Bayesian Methods for Ion Selective Electrodes

With the increasing use of ion‐selective electrodes in environmental and health applications, it is important to know the precision of estimated concentrations. A Bayesian model for non‐linear calibration is introduced which provides estimates of measurement precision by incorporating uncertainty in calibration parameters and inherent random noise in emf response. The analysis of lead in 17 soil samples demonstrates that large gains in precision are possible when calibrations are extended to include multiple electrodes and standard addition data. The results highlight the need for improved calibration and routine use of standard addition as ion selective electrodes become increasingly popular for demanding, real world applications.     

Assessment of the determination of heavy metals in organic soil improvers by ICP–OES

Directive 86/278/EEC sets maximum levels of heavy metals in sewage sludge used in agriculture to regulate the risk of using these organic soil improvers. The assessment of the compliance of soil improvers with this legislation should be supported on measurements with adequately low uncertainty. This work presents a strategy for assessing the performance of the determination of aqua regia extractable Cu, Zn and Cr in organic soil improvers and urban sewage sludges following EN 13650 standard. The measurement procedure validation involves checking the adequacy of the linear weighted regression model for ICP–OES calibration, the determination of the limit of quantification, the assessment of measurement repeatability, intermediate precision and trueness, and the evaluation of the measurement uncertainty using the differential approach. Routine tests quality control, including the estimated measurement uncertainty, is checked through the analysis of control standards, equivalent to calibrators, and reference materials from proficiency tests. Since the estimated relative expanded uncertainty is smaller than the defined target value (40 %), measurements are fit for assessing compliance of the mass fraction of heavy metals in organic soil improvers with the council directive.     

Determination of Parameter Uncertainty for Quantitative Analysis of Shaddock Peel Pectin using Linear and Nonlinear Near-infrared Spectroscopic Models

Fourier transform near-infrared spectrometry has been used in combination with multivariate chemometric methods for wide applications in agriculture and food analysis. In this paper, we used linear partial least square and nonlinear least square support vector machine regression methods to establish calibration models for Fourier transform near-infrared spectrometric determination of pectin in shaddock peel samples. In particular, the tunable kernel parameters of the linear and nonlinear models were set changing in a moderate range and were optimally selected in conjunction with a Savitzky–Golay smoother. The smoothing parameters and the linear/nonlinear modeling parameters were combined for simultaneous optimization. To investigate the robustness of calibration models, parameter uncertainty were estimated in a direct way for the optimal linear and nonlinear models. Our results show that the nonlinear least square support vector machine method gives more accurate predictive results and is substantially more robust compared to the spectral noise when compared with the linear partial least square regression. Furthermore, the optimized least square support vector machine model was evaluated by the randomly selected test samples and the model test effect was much satisfactory. We anticipate that these linear and nonlinear methods and the methodology of determination of model parameter uncertainty will be applied to other analytes in the fields of near-infrared or Fourier transform near-infrared spectroscopy.     

Presentation of differential laser-induced fluorimetry as a reference measurement procedure for determination of total uranium content in ores and similar matrices

The metrological principle of ‘differential technique in laser-induced fluorimetry’ analysis is discussed and recommended as a reference measurement procedure for determination of total uranium content in ores and similar matrices. The estimated relative expanded uncertainty values obtained for uranium content in standard IAEA samples are, S 1, 0.04 g/kg, S 2, 0.06 g/kg, S 3, 0.04 g/kg, and for S 4, 0.10 g/kg, respectively. These low uncertainty values obtained for uranium show high metrological quality of differential technique. This reference measurement procedure guarantees the quality of an analytical result (accuracy, high precision, reliability, comparability, and traceability). Laser-induced fluorimetry will be useful for the analysis of uranium in ores, certification of reference materials, borehole core assay, and other diverse applications in nuclear fuel cycle. Differential technique in spectrophotometry/laser fluorimetry has inherent high metrological quality. In principle, laser-induced fluorimetry is an ideal technique for the very accurate determination of uranium by the use of appropriate fluorescence-enhancing reagents and methodology depending upon the concentration of uranium and sample matrices.     

离子色谱法测定地下水中硝酸盐氮含量的不确定度评定

采用不确定度连续传递模式,讨论了不同回归方式对离子色谱法测定岩溶地下水中硝酸根分析结果不确定度评定的差异.结果表明：（1）测定结果的不确定度主要来源于标准溶液配制过程引入的不确定度、校准曲线拟合及回归过程产生的不确定度和仪器测定过程引入的不确定度三部分;（2）不同校准曲线回归方式对测定结果的不确定度评定在不同测量水平上有不同的影响,当地下水中硝酸根含量越低,差异越大.此外,对不确定度评定过程中的各个分量进行量化,通过合成得到硝酸根测定结果的不确定度评定模型.     

Determination of measurement uncertainty for the determination of triazines in groundwater from validation data

Laboratories are increasingly urged to submit full uncertainties of their analytical results rather than only standard deviations. The determination of measurement uncertainties in compliance with the Guide to the Expression of Uncertainty in Measurement (GUM) is demonstrated using the validation approach explicitly endorsed by the recent edition of the EURACHEM guide for the determination of measurement uncertainty. Measurement uncertainty was split into uncertainty of the sample mass, uncertainty of the concentration of the stock standard solution, uncertainty of the calibration and uncertainty connected to within- and between-series precision. Uncertainties of sample mass and of the concentration of the stock standard solution were 0.26 and 1.14% for all analytes, which is negligible compared with the contributions of precision and calibration. Uncertainty of calibration was estimated from the calibration graph. Relative uncertainty of calibration was found to be strongly concentration dependent and to be the main uncertainty contribution below 0.2 microgram L-1. Precision was split into within-series and between-series standard deviation, which dominate the combined standard uncertainty at higher concentrations. The results obtained from these calculations are compared with results for a certified reference material and with the performance in an interlaboratory comparison. It was found that all results agreed within their uncertainty with the target values, showing that the estimated uncertainties are realistic.     

Estimation of the quantification uncertainty from flow injection and liquid chromatography transient signals in inductively coupled plasma mass spectrometry

The quality of the quantitative results obtained from transient signals in high-performance liquid chromatography–inductively coupled plasma mass spectrometry (HPLC–ICPMS) and flow injection–inductively coupled plasma mass spectrometry (FI–ICPMS) was investigated under multielement conditions. Quantification methods were based on multiple-point calibration by simple and weighted linear regression, and double-point calibration (measurement of the baseline and one standard). An uncertainty model, which includes the main sources of uncertainty from FI–ICPMS and HPLC–ICPMS (signal measurement, sample flow rate and injection volume), was developed to estimate peak area uncertainties and statistical weights used in weighted linear regression. The behaviour of the ICPMS instrument was characterized in order to be considered in the model, concluding that the instrument works as a concentration detector when it is used to monitorize transient signals from flow injection or chromatographic separations. Proper quantification by the three calibration methods was achieved when compared to reference materials, although the double-point calibration allowed to obtain results of the same quality as the multiple-point calibration, shortening the calibration time. Relative expanded uncertainties ranged from 10–20% for concentrations around the LOQ to 5% for concentrations higher than 100 times the LOQ.     

Some aspects of the evaluation of measurement uncertainty using reference materials

To ensure and to confirm the required traceability according to the definition given in the International Vocabulary of Basic and Standard Terms in Metrology, three main aspects need to be considered in practice: “stated reference”, “unbroken chain of calibration” and “stated uncertainty”. For a certain spectrochemical result, each of the aspects above mentioned is highly dependent on measurement uncertainty, both on its magnitude and how it was estimated. The paper describes the experience of the Romanian National Institute of Metrology (INM) in estimating measurement uncertainty during certification of reference materials, in metrological calibration and during specific analytical processes. Practical examples of the use of reference materials or certified reference materials issued by the INM to estimate measurement uncertainty are discussed for their applicability in spectrochemical and turbidity analysis. Some aspects of the use of analysis of variance (ANOVA) to obtain additional information on the components of measurement uncertainty and to identify the magnitude of individual random effects are presented.     

Some aspects of the evaluation of measurement uncertainty using reference materials

To ensure and to confirm the required traceability according to the definition given in the International Vocabulary of Basic and Standard Terms in Metrology, three main aspects need to be considered in practice: "stated reference", "unbroken chain of calibration" and "stated uncertainty". For a certain spectrochemical result, each of the aspects above mentioned is highly dependent on measurement uncertainty, both on its magnitude and how it was estimated. The paper describes the experience of the Romanian National Institute of Metrology (INM) in estimating measurement uncertainty during certification of reference materials, in metrological calibration and during specific analytical processes. Practical examples of the use of reference materials or certified reference materials issued by the INM to estimate measurement uncertainty are discussed for their applicability in spectrochemical and turbidity analysis. Some aspects of the use of analysis of variance (ANOVA) to obtain additional information on the components of measurement uncertainty and to identify the magnitude of individual random effects are presented.     

2011年约稿： 电感耦合等离子体原子发射光谱法测定铜合金中锆量的不确定度评定

讨论了采用电感耦合等离子体发射光谱法测定铜合金中锆量分析结果不确定度产生的原因。建立了数学模型,对测量重复性,标准溶液,标准曲线变动性,试液体积,试样称量,数字修约等引起的不确定分量进行评定,计算了合成标准不确定度和扩展不确定度,并给出铜合金中锆量测定结果的报告。评定结果表明：测量重复性,标准曲线线性回归引起的不确定度对总不确定度影响最大。所以,在测定中应进行多次平行测定,特别注意标准曲线的校正和绘制校准曲线所用标准样品的选择。     

Development of metrological models for internal standard single-point and multi-point calibrations for the assessment of tear gas weapons compliance with legislation

Tear gases are the most widely used non-lethal weapons, both by security forces and by the general public. The pepper spray, whose active agent is capsaicin, is the only self-defence aerosol allowed in Portugal, where capsaicin concentration must be below 5 g/100 mL. The cost-effective evaluation of the compliance of self-defence weapons with legislation involves the use of two measurement procedures with increasing quantitative capability. Samples are first assessed by preliminary measurement procedure based on single-point GC–MS calibration. Whenever the measurement uncertainty from this assessment makes evaluation inconclusive, the evaluation of sample compliance using multi-point GC–MS calibration is performed. Metrological models including sound criteria for the evaluation of sample compliance with legislation were developed for both measurement procedures. Such models include the evaluation of the impact of instrumental performance, calibration model, sample dilution and standards preparation on measurement uncertainty. The relative expanded uncertainty, in the studied range (capsaicin 3–7 g/100 mL), of measurements supported in single-point calibrations ranged from 10 to 22% and the ones supported on multi-point calibrations from 8 to 12% depending on capsaicin concentration and daily GC–MS repeatability. Measurements are fit for the intended use since they present a relative expanded uncertainty smaller than a target value of 30, or 15%, for measurements supported in single- or multi-point calibrations, respectively.     

Evaluation of measurement uncertainty for analytical procedures using a linear calibration function

In the EURACHEM/CITAC draft ”Quantifying uncertainty in analytical measurement” estimations of measurement uncertainty in analytical results for linear calibration are given. In this work these estimations are compared, i.e. the uncertainty deduced from repeated observations of the sample vs. the uncertainty deduced from the standard residual deviation of the regression. As a result of this study it is shown that an uncertainty estimation based on repeated observations can give more realistic values if the condition of variance homogeneity is not correctly fulfilled in the calibration range. The complete calculation of measurement uncertainty including assessment of trueness is represented by an example concerning the determination of zinc in sediment samples using ICP-atomic emission spectrometry. Received: 9 February 2002 Accepted: 17 April 2002     

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.     

Towards future reference systems for GM analysis

Despite the fact that the measurement unit for the quantification of GMOs in food and feed products has not yet been unambiguously agreed upon in Europe, international trade requires reliable GMO analysis measuring comparably the GMO content of products. The two reference systems, based either on mass fractions or on copy number ratios, and their metrological traceability chains are presented and discussed. It is concluded that, properly established and expressed, measurement results in copy number ratios can provide a metrologically sound reference system. In this case, certified reference materials used for calibration and quality control can be independent of each other and the uncertainty derived from calibration can correctly be included in the overall uncertainty of the GMO measurement. However, further efforts are required to establish this metrological system.     

Advantages of PARAFAC calibration in the determination of malachite green and its metabolite in fish by liquid chromatography-tandem mass spectrometry

This paper reports the properties and advantages of the three-way calibration models based on parallel factor analysis (PARAFAC) in the simultaneous determination of malachite green (MG) and its metabolite (leucomalachite green, LMG) in trout. A recently method proposed by community reference laboratory AFSSA-LERMVD (Fougères, France) has been used. The method is based on liquid chromatography-triple quadrupole mass spectrometry (LC-MS/MS) in multiple reaction monitoring (MRM) mode. The validation of the method has been carried out taking into account the Decision 2002/657/EC. The figures of merit for PARAFAC and univariate calibration models of six non-consecutive days analyzed during a month were evaluated. With the samples of the first 3 days, calibration models were built and the fish fortification samples of the other days were predicted. Decision limits (CCalpha, alpha=0.01), detection capabilities (CCbeta, beta=0.05) and mean relative errors in absolute value (in calibration and with test samples) obtained with PARAFAC calibrations were more homogeneous than the ones obtained with the univariate calibrations, especially in LMG. These figures of merit were in the range of 0.2-0.83 microg kg(-1) (CCbeta) and 0.2-0.49 microg kg(-1) (CCalpha), whereas mean relative errors in absolute value were in the range of 1.1-7.4% in calibration and 3-12% in test samples for MG and LMG with PARAFAC calibrations. The PARAFAC calibrations allow detecting the test samples which are not similar to the calibration samples and in this way their wrong quantification is avoided.     

Uncertainties in Determination of pH

 A statistical analysis of multi-point calibration procedure for practical measurement of pH under laboratory conditions is given. The procedure is shown to provide the necessary elements for simple assignment of an uncertainty to a pH measurement – an essential element of quality control. Performance of ordinary least squares regression for prediction of confidence limits is compared to orthogonal regression, inverse regression and Monte Carlo simulations. In case of pH measurement by multi-point calibration procedure, methods considering uncertainties in both axes are found to be statistically more satisfactory than ordinary least squares regression. By analysis of 50 pH calibration data, randomly selected from 250 5-point glass electrode calibrations, it is found that the practical differences, however, are of minor importance. The significance of uncertainty in pH is demonstrated for an example from metal ion speciation in aqueous solution. Received September 20, 1999. Revision April 19, 2000.     

Some aspects of the evaluation of measurement uncertainty using reference materials

 In practice there are three aspects that need to be considered in order to achieve the required traceability according to its definition: the 'stated reference', the 'unbroken chain of calibrations' and the "stated uncertainty". For a certain chemical result, each of these aspects highly depends on the measurement uncertainty, both on its magnitude and how it was estimated. Therefore, the paper describes the experience of the Romanian National Institute of Metrology in estimating measurement uncertainty during the certification of reference materials (RMs), in metrological activities (calibration, pattern approval, periodical verification, etc.), as well as during the analytical measurement process. Practical examples of estimation of measurement uncertainty using RMs or certified reference materials are discussed for their applicability in spectrophotometric and turbidimetric analysis. Use of the analysis of variance to obtain some additional information on the components of measurement uncertainty and to identify the magnitude of individual random effects is described. Received: 12 November 1999 / Accepted: 25 February 2000     

Single Laboratory Validation of a Method for the Determination of Total Inorganic Arsenic by Hydride Generation Atomic Absorption Spectrometry

The purpose of this study consists in reporting of single laboratory validation of a method for the determination of total inorganic arsenic by hydride generation atomic absorption spectrometry from natural and residual water samples. Applicability, fitness for purpose, selectivity, and sensitivity were discussed. A calibration study was realized, linear working range (0.4–4 μg·L^?1), detection (0.11 μg·L^?1), and quantification (0.38 μg·L^?1) limits being determined. It was also proven that the method is accurate and precise. Following the bottom-up approach measurement, uncertainty was estimated (method validation data were used).     

A comparison in the evaluation of measurement uncertainty in analytical chemistry testing between the use of quality control data and a regression analysis

The evaluation of measurement uncertainties has been widely applied to the calibration of measurement instruments, whereas its application to tests, despite increasing requirements, is a more recent phenomenon. The generalization of the evaluation of measurement uncertainties to tests has been a gradual process, in line with changes in the requirements of the normative framework that regulates the accreditation of tests laboratories and also as the perceived good practices have evolved. The sole identification of the relevant sources of uncertainty was followed by the requirement to provide a simplified estimate of the measurement uncertainty, and it is now an accepted requirement to properly evaluate the expanded measurement uncertainty associated with any tests. In this study, the evaluation of measurement uncertainty associated with the determination of sulfate in water will be attempted using a procedure that includes linear regression, with the regression parameters provided with associated uncertainties, and a Monte Carlo method applied as a validation tool of the conventional mainstream evaluation method, concerning the approximations in terms of linearization of the model and the assumed shape of the output distribution introduced by this approach.     

Estimation of uncertainty for the determination of mercury in food by CVAAS

This paper is aimed at reporting a full validation of a Cold Vapour Atomic Absorption Spectrometry (CVAAS) method for mercury determination in fishery products. Method precision, trueness, limit of detection and limit of quantification are evaluated. The uncertainty of measurement is estimated following the bottom-up approach in conjunction with the validation data as suggested for complex analysis. The precision is evaluated using a pooled relative standard deviation and the recovery is added to the measurement uncertainty budget. Uncertainties of weight of sample, dilution factor, calibration, work solution and analyte amount are also assessed. The most relevant uncertainty sources result those associated to amount of mercury determined in the final sample solution, to method precision and to recovery. The relative contributions have different weights according to the analyst decision regarding recovery correction of results. In conclusion, the adopted CVAAS method fully complies with EU requirements. Presented at AOAC Europe/Eurachem Symposium March 2005, Brussels, Belgium