Certification of a low value electrolytic conductivity solution using traceable measurements

Reliable measurement results of electrolytic conductivity (EC), in particular for low values, must be metrologically traceable and be based on a realistic measurement uncertainty budget. The use of certified reference materials (CRMs) can help to achieve this goal. This paper presents results from all stages of the certification of an EC CRM with a conductivity of 1.5 μS cm^?1, including the preparation of the batch solution and the evaluation of the homogeneity and stability of the bottled CRM. An uncertainty budget is presented for the CRM, including the main contributions from each of these sources. The CRM batch remained stable within its certified uncertainty for more than 1 year.     

Uncertainty sources in UV-Vis spectrophotometric measurement

An overview is given of the most important uncertainty sources that affect analytical UV-Vis spectrophotometric measurements. Altogether, eight uncertainty sources are discussed that are expected to have influence in chemical analysis. It is demonstrated that the well-known intrinsic (or “physical”) sources of uncertainty that originate from the instrument itself (repeatability of spectrophotometer reading, spectrophotometer drift, stray light, etc.) often have significantly lower contributions to the combined uncertainty of the result than the “chemical” sources of uncertainty that originate from the object under study (interference from the constituents of the matrix, decomposition of the photometric complex, etc.). Although selectivity of a photometric procedure is often considered more a validation topic than an uncertainty topic, it is very often important to include it also in the uncertainty budget.Usually the most difficult part of uncertainty estimation of a chemical measurement result is to evaluate the magnitude of the actual uncertainty components, especially the chemical ones. For most of the uncertainty sources discussed in this paper, approaches for their evaluation are given. A generic uncertainty budget for absorbance is presented. Electronic Supplementary Material Supplementary material is available for this article at     

Implementing combined uncertainty according to GUM into a commercial gamma spectrometric software

Measurement uncertainty is an important part of a measurement result that still often is neglected. A complete combined uncertainty budget can be calculated for non-routine measurements. However, for routine measurements, this work becomes time-consuming since every measurement result requires an uncertainty analysis. By analysing the uncertainty on a measurement system level in e.g. high resolution gamma spectrometry, the uncertainty analysis will be universal for a particular measurement geometry. The problem is then reduced to implementing the combined uncertainty into measurement software. This work shows how this analysis can be done and implemented into a commercial software for gamma spectrometric measurements.     

Approach to accuracy assessment of the glass-electrode potentiometric determination of acid-base properties

Thermodynamic data are suitable subject for investigating strategies and concepts for the evaluation of complete measurement uncertainty budgets in situations where the measurand cannot be expressed in a mathematical formula. Some suitable approaches are the various forms of Monte Carlo simulations in combination with computer-intensive statistical methods that are directed to an evaluation of empirical distribution curves for the uncertainty budget. Basis of the analysis is a cause-and-effect diagram. Some experience is available with cause-and-effect analysis of thermodynamic data derived from spectrophotometric data. Another important technique for the evaluation of thermodynamic data is glass-electrode potentiometry. On basis of a newly derived cause-and-effect diagram, a complete measurement uncertainty budget for the determination of the acidity constants of phosphoric acid by glass-electrode potentiometry is derived. A combination of Monte Carlo and bootstrap methods is applied in conjunction with the commercially available code SUPERQUAD. The results suggest that glass-electrode potentiometry may achieve a high within-laboratory precision because major uncertainty contributions become evident via interlaboratory comparisons. This finding is further underscored by analysing available literature data.     

An approach to detection capabilities estimation of analytical procedures based on measurement uncertainty

Detection capabilities are important performance characteristics of analytical procedures. There are several conceptual approaches on the subject, but in most of them a level of ambiguity is presented. It is not clear which conditions of measurements should be used, and there is a relative lack of definition concerning blanks. Moreover, there are no systematic experimental studies concerning the influence of uncertainty associated with bias evaluation. A new approach based on measurement uncertainty is presented for estimating quantities that characterize capabilities of detection. It can be applied to different conditions of measurement and it is not necessary to perform an additional experiment with blanks. Starting from a modelling process of the combined uncertainty of concentration, it is possible to include in the estimated quantities the effects due to random errors and the uncertainty associated to evaluation of bias. The detection capabilities are then compared with the results obtained using some other relevant approaches. Slightly higher values were obtained with the measurement uncertainty approach due to inclusion of uncertainty associated with bias.     

Uranium assay determination using Davies and Gray titration: an overview and implementation of GUM for uncertainty evaluation

The International Organization for Standardization (ISO) Guide to the expression of Uncertainty in Measurement (GUM) was developed to meet the demand for a standardized way of evaluating and expressing uncertainties. The Davies and Gray (D&G) titrimetry method is routinely used in nuclear safeguards for uranium accountability measurement and a statement of the uncertainty that can reasonably be attributed to the measured assay value is therefore of importance. A mathematical model for an uncertainty evaluation of D&G measurements in compliance with ISO GUM is presented. This is illustrated by a numerical example and the utilization of the uncertainty budget is explored.     

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.     

Verification of uncertainty budgets

The quality of analytical results is expressed by their uncertainty, as it is estimated on the basis of an uncertainty budget; little effort is, however, often spent on ascertaining the quality of the uncertainty budget. The uncertainty budget is based on circumstantial or historical data, and therefore it is essential that the applicability of the overall uncertainty budget to actual measurement results be verified on the basis of current experimental data. This should be carried out by replicate analysis of samples taken in accordance with the definition of the measurand, but representing the full range of matrices and concentrations for which the budget is assumed to be valid. In this way the assumptions made in the uncertainty budget can be experimentally verified, both as regards sources of variability that are assumed negligible, and dominant uncertainty components. Agreement between observed and expected variability is tested by means of the T-test, which follows a chi-square distribution with a number of degrees of freedom determined by the number of replicates. Significant deviations between predicted and observed variability may be caused by a variety of effects, and examples will be presented; both underestimation and overestimation may occur, each leading to correcting the influence of uncertainty components according to their influence on the variability of experimental results. Some uncertainty components can be verified only with a very small number of degrees of freedom, because their influence requires samples taken at long intervals, e.g., the acquisition of a new calibrant. It is therefore recommended to include verification of the uncertainty budget in the continuous QA/QC monitoring; this will eventually lead to a test also for such rarely occurring effects.     

Uncertainty budget for high temperature heat flux DSCs

This study addresses the lack of published information regarding uncertainty for high temperature heat flux differential scanning calorimeters. No data were found in the existing literature stating an uncertainty budget for temperatures above 1,000 °C. The presented results identify the main influencing factor for uncertainty with the instruments used—measurement repeatability—up to a temperature of 1,400 °C. Results show findings from analyzing a series of repeated baseline and sapphire measurements and the influence from different working equations. The uncertainty budget for temperature calibration of DSCs is crucial in cases where accuracy in temperature is significant. Data are also provided from repeated temperature calibrations on the melting point of pure metals from a supplied standard set that comes with the instrument. In addition, carbon eutectics have been used to address an issue resulting from the lack of available calibration materials for high temperatures up to 1,500 °C (above the melting point of gold).     

An uncertainty evaluation for multiple measurements by GUM, III: using a correlation coefficient

After a measurement, a measured value and a measurement uncertainty are produced as a measurement result. By a repeated measurement, another measurement result is produced. Between the individual results of the two measurements, it is shown that there may be a significant correlation. A correlation coefficient can be determined when a GUM-compliant uncertainty budget for a measurement is available. Utilizing the correlations between the N individual results, an equation is derived to combine the N individual uncertainties of N measurements. Using the newly derived equation including the correlation coefficient, three measurement uncertainties of three measurement results are combined as an example. The combined uncertainty is compared with the uncertainty of a measurement which treats the three individual measurements as one process. Papers published in this section do not necessarily reflect the opinion of the editors, the editorial board, or the publisher.     

Evaluation of the uncertainty of environmental measurements of radioactivity

Results obtained by measurement of radioactivity have traditionally been associated with an expression of their uncertainty, based on the so-called counting statistics. This is calculated together with the actual result on the assumption that the number of counts observed has a Poisson distribution with equal mean and variance. Most of the nuclear scientific community has, therefore, assumed that it already complied with the latest ISO 17025 requirements. Counting statistics, however, express only the variability observed among repeated measurements of the same sample under the same counting conditions, which is equivalent to the term repeatability used in quantitative analysis. Many other sources of uncertainty need to be taken into account before a statement of the uncertainty of the actual result can be made. As the first link in the traceability chain calibration is always an important uncertainty component in any kind of measurement. For radioactivity measurements in particular we find that counting geometry assumes the greatest importance, because it is often not possible to measure a standard and a control sample under exactly the same conditions. In the case of large samples we have additional uncertainty components associated with sample heterogeneity and its influence on self-absorption and counting efficiency. In this paper we prepared an uncertainty budget for existing data for ¹³⁷Cs in Danish soil, which is shown to account adequately for all sources of uncertainty. This revised version was published online in July 2006 with corrections to the Cover Date.     

Acidity constants in different media (I=0 and I=0.1 M KCl) from the uncertainty perspective

Procedures for estimating the measurement uncertainty for the acidity constant Ka (or the pKa value) in different media (I=0 and I=0.1 mol L(-1) KCl), as determined by potentiometric titration, are presented. The uncertainty budgets (the relative contributions of the different input quantities to the uncertainty in the result) of the pKa (I=0) and pKa (I=0.1 mol L(-1) KCl) values are compared. Unlike the values themselves, the uncertainties and uncertainty budgets of the values are comparable. The uncertainty estimation procedures are based on mathematical models of pKa measurement and involve the identification and quantification of individual uncertainty sources according to the ISO GUM approach. The mathematical model involves 52 and 48 input parameters for pKa (I=0) and pKa (I=0.1 mol L(-1) KCl), respectively. The relative importance of each source of uncertainty is discussed. In both cases, the main contributors to the uncertainty budget are the uncertainty components due to the hydrogen ion concentration/activity measurement, which provide 63.7% (for pKa (I=0)) and 89.3% (for pKa (I=0.1 mol L(-1) KCl)) of the uncertainty. The remaining uncertainty contributions arise mostly from the limited purity of the acid. From this work, it is clear that the uncertainties of the pKa (I=0.1 mol L(-1) KCl) values tend to be lower than those of the pKa (I=0) values. The main reasons for this are that: (1) the uncertainty due to the residual liquid junction potential is nominally absent in the case of pKa (I=0.1 mol L(-1) KCl) due to the similarly high concentrations of background electrolyte in the calibration solutions and measured solution; (2) the electrode system is more stable in solutions containing the 0.1 mol L(-1) KCl background electrolyte and so the readings obtained in these solutions are more stable.     

Uncertainty budget for multi-elemental analysis of plant nutrients in conifer foliar material using inductively coupled plasma atomic emission spectrometry (ICP-AES)

Measurement uncertainties evaluated according to GUM were given in an uncertainty budget for the measurement of mass fractions of 12 elements in conifer tree needle materials. The measurement was performed using ICP-AES, with prior microwave digestion of the dried sample material. The uncertainty budget for Ca as an example showed that correction for a systematic error was the main source of measurement uncertainty. The key to reduced measurement uncertainty therefore lies in identifying the main sources of systematic errors, and reducing the uncertainty associated with their correction. The usefulness of the uncertainty budget was demonstrated in its application to method validation, to the design of a quality control program, and finally for guiding method optimization.     

Approaching target uncertainty in proficiency testing schemes: experience in the field of water measurement

Good correspondence between evaluations of the proficiency testing data for water measurements according to different scoring schemes was found as a result of implementation of the measurement quality according to the target uncertainty defined in the Drinking Water Directive. The accuracy of the evaluation is determined by the uncertainty of the assigned value, and this uncertainty should be in correspondence with the target uncertainty. Modification of the zeta-score by the thorough application of the target uncertainty is presented. It is convenient for generalised presentation of the proficiency testing data. The allowed bias is included as a linear term on the measured value scale, as it is treated in uncertainty analysis. The importance of implementation of the target measurement uncertainty in other fields of the routine measurements is indicated.     

Setting up a decision rule from estimated uncertainty: emission limit value for PCDD and PCDF incineration plants in Wallonia, Belgium

Complex analytical procedures are often required to prove the non-compliance with a specific legislation. In the case of a small overlap of the limit, integration of the method uncertainty in the decision-making process is essential. The decision rule proposed in Wallonia, Belgium, for the non-compliance of waste incineration plants with the EU limit value for PCDD and PCDF emissions is presented. The method uncertainty was estimated annually over 6 years from duplicate measurements using two top-down approaches. Depending on the congener, the standard uncertainty varies from 30 to 85%, with a good correlation between calculations. The analytical contribution was estimated using a bottom-up evaluation. The impact of the sampling step was deduced from the whole estimation and represents more than 80% of the total uncertainty budget. No optimisation is foreseen at this time because of practical field constraints. Based on the average fraction of each congener, the uncertainty associated with the measurement result has been established and shows a high stability over the years. Using this value, a guard band has been calculated and will be proposed to the regulatory body. Presented at the Measurement Uncertainty Symposium, Berlin, Germany, April 2008.     

Uncertainty budget for final assay of a pharmaceutical product based on RP–HPLC

Compliance with specified limits for the content of active substance in a pharmaceutical drug requires knowledge of the uncertainty of the final assay. The uncertainty of measurement is based on the ISO recommendation as expressed in the Guide to the Expression of Uncertainty in Measurement (GUM). The reported example illustrates the estimation of uncertainty for the final determination of a protein concentration by HPLC using UV detection, using the approach described by EURACHEM/CITAC. The combined standard uncertainty for a protein concentration of 2400 µmol/L was estimated to be 14 µmol/L.. All known and potential uncertainty components are presented in Ishikawa diagrams and were carefully evaluated using Type A or Type B estimates. Special efforts were made to avoid duplication or omission of significant contributions to the combined uncertainty. Hence, before accepting the uncertainty budget, the estimated combined standard uncertainty was verified using the variation observed in a number of quality control samples.     

On the use of the ‘uncertainty budget’ to detect dominant terms in the evaluation of measurement uncertainty

In the evaluation of measurement uncertainty, the uncertainty budget is usually used to identify dominant terms that contribute to the uncertainty of the output estimate. Although a feature of the GUF method, it is also recommended as a qualitative tool in MCM by using ‘nonlinear’ equivalents of uncertainty contributions and sensitivity coefficients. In this paper, the use of ‘linear’ and ‘nonlinear’ parameters is discussed. It is shown that when and only when the standard uncertainty of the output estimate is nearly equal to the square root of the sum of the squares of the individual uncertainty contributions, will the latter be a reliable tool to detect the degree of contribution of each input quantity to the measurand uncertainty.     

Metrological traceability chain for PCBs: I.N.Ri.M. activity

Metrology in chemistry has its own features, which distinguish it from classical metrology: due to the lack of primary methods applicable in routine measurements, metrological traceability of measurement results can be achieved by using in a proper way suitable certified reference materials (CRMs), which can assure a direct relation to a reference. This article deals with the activity of the Italian National Institute of Metrological Research (Istituto Nazionale di Ricerca Metrologica—I.N.Ri.M.) on the analysis of various polychlorinated biphenyls congeners in organic solution by means of gas-chromatography coupled with mass spectrometry. The metrological traceability approach in the quantification step is pursued via calibration solutions prepared by gravimetrically diluting a CRM. The uncertainty for the calibration solutions was evaluated taking into account all the relevant contributions.     

SI-traceable values for cadmium concentration in the water samples of IMEP-6

 The certification measurement for the cadmium concentration in the samples as performed by Isotope Dilution (ID) using Inductively Coupled Plasma Mass Spectrometry (ICP-MS) is described in framework of the International Measurement Evaluation Programme (IMEP). By using a primary method of measurement (ID), making up a full uncertainty budget and using a sensitive technique (ICP-MS), reference values traceable to SI can be obtained for this material. The uncertainty budget is performed in accordance with the ISO and EURACHEM guides on uncertainty. A comparison is made with certification results of other experienced laboratories also using primary methods where possible. Received: 8 July 1996/Revised 26 August 1996/Accepted: 1 September 1996     

SI-traceable values for cadmium concentration in the water samples of IMEP-6

 The certification measurement for the cadmium concentration in the samples as performed by Isotope Dilution (ID) using Inductively Coupled Plasma Mass Spectrometry (ICP-MS) is described in framework of the International Measurement Evaluation Programme (IMEP). By using a primary method of measurement (ID), making up a full uncertainty budget and using a sensitive technique (ICP-MS), reference values traceable to SI can be obtained for this material. The uncertainty budget is performed in accordance with the ISO and EURACHEM guides on uncertainty. A comparison is made with certification results of other experienced laboratories also using primary methods where possible. Received: 8 July 1996/Revised 26 August 1996/Accepted: 1 September 1996