by this assumption of the quality of calibrators preparation, based on Monte Carlo simulations. This method was successfully applied to the voltammetric measurements of uric acid in human serum, using a working nanocarbon electrode modified with Cu-nanocarbon-lignin, since the uncertainty model adapts to the uncertainty of cumulative volume additions. The validated procedure was checked through the analysis of spiked physiological serum samples and human serum samples, by assessing the metrological compatibility between estimated and reference values. The measurements are reported with an expanded uncertainty not larger than a target value of 0.56 mg dL^-1. The used spreadsheet is made available as supplementary material.