Expression of results with uncertainty for the determination of pesticides in melon--experience in a proficiency test.

The expression of results with an uncertainty through the "bottom-up" approach, involving the estimation and combination of all the sources of uncertainty, represents a challenge when the analytical method includes mass transfer steps (MTS). These steps (e.g. extraction, evaporation, digestion, etc.) with inherently different from 100% recoveries lack models capable of describing their precision and efficiency. Recently, a new methodology was published aimed at the estimation of the performance of these critical steps. Comparison of the experimental dispersion from the replicated analysis of spiked samples with the combination of the uncertainty associated with gravimetric, volumetric and instrumental quantification steps (described by well established models) allows the estimation of the MTS uncertainty. Evaluation of the behaviour of the MTS within the analytical range supports the use of developed estimations over a wide concentration range. This methodology was applied, with success, to the determination of pesticide residues in melon in one particular proficiency test organised by the Food Analysis Performance Assessment Scheme (FAPAS) between November 2000 and February 2001.     

Uncertainty due to the quantification step in analytical methods

The quantification step is an important source of uncertainty in analytical methods, but it is frequently misunderstood and disregarded. In this paper, it is shown how this uncertainty is closely related to the linear response range of a method, and to the Pearson correlation coefficient of the calibration line. So, if there is a need for a pre-fixed quantification uncertainty, the linear response range will be affected. Some practical cases are given showing the quantification uncertainty significance. The theoretical equation giving the value of the quantification uncertainty is deduced from which new conclusions can be taken out. Because of that, the quantification uncertainty can easily be calculated and the parameters that really affect its value are shown along the paper. Some final considerations about detection limits and two-point calibration lines are also given. The paper can also be considered a reflection on uncertainty owed to calibration and on their consequences on the analytical methodology.     

An IUPAC-based approach to estimate the detection limit in co-extraction-based optical sensors for anions with sigmoidal response calibration curves

An approach based on IUPAC methodology to estimate the limit of detection of bulk optode-based analytical methods for anions has been developed. The traditional IUPAC methodology for calculating the detection limit was modified to be adapted to particular cases where the calibration curves have a sigmoidal profile. Starting from the different full theoretical models for every co-extraction mechanism of the analyte in the membrane in bulk optodes, several particular simplified models at low analyte concentration were obtained and validated. The slope of the calibration curve at low analyte concentration was calculated from the first derivative of the simplified equation and, subsequently, the detection limit was estimated. This fitted-for-purpose estimation strategy was applied to anion quantification for in-house bulk optode-based analytical methods, and the estimated limits of detection were compared with those obtained by applying classical geometrical methodology. This way of establishing the detection limit yields values that maintain their true statistical and probabilistic aspects. It can be easily applied to any analytical system which yields non-linear calibration curves at low analyte concentration.     

Uncertainty in analytical results from solid materials with electrothermal atomic absorption spectrometry: a comparison of methods

The combined uncertainty in the analytical results of solid materials for two methods (ET-AAS, analysis after prior sample digestion and direct solid sampling) are derived by applying the Guide to the Expression of Uncertainty in Measurement from the International Standards Organization. For the analysis of solid materials, generally, three uncertainty components must be considered: (i) those in the calibration, (ii) those in the unknown sample measurement and (iii) those in the analytical quality control (AQC) process. The expanded uncertainty limits for the content of cadmium and lead from analytical data of biological samples are calculated with the derived statistical estimates. For both methods the expanded uncertainty intervals are generally of similar width, if all sources of uncertainty are included. The relative uncertainty limits for the determination of cadmium range from 6% to 10%, and for the determination of lead they range from 8% to 16%. However, the different uncertainty components contribute to different degrees. Though with the calibration based on reference solutions (digestion method) the respective contribution may be negligible (precision < 3%), the uncertainty from a calibration based directly on a certified reference material (CRM) (solid sampling) may contribute significantly (precision about 10%). In contrast to that, the required AQC measurement (if the calibration is based on reference solutions) contributes an additional uncertainty component, though for the CRM calibration the AQC is “built-in”. For both methods, the uncertainty in the certified content of the CRM, which is used for AQC, must be considered. The estimation of the uncertainty components is shown to be a suitable tool for the experimental design in order to obtain a small uncertainty in the analytical result.     

Empirical versus modelling approaches to the estimation of measurement uncertainty caused by primary sampling

Measurement uncertainty is a vital issue within analytical science. There are strong arguments that primary sampling should be considered the first and perhaps the most influential step in the measurement process. Increasingly, analytical laboratories are required to report measurement results to clients together with estimates of the uncertainty. Furthermore, these estimates can be used when pursuing regulation enforcement to decide whether a measured analyte concentration is above a threshold value. With its recognised importance in analytical measurement, the question arises of 'what is the most appropriate method to estimate the measurement uncertainty?'. Two broad methods for uncertainty estimation are identified, the modelling method and the empirical method. In modelling, the estimation of uncertainty involves the identification, quantification and summation (as variances) of each potential source of uncertainty. This approach has been applied to purely analytical systems, but becomes increasingly problematic in identifying all of such sources when it is applied to primary sampling. Applications of this methodology to sampling often utilise long-established theoretical models of sampling and adopt the assumption that a 'correct' sampling protocol will ensure a representative sample. The empirical approach to uncertainty estimation involves replicated measurements from either inter-organisational trials and/or internal method validation and quality control. A more simple method involves duplicating sampling and analysis, by one organisation, for a small proportion of the total number of samples. This has proven to be a suitable alternative to these often expensive and time-consuming trials, in routine surveillance and one-off surveys, especially where heterogeneity is the main source of uncertainty. A case study of aflatoxins in pistachio nuts is used to broadly demonstrate the strengths and weakness of the two methods of uncertainty estimation. The estimate of sampling uncertainty made using the modelling approach (136%, at 68% confidence) is six times larger than that found using the empirical approach (22.5%). The difficulty in establishing reliable estimates for the input variable for the modelling approach is thought to be the main cause of the discrepancy. The empirical approach to uncertainty estimation, with the automatic inclusion of sampling within the uncertainty statement, is recognised as generally the most practical procedure, providing the more reliable estimates. The modelling approach is also shown to have a useful role, especially in choosing strategies to change the sampling uncertainty, when required.     

Estimation of precision and efficiency mass transfer steps for the determination of pesticides in vegetables aiming at the expression of results with reliable uncertainty

A 'bottom-up' approach for the expression of results obtained from analytical methods that include analytical steps with recovery inherently different from 100% [mass transfer steps (MTS): extraction, evaporation, clean-up procedures, digestion, etc.] is presented. The estimation of the combination of all MTS uncertainty involves the comparison of the experimental dispersion of replicated analyses of spiked samples with the estimation of the uncertainty obtained for the combination of all uncertainty sources except MTS ones ('incomplete' estimation). The estimation of MTS uncertainty by difference is performed after evaluating the statistical difference between the 'incomplete' estimation and the experimental dispersion (F-test). When the two estimations are statistically equivalent, the MTS uncertainty is considered to be negligible in relation to the other sources budget. The assumption of constancy of MTS performance within the analytical range is tested through single analyses at several concentration levels and is evaluated by the inclusion of the expected values at the intervals resulting from the combination of the MTS uncertainty estimation performed at one concentration level and the 'incomplete' estimation. The developed methodology can also be useful for method optimisation and validation and for the detection of small trends in results. The determination of pesticides in sweet peppers by GC-NPD was used to explore the above concepts.     

Evaluation of the analytical method performance for incurred samples

A methodology for the evaluation of the performance of an analytical method for incurred samples is presented. Since this methodology is based on intra-laboratory information, it is suitable for analytical fields that lack reference materials with incurred analytes and it can be used to evaluate the analytical steps prior to the analytical portion, which are usually excluded in proficiency tests or at the certification of reference materials. This methodology can be based on tests performed on routine samples allowing the collection of information on the more relevant combinations analyte/matrix; therefore, this approach is particularly useful for analytical fields that involve a high number of analyte/matrix combinations, which are difficult to cover even considering the frequent participation in expensive proficiency tests.This approach is based on the development of a model of the performance of the analytical method based on the differential approach for the quantification of measurement uncertainty and on the comparison of recovery associated with each one of the analytical steps whose performance can vary with the analyte origin, for spiked and incurred samples.This approach was applied to the determination of pesticide residues in apples. For the analytes covered, no evidence was found that the studied sample processing and extraction steps performance for this matrix varies with the analyte origins.     

Measurement uncertainty of food carotenoid determination

For consistent interpretation of an analytical method result it is necessary to evaluate the confidence that can be placed in it, in the form of a measurement uncertainty estimate. The Guide to the expression of Uncertainty in Measurement issued by ISO establishes rules for evaluating and expressing uncertainty. Carotenoid determination in food is a complex analytical process involving several mass transfer steps (extraction, evaporation, saponification, etc.), making difficult the application of these guidelines. The ISO guide was interpreted for analytical chemistry by EURACHEM, which includes the possibility of using intra- and interlaboratory information. Measurement uncertainty was estimated based on laboratory validation data, including precision and method performance studies, and also, based on laboratory participation in proficiency tests. These methods of uncertainty estimation were applied to analytical results of different food matrices of fruits and vegetables. Measurement uncertainty of food carotenoid determination was 10–30% of the composition value in the great majority of cases. Higher values were found for measurements near instrumental quantification limits (e.g. 75% for β-cryptoxanthin, and 99% for lutein, in pear) or when sample chromatograms presented interferences with the analyte peak (e.g. 44% for α-carotene in orange). Lower relative expanded measurement uncertainty values (3–13%) were obtained for food matrices/analytes not requiring the saponification step. Based on these results, the saponification step should be avoided if food carotenoids are not present in the ester form. Food carotenoid content should be expressed taking into account the measurement uncertainty; therefore the maximum number of significant figures of a result should be 2.     

Calibration uncertainty

Methods recommended by the International Standardization Organisation and Eurachem are not satisfactory for the correct estimation of calibration uncertainty. A novel approach is introduced and tested on actual calibration data for the determination of Pb by ICP-AES. The improved calibration uncertainty was verified from independent measurements of the same sample by demonstrating statistical control of analytical results and the absence of bias. The proposed method takes into account uncertainties of the measurement, as well as of the amount of calibrant. It is applicable to all types of calibration data, including cases where linearity can be assumed only over a limited range. Received: 25 August 2001 Accepted: 21 December 2001     

A new terminology for the approaches to the quantification of the measurement uncertainty

A new terminology for the approaches to the quantification of the measurement uncertainty is presented, with a view to a better understanding of the available methodologies for the estimation of the measurement quality and differences among them. The knowledge of the merits, disadvantages and differences in the estimation process, of the available approaches, is essential for the production of metrologically correct and fit-to-purpose uncertainty estimations. The presented terminology is based on the level of the analytical information used to estimate the measurement uncertainty (e.g., supralaboratory or intralaboratory information), instead of the direction of information flow (“bottom-up” or “top-down”) towards the level of information where the test is performed, avoiding the use of the same designation for significantly different approaches. The proposed terminology is applied to the approaches considered on 19 examples of the quantification of the measurement uncertainty presented at the Eurachem/CITAC CG4 Guide, Eurolab Technical Report 1/2002 and Nordtest Technical Report 537. Additionally, differences of magnitude in the measurement uncertainty estimated by various approaches are discussed.     

To what extent can an uncertainty calculation be general?

 It is argued that results of uncertainty calculations in chemical analysis should be taken into consideration with some caution owing to their limited generality. The issue of the uncertainty in uncertainty estimation is discussed in two aspects. The first is due to the differences between procedure-oriented and result-oriented uncertainty assessments, and the second is due to the differences between the theoretical calculation of uncertainty and its quantication using the validation (experimental) data. It is shown that the uncertainty calculation for instrumental analytical methods using a regression calibration curve is result-oriented and meaningful only until the next calibration. A scheme for evaluation of the uncertainty in uncertainty calculation by statistical analysis of experimental data is given and illustrated with examples from the author's practice. Some recommendations for the design of corresponding experiments are formulated.     

Speciation analysis of chromium in drinking water samples by ion-pair reversed-phase HPLC–ICP-MS: validation of the analytical method and evaluation of the uncertainty budget

The approach presented in this article refers to the modification of a method for the detection and quantitative determination of chromium species in water by high-performance liquid chromatography inductively coupled plasma mass spectrometry. The main aim of this work was to establish a detailed validation of the analytical procedure and an estimation of the budget of measurement uncertainty which was helpful in recognizing the critical points of the presented method. As a result of the method validation experiment, the obtained limit of quantification, repeatability and intermediate precision were satisfied for the quantification Cr(III) and Cr(VI) in water matrices. The trueness of the method was verified via an estimation of the recovery of the spiked real samples. The recovery rate of both determined analytes was found to be between 93 and 115 %. Considering that the validation of the method and the evaluation of measurement uncertainty are crucial for quantitative analysis, the above-mentioned assessment of the uncertainty budget was performed in two different ways: a modelling approach and a single-laboratory validation approach. The measurement uncertainties of the results were found to be 4.4 and 7.8 % for Cr(III), 4.2 and 7.9 % for Cr(VI) using the classical concept and method validation data, respectively. This paper is the first publication to presenting all the steps needed to evaluate the measurement uncertainty for the speciation analysis of chromium species. In summary, the obtained results demonstrate that the method can be applied effectively for its intended use.     

Uncertainty in liquid chromatographic analysis of pharmaceutical product: influence of various uncertainty sources

An ISO GUM measurement uncertainty estimation procedure was developed for a liquid-chromatographic drug quality control method-assay of simvastatin in drug formulation. In quantification of uncertainty components several practical approaches for including difficult-to-estimate uncertainty sources (such as uncertainty due to peak integration, uncertainty due to nonlinearity of the calibration curve, etc.) have been presented. Detailed analysis of contributions of the various uncertainty sources was carried out. The results were calculated based on different definitions of the measurand and it was demonstrated that unequivocal definition of the measurand is essential in order to get rigorous uncertainty estimate. Two different calibration methods - single-point (1P) and five-point (5P) - were used and the obtained uncertainties and uncertainty budgets were compared. Results calculated using 1P and 5P calibrations agree very well. The uncertainty estimate for 1P is only slightly larger than with 5P calibration.     

Measurement uncertainty from physical sample preparation: estimation including systematic error

A methodology is proposed, which employs duplicated primary sampling and subsequent duplicated physical preparation coupled with duplicated chemical analyses. Sample preparation duplicates should be prepared under conditions that represent normal variability in routine laboratory practice. The proposed methodology requires duplicated chemical analysis on a minimum of two of the sample preparation duplicates. Data produced from the hierarchical design is treated with robust analysis of variance (ANOVA) to generate uncertainty estimates, as standard uncertainties ('u' expressed as standard deviation), for primary sampling (ssamp), physical sample preparation (sprep) and chemical analysis (sanal). The ANOVA results allow the contribution of the sample preparation process to the overall uncertainty to be assessed. This methodology has been applied for the first time to a case study of pesticide residues in retail strawberry samples. Duplicated sample preparation was performed under ambient conditions on two consecutive days. Multi-residue analysis (quantification by GC-MS) was undertaken for a range of incurred pesticide residues including those suspected of being susceptible to loss during sample preparation procedures. Sampling and analytical uncertainties dominated at low analyte concentrations. The sample preparation process contributed up to 20% to the total variability and had a relative uncertainty (Uprep%) of up to 66% (for bupirimate at 95% confidence). Estimates of systematic errors during physical sample preparation were also made using spike recovery experiments. Four options for the estimation of measurement uncertainty are discussed, which both include and exclude systematic error arising from sample preparation and chemical analysis. A holistic approach to the combination and subsequent expression of uncertainty is advised.     

Estimation of measurement uncertainty in organic analysis: two practical approaches

Estimation of measurement uncertainty has become a more regularly performed part of the whole analytical process. However, there is still much on-going discussion in the scientific community about ways of building up the uncertainty budget. This study describes two approaches for estimation of measurement uncertainty in organic analysis: one which can be used for single sets of measurements and the other based on validation studies. In both cases the main contributions to the uncertainty are presented and discussed for the analysis of PCBs in mussel tissue, but the approaches can be extended to other organic pollutants in environmental/food samples. The main contributions to the uncertainty budget arise from calibration, sample preparation, and GC–MS measurements. A comparison of the relevant sources and their contributions to the expanded uncertainty is presented.     

Estimation scheme for level-dependent uncertainty of analytical result: application for determination of 1-hydroxypyrene in urine

The estimation scheme of uncertainty of determination of 1-hydroxypyrene (1-OHP) in urine was developed analysing the main stages of the analytical procedure: (1) preparation of 1-OHP standards, (2) creation of the calibration curve for the high performance liquid chromatography (HPLC) analysis method with the evaluation of recovery, (3) measuring procedure of aliquot of urine, (4) adjusting the pH of aliquot and hydrolysis with enzyme, (5) solid phase extraction, (6) concentration of the extract, (7) injection of the extract to chromatograph and analysing by the HPLC method, (8) calculation of 1-OHP mass from the calibration curve, (9) calculation of 1-OHP concentration in urine. The evaluation of the uncertainty is based on quantification of individual components. Combined uncertainty was calculated using the law of propagation of uncertainties according to the EURACHEM/CITAC guidelines. Level dependence of the uncertainty arises from the calibration curve. The limits of detection and quantification were found to be equal to 0.03 and 0.1 ng/mL, respectively. The calculated expanded level-dependent uncertainty covers 47–27–25% within the concentration range 0.03–0.1–0.4 ng/mL with the materials and equipment used. These parameters could easily be recalculated according to the proposed scheme if there are some changes in the analysis procedure.     

Correction function on biased results due to matrix effects: Application to the routine analysis of pesticide residues

A new strategy to carry out the correction of analytical results affected by systematic errors due to the matrix effect is proposed. Two types of external calibrations must be established with the purpose to estimate the matrix effect: solvent calibration (SC) and matrix-matched calibration (MC). These calibration curves are statistically compared and a correction function (CF) is proposed with the aim to simplify the resolution to the problems associated with the incidence of matrix systematic error in the analytical results. Applying this correction function to the results obtained from the solvent calibration, it is possible to make a prediction of the values that would be obtained when the matrix-matched calibration is applied. On the other hand, a rigorous study of the associated uncertainty is developed and applied to the calculated correction function. Finally, this correction function is validated by means of obtained data of recovery studies carried out by a traditional methodology. The methodology has been satisfactorily applied to the quantification of the pesticide procymidone by HPLC for assessing dermal exposure.     

Low uncertainty reverse isotope dilution ICP-MS applied to certifying an isotopically enriched Cd candidate reference material: A case study

An analytical method is presented based on reverse isotope dilution single detector inductively coupled plasma magnetic sector mass spectrometry (ID-ICP-SMS) and applied to the specific case of the certification of a (111)Cd enriched candidate Cd spike calibration material (nominal mass fraction 10 mg kg(-1) in 5% HNO3 solution). Uncertainty propagation was used as a tool for both determining the analytical approach and validating it. The robustness of close to "exact matching" reverse IDMS to correction of measured isotope intensities for multiplicative (mass discrimination) and (semi)additive effects (dead time, instrumental background, and isobaric interference) is discussed. The very low experimental relative standard deviation of the mean (0.08%) of eight replicate determinations indicated that all significant sources of uncertainty had probably been taken into account for the estimation of the final combined uncertainty statement (U(c) = 0.17%, k = 1). IRMM-621 was used as comparator. Uncertainties on IUPAC isotopic abundances of 111Cd and 112Cd, for the natural Cd solution involved between the two enriched materials, formed nearly 60% of U(c). The repeatability of the isotope ratio measurements contributed less than 10%. Correction for procedural blank necessitated somewhat unusual calculations (potential contamination of an enriched material with natural Cd). The procedure also involved a quadrupole based ICP-MS judged to be appropriate for the characterization of the isotopic composition. For comparison purposes, direct IDMS results are simulated using identical experimental input data. Finally, a significant background signal in the 106-116 mass region, observed only with the magnetic sector instrument, was attributed to argon based isobaric interferences.     

Uncertainty evaluation in the analysis of biological samples by sector field inductively coupled plasma mass spectrometry. Part A: measurements of Be,Cd, Hg,Ir, Pb,Pd, Pt,Rh, Sb,U, Tl and W in human serum

A protocol that utilises data (trueness/recovery, precision and robustness) from validation tests to calculate measurement uncertainty was described and applied to a sector field inductively coupled plasma mass spectrometry (SF‐ICP‐MS)‐based method for the determination of Be, Cd, Hg, Ir, Pb, Pd, Pt, Rh, Sb, U, Tl and W in human serum. The method was validated according to criteria issued by international bodies such as AOAC, Eurachem and ISO and the uncertainty in the analytical measurements was estimated following the Eurachem/Citac guide. The methodology was based on dilution of human serum with water and analysis by serum‐matched standard calibration. The method quantification limits ranged 0.02 µg/L (Tl, Ir) to 0.26 µg/L (Hg). The coefficients of regression were greater than 0.9991 over a range of two orders of magnitude of concentration. The mean trueness was 101% and the mean recovery on three levels of fortification (1‐, 1.5‐, and 2‐times the baseline serum level) ranged between 93.3% and 106%. The maximum relative standard deviation values for repeatability and within‐laboratory reproducibility were 12.8% and 13.5%. The method was robust to slight variations of some critical factors relevant to the sample preparation and SF‐ICP‐MS instrumentation. The relative expanded uncertainty over three levels of concentration ranged from 11.6% (Hg) to 27.6% (Pt), and the uncertainty on the within‐laboratory reproducibility, which included factors such as time, analyst and calibration, represented the main contribution to the overall uncertainty. Copyright © 2010 John Wiley & Sons, Ltd.