A model to set measurement quality objectives and to establish measurement uncertainty expectations in analytical chemistry laboratories using ASTM proficiency test data

A model is presented that correlates historical proficiency test data as the log of interlaboratory standard deviations versus the log of analyte concentrations, independent of analyte (measurand) or matrix. Analytical chemistry laboratories can use this model to set their internal measurement quality objectives and to apply the uncertainty budget process to assign the maximum allowable variation in each major step in their bias-free measurement systems. Laboratories that are compliant with this model are able to pass future proficiency tests and demonstrate competence to laboratory clients and ISO 17025 accreditation bodies. Electronic supplementary material to this paper can be obtained by using the Springer LINK server located at http://dx.doi.org/ 10.1007/s007690100398-y. Received: 31 March 2001 Accepted: 11 September 2001     

Customers' needs in relation to uncertainty and uncertainty budgets

 The general requirement of Quality Management standards to include in test reports a statement of the uncertainty of the results reflects the fact that a test result is rather useless without a knowledge of its accuracy. After an outline of the basic concepts of uncertainty, the need for uncertainty statements is illustrated for different ranges of applications. Received: 23 December 1997 · Accepted: 3 March 1998     

Measurement uncertainty in microbiological cultivation methods

Microbiological analyses are carried out on clinical, food, feed and environmental samples. The aims of the analyses are diagnostic or estimation of the safety or the quality of the sample. Important decisions are made on the basis of microbiological analyses. Little attention, however, is paid to the uncertainty of measurement of microbiological analyses. In microbiological cultivation techniques the result is obtained by counting individual objects. The normally low number of counted objects strongly affects the result of the analysis and its uncertainty. Because of the importance of the particle statistical variation to the uncertainty, the approaches developed for chemical analyses are not directly applicable to microbiology. This paper discusses microbial analyses and describes a novel guidance document for the estimation of measurement uncertainty in culturing methods [1]. Received: 7 October 2000 Accepted: 8 March 2001     

Measurement uncertainty and its meaning in legal metrology of environmental chemistry and public health

 The need for reliability of measurements supporting legal decisions in environmental policy or medical diagnosis and treatment is well known and widely accepted. This prerequisite can be met only by ensuring that legal measurements are accurate and traceable to national or international standards. Consequently, an outline of the organizational structure of the Romanian National Institute of Metrology (INM) for ensuring uniformity, consistency and accuracy of all measurements including legal measurements performed in chemical laboratories is presented. Since reliable measurements can only be accomplished within an appropriate traceability chain, the experience of the INM in identification and evaluation of measurement uncertainty in legal activities concerning the environment and health is reviewed. Practical examples of measurement uncertainty evaluation in spectrophotometric determination of five analytes, commonly determined in environmental and clinical chemistry are described. The implications of measurement uncertainty for interpretation of regulatory compliance are discussed. Received: 3 January 1998 · Accepted: 9 June 1998     

Evaluating uncertainty in analytical measurements: the pursuit of correctness

 Simple in principle, the evaluation of uncertainty, especially in chemical analysis, is not a routine task and needs great care to be correct. This can be seen, particularly, from an examination of the EURACHEM Guide, Quantifying Uncertainty in Analytical Measurement (1995), which is the most important document on the subject. The examination reveals, in the author's opinion, a shortage of correctness in some principal details of the uncertainty estimation process as presented in worked examples in the Guide, and the author has therefore formulated some "in pursuit of correctness" rules for estimating uncertainty. The rules and respective comments are concerned with the following items: (1) choosing an appropriate distribution function in type B evaluation of uncertainty, (2) the necessity for consideration of separate contributions to the combined uncertainty, and (3) taking account of actual influence factors in the uncertainty estimation process. Furthermore, the problem of estimation of conditional versus overall uncertainty is touched upon in connection with comparative trials where only internal consistency of results is required. Received: 29 January 1998 · Accepted: 10 February 1998     

A view of uncertainty at the bench analytical level

 The problem with which analytical laboratories are confronted, after traceability of their results has been demonstrated, is correctly estimating their uncertainty– to which traceability is also to some extent subject. While the general principles for calculating the uncertainty of physical measurements are applicable to chemical metrology, some refinements are needed, especially careful selection and planning the level at which uncertainty will be estimated by each laboratory in accordance with its capacity and required demands. Depending on the particular decision to be made, the mechanism to be used to estimate the uncertainty varies markedly; also, the rigour of the estimation increases with increasing stringency of the demands. This paper describes the primary sources of uncertainty in chemical metrology and discusses different approaches to its estimation in relation to the type of analytical laboratory concerned. The view presented tries to be close to the bench analytical level, in order to be practical and flexible for laboratories, although it could sometimes be considered slightly heterodox. Received: 25 March 1997 · Accepted: 20 September 1997     

Chemical metrology, chemistry and the uncertainty of chemical measurements

Chemical results normally involve traceability to two reference points, the specific chemical entity and the quantity of this entity. Results must also be traceable back to the original sample. As a consequence, any useful estimation of uncertainty in results must include components arising from any lack of specificity of the method, the variation between repeats of the measurement and the relationship of the result to the original sample. Chemical metrology does not yet incorporate uncertainty arising from any lack of specificity from the method selected or the traceability of the result to the original sample. These sources of uncertainty may however have much more impact on the reliability of the result than will any uncertainty associated with the repeatability of the measurement. Uncertainty associated with sampling may amount to 50–1000% of the reported result. Chemical metrology must be expanded to include estimations of uncertainty associated with lack of specificity and sampling. Received: 29 May 2001 Accepted: 17 December 2001     

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     

Measurement uncertainty distributions and uncertainty propagation by the simulation approach

A complete and accurate evaluation of measurement uncertainty requires the knowledge of the uncertainty distributions. The latter are rarely determined or verified experimentally, and hence up to now only crude estimates or assumptions based on intuition have been used. The simulation of experimental results is readily accessible and provides a more relia-ble solution to this problem. When using an appropriate model of measurement and after determina-tion of input value parameters by present state-of-the-art techniques, simulation data supply reliable information about the distribution of the output results of a complex measurement. The method permits simple variation of preposition and therefore ready analysis of various features influencing the measurement of uncertainty intervals. In the paper we described examples of such evaluations related to the preparation of certified reference materials, where there is excellent agreement between the traditional and simulation approaches. And evaluation of more complex measurements of diffusion coefficients by the open capillary method, where uncertainty of the simulated result is more realistic than the re-sult from the traditional error method due to non-linearity and probably Cauchy distribution in some steps. Received: 17 March 2000 Accepted: 25 July 2000     

Derived measurement standards of reduced uncertainty – A contradiction?

 If the value of a derived measurement standard is assigned by comparison with a reference standard of the same quantity, the uncertainty is increased by the additional uncertainty on the difference measurement. This basic fact has lead to the general belief that the uncertainty of derived standards is always larger than that of the reference standards. However, if the value of a derived standard is assigned by comparison with several independent reference standards using an appropriate average, the increase of uncertainty due to the uncertainty on difference measurement may be counterbalanced by the the well-known decrease of uncertainty through averaging. The gain of accuracy made possible by this mechanism is restricted to second-generation standards. Further gain through iteration is prevented by correlation between standards derived from the same set of reference standards. As a consequence, the concept of metrological hierarchy levels, relating to traceability chains, becomes questionable for traceability networks.     

An uncertainty evaluation for multiple measurements by GUM

An approach for uncertainty evaluation is proposed to determine the overall uncertainty by combining the uncertainties of the individual results from multiple measurements. It is accomplished by the separate combinations of the individual random and systematic components of the uncertainties of the individual results. The approach is useful when the individual results are not statistically different. It is recognized that, owing to the correlation, the uncertainty resulting from systematic effects is not reduced by multiple measurements. On the contrary, the uncertainty resulting from random effects can be reduced. Received: 3 May 2002 Accepted: 16 July 2002     

Evaluation of uncertainty of reference materials

 Certification of reference materials is far more than just characterisation of a selected homogeneous batch of material. From the perspective of the ISO Guide on the Expression of Uncertainty in Measurement (GUM) all uncertainty sources relevant to the user of an individual certified reference material (CRM) sample at a moment in time should be part of the CRM uncertainty. This not only includes the full uncertainty of the batch characterisation (rather than the statistical variation), but also all uncertainties related to possible between-bottle variation, instability upon long-term storage and instability during transport to the customer. Received: 21 April 1999 · Accepted: 24 September 1999     

Evaluation of uncertainty utilising the component by component approach

 This paper reviews the so-called "component by component approach" of evaluating measurement uncertainty. An overview of the evaluation process is given followed by an in-depth discussion of some of the differences between this approach and the approach of utilising validation data. Some of the advantages and disadvantages of using the component by component approach are outlined at the end. Received: 4 August 1999 · Accepted: 11 November 1999     

Traceability and analytical chemistry

 The basic concepts of traceability as they are defined by the Comité Consultatif pour la Cluantité de Matière are contrasted with the practical exploitation in chemical analysis. The applicability of traceability concepts are tested for their practical applicability on four different analytical methodologies, neutron activation analysis, plasma mass spectrometry, beam microscopical analysis and speciation analysis of organometallic compounds. Received: 31 March 1998 · Accepted: 6 June 1998     

A framework for the application and materials in analytical chemistry

 Working group 5 of EuraChem Nederland has developed a framework for the implementation of reference materials in analytical chemistry. In this discussed paper, the framework is proposed as a tool for the development of standard operation procedures (SOPs) in laboratories. The implementation of (certified) reference materials in these SOPs is of major importance in establishing comparability and traceability in measurement results, which in turn play a crucial role in measurement in support of trade, environmental issues, and characterisation of materials. Recent developments in the field of uncertainty analysis require the application of reference materials. It is recognised that the calculation of the combined measurement uncertainty becomes almost impossible without the use of certified reference materials with a stated uncertainty. Received: 1 December 1995 Accepted: 20 December 1995     

Should non-significant bias be included in the uncertainty budget?

The bias of an analytical procedure is calculated in the assessment of trueness. If this experimental bias is not significant, we assume that the procedure is unbiased and, consequently, the results obtained with this procedure are not corrected for this bias. However, when assessing trueness there is always a probability of incorrectly concluding that the experimental bias is not significant. Therefore, non-significant experimental bias should be included as a component of uncertainty. In this paper, we have studied if it is always necessary to include this term and which is the best approach to include this bias in the uncertainty budget. To answer these questions, we have used the Monte-Carlo method to simulate the assessment of trueness of biased procedures and the future results these procedures provide. The results show that non-significant experimental bias should be included as a component of uncertainty when the uncertainty of this bias represents at least a 30% of the overall uncertainty. Received: 29 May 2001 Accepted: 10 December 2001     

Measurement uncertainty of microbiological viable counts

Estimation of the uncertainty of microbiological viable counts by the statistical analysis of series of observations is impractical because the observed value, the number of colonies, usually determines a large share of the uncertainty. Every test result, therefore, has a unique uncertainty and no general method-specific values exist. The most practical ways to estimate the uncertainty are based on mathematical models and assumed statistical distributions where the observed value is a significant parameter. The article describes the traditional solution based on the Poisson distribution and more advanced models based on the negative binomial distribution. The latter model is capable of combining technical and procedural components of uncertainty with the inevitable random scatter of microbial suspensions. The additional uncertainty due to subsampling in the confirmation of presumptive positives is estimated with the help of a binomial model. Traceability issues are discussed.Presented at the Metro Trade Workshop on Traceability and Measurement Uncertainty in Testing, 30–31 January 2003, Berlin, Germany     

Study of the uncertainty in gravimetric analysis of the Ba ion

The determination of barium by the gravimetric method, in which the precipitation of BaSO₄ was formed and weighed, coupled with instrumental measurement of trace constituents was studied. The analyte’s remaining in the filtrate and washes, mechanical loss, contaminants in the precipitate are the main influencing factors of uncertainty. A series of condition tests have been done, to reduce the effect of the factors mentioned above and the optimum test condition was found. The determination was carried out with a strictly defined operational procedure. The trace amounts of barium in the filtrate, washes and mechanical loss were determined by ICP-AES, the chloride occluded in the precipitate was determined by ion chromatography (IC), calculated as BaCl₂ and barium, and sodium by FAAS, calculated as Na₂SO₄. The average mass of barium in the filtrate contributes about 0.06% relative to that of the total barium, in washes about 0.09%, mechanical loss about 0.06%, contaminants of BaCl₂ about 0.08% and Na₂SO₄ about 0.05%. All the trace constituents were determined and corrected on a sample-by-sample basis. Sources of uncertainty were assessed thoroughly. The uncertainty of this combined gravimetric-instrumental method was improved remarkably compared with that of gravimetric method alone. The expanded uncertainty (k =2) is 0.08%. Received: 15 June 2000 Accepted: 25 December 2001     

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     

Measurement uncertainty of selenium determination in the reference material Seronorm Trace Elements Serum by hydride generation atomic fluorescence spectrometry

 An analytical result is not considered to be complete without a statement of the measurement uncertainty associated with it. Evaluation of measurement uncertainty is therefore an essential part of every determination. In the present study the measurement uncertainty of the result of determination of selenium in the reference material Seronorm Trace Elements Serum was studied. The combination of a digestion procedure using sulfuric acid, V₂O₅ in H₂SO₄ and hydrogen peroxide and the continuous flow approach of hydride generation atomic fluorescence spectrometry (HG-AFS) detection was used for selenium determination. The total uncertainty budget was calculated with the help of the GUM Workbench program, in which computations follow the rules of the ’ISO guide to the expression of uncertainty in measurement’. The major sources of uncertainty were found to be due to the recovery of the procedure, measurement of peak heights and the purity of Na₂SeO₃. A selenium mass fraction of 77.1±4.8 ng/g (with a coverage factor of 2.1, 95% probability) was determined, which is comparable with the recommended value of 80 ng/g. Received: 13 September 2002 Accepted: 23 December 2002 Acknowledgements We would like to thank Tinkara Buˇcar, B.Sc. for useful discussions and the IAEA Vienna, for financial support of the project 11553/RO. Presented at CERMM-3, Central European Reference Materials and Measurements Conference: The function of reference materials in the measurement process, May 30–June 1, 2002, Rogaška Slatina, Slovenia Correspondence to V. Stibilj