Evaluation and validation of detailed and simplified models of the uncertainty of unified [Formula: see text] measurements in aqueous solutions.

The use of the unified pH concept, [Formula: see text] , applicable to aqueous and non-aqueous solutions, which allows interpreting and comparison of the acidity of different types of solutions, requires reliable and objective determination. The [Formula: see text] can be determined by a single differential potentiometry measurement referenced to an aqueous reference buffer or by a ladder of differential potentiometric measurements that allows minimisation of inconsistencies of various determinations. This work describes and assesses bottom-up evaluations of the uncertainty of these measurements, where uncertainty components are combined by the Monte Carlo Method (MCM) or Taylor Series Approximation (TSM). The MCM allows a detailed simulation of the measurements, including an iterative process involving in minimising ladder deviations. On the other hand, the TSM requires the approximate determination of minimisation uncertainty. The uncertainty evaluation was successfully applied to measuring aqueous buffers with pH of 2.00, 4.00, 7.00, and 10.00, with a standard uncertainty of 0.01. The reference and estimated values from both approaches are metrologically compatible for a 95% confidence level even when a negligible contribution of liquid junction potential uncertainty is assumed. The MCM estimated pH values with an expanded uncertainty, for the 95% confidence level, between 0.26 and 0.51, depending on the pH value and ladder inconsistencies. The minimisation uncertainty is negligible or responsible for up to 87% of the measurement uncertainty. The TSM quantified measurement uncertainties on average only 0.05 units larger than the MCM estimated ones. Additional experimental tests should be performed to test these uncertainty models for analysis performed in other laboratories and on non-aqueous solutions.

Impact of recovery correction or subjecting calibrators to sample preparation on measurement uncertainty: PAH determinations in waters.

The decision on the fitness of a measurement for its intended use and the interpretation of an analytical result requires the assessment of the measurement uncertainty. Frequently, the determination of analytes in complex matrices involves demanding sample preparations in which analyte losses are observed. These losses should be considered when reporting the results, which can be corrected for low recovery by taking the mean recovery observed in the analysis of reference items (e.g. spiked samples) or, alternatively, by subjecting calibrators to the same pre-treatment performed on the samples. In these cases, neat (NC) or adjusted (AC) calibrators are used, respectively. The way analyte losses are handled impacts on the measurement uncertainty. The top-down evaluation of the measurement uncertainty involves combining precision, trueness and additional uncertainty components. The trueness component is quantified by pooling various analyte recovery determinations. This work assesses and compares the uncertainty of polycyclic aromatic hydrocarbons (PAHs) measurements in water based on HPLC-FD calibrations with NC or AC. The trueness component is estimated by pooling mean recoveries observed from the analysis of different spiked samples to which mean recovery uncertainty and degrees of freedom are used to estimate a weighted mean recovery and respective uncertainty. The performance of measurements based on NC and AC are associated with equivalent uncertainty except when large analyte losses are observed, namely in the determination of Naphtalene. In this case, the processing of AC reduces the expanded relative uncertainty from 9.9% to 3.5%. The evaluated expanded uncertainty ranged from 3.5% to 12% of the measured value.

Top-down evaluation of matrix effects uncertainty.

Many measurements in chemistry are affected by matrix effects responsible for larger deviation between results from the analysis of various matrices than observed from the replicate analysis of the same matrix. The identification of cases where matrix effects are relevant is useful to know if measurement robustness to matrix effects can significantly reduce the measurement uncertainty, e.g. by performing time-consuming standard addition calibrations or additional matrix clean-up. This work presents a methodology to estimate the percentage contribution of matrix effects to the measurement uncertainty by comparing the intermediate precision estimated from the analysis of a sample with the dispersion of analyte recovery observed form the analyses of samples with different matrices. The measurement model was divide in two intervals of the studied quantity: Interval I between the limit of detection and two times the limit of quantification, where the absolute measurement uncertainty is constant, and Interval II above or equal to two times the limit of quantification where the relative measurement uncertainty is constant. The division of measurements scope in these intervals allowed the comparison of information collected at different values of the studied quantity. The developed methodology was successfully applied to the analysis of total Cr, Cu, Li, Mn and Zn using a procedure developed by OSPAR and acid extractable Ni and Pb according to the EPA3051A standard in marine sediments. Matrix effects are responsible for 7.7 to 79% of the global uncertainty. For Interval II, the relative expanded uncertainty ranged from 12% to 25% and is fit for the environmental monitoring of sediments according to the way the performance of laboratories is assessed in QUASIMEME proficiency tests. The developed measurement uncertainty models produced results compatible with reference values of one Certified Reference Material and 65 proficient test samples independent of the ones used to estimate the measurement uncertainty. The used data and performed calculations are presented in a user-friendly MS-Excel spreadsheet, available as Electronic Supplementary Material, that can be used for other determinations.

Designing valid and optimised standard addition calibrations: Application to the determination of anions in seawater.

A strategy for designing valid standard addition calibrations and for optimising their uncertainty is presented. The design of calibrations involves the development of models of the sensitivity and precision of the instrumental signal, in a wide range of analyte concentration (or any other studied quantity), and the definition of sample dilution and standard addition procedures that allow fulfilling the assumptions of the linear unweighted regression model in, typically, a smaller range of standard addition calibrations. Calibrators are prepared by diluting the sample and adding analyte with negligible uncertainty to fit in a concentration range where signals are homoscedastic. The minimisation of the uncertainty is supported on detailed measurement uncertainty models function of the calibrators preparation procedure and of analytical instrumentation performance. The number of collected signals replicates is defined by balancing their impact on the estimated expanded uncertainty, the resources needed and the target (maximum) uncertainty for the intended use of measurements. The calibration design strategy was successfully applied to the determination of the mass concentration (mg L(-1)) of Cl(-), Br(-), NO3(-) and SO4(-2) in seawater by ion chromatography. A target expanded uncertainty of 20% was defined for the determination of Cl(-), NO3(-) and SO4(-2), or 40% for the determination of the smaller mass concentration of Br(-). The developed measurement model produced reliable predictions of the measurement uncertainty from approximate concentration of the analyte in the sample, before its accurate quantification, thus proving optimisation is effective. Predictions are more prone to the variability of the measurement uncertainty estimation if based on low number of calibrators signals. The reported relative expanded uncertainty ranged from 7.1% to 49%.

Detailed uncertainty budget for major and minor ions in stock combined calibration standards--influence of impurities in chemicals.

A general methodology for a systematic evaluation of the uncertainty was derived for each particular ion in stock combined calibration standards in which concentrations of different ions extend over up to five orders of magnitude resulting in detailed uncertainty budgets with the aim of recognising the major contributions to combined uncertainties. This work confirmed that it is justifiable that the mass fraction of impurities in other chemicals is taken into account when calculating the mass concentration of an ion in combined calibration standard solution similarly to what is already common practice in accounting for the purity of chemical. It was proven that impurities in chemicals which are sources of major ions have significant effect on uncertainty budget of minor ions; already if the major ion exceeds 25 times the minor ion's concentration. For several ions it was confirmed that mass fraction of the impurities was the major source of uncertainty.

Worst case uncertainty estimates for routine instrumental analysis.

A methodology for the worst case measurement uncertainty estimation for analytical methods which include an instrumental quantification step, adequate for routine determinations, is presented. Although the methodology presented should be based on a careful evaluation of the analytical method, the resulting daily calculations are very simple. The methodology is based on the estimation of the maximum value for the different sources of uncertainty and requires the definition of limiting values for certain analytical parameters. The simplification of the instrumental quantification uncertainty estimation involves the use of the standard deviation obtained from control charts relating to the concentrations estimated from the calibration curves for control standards at the highest calibration level. Three levels of simplification are suggested, as alternatives to the detailed approach, which can be selected according to the proximity of the sample results to decision limits. These approaches were applied to the determination of pesticide residues in apples (CEN, EN 12393), for which the most simplified approach showed a relative expanded uncertainty of 37.2% for a confidence level of approximately 95%.