Approaches to uncertainty evaluation based on proficiency testing schemes in chemical measurements

Since the advent of the Guide to the Expression of Uncertainty in Measurement (GUM) founding the principles of uncertainty evaluation, numerous projects have been carried out to develop alternative practical methods when it is impossible to model technical or economical aspects of the measurement process. These methods can use all the experimental data available to the laboratories, such as repeatability, reproducibility, quality-control charts, etc. The studies presented in this paper compare the results obtained by the modelling method from GUM with the uncertainties found by applying alternative methods. They show two examples, one in the field of environmental monitoring, the other in the biomedical field, based on the exploitation of PT schemes results. Presented at BERM-11, October 2007, Tsukuba, Japan.     

Visualisation of proficiency test exercise results in Kiri plots

A novel graphical method (‘Kiri plots’) for the presentation of proficiency test exercise results is presented. The Kiri plot visualises the evaluation of the proficiency test results based on three statistical tests (the z score, the zeta score and the relative uncertainty outlier test) by defining six zones including a central “in agreement” zone.     

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.     

A new approach for proficiency test exercise data evaluation

In this paper, a new data evaluation method for proficiency test exercises consisting of a combination of a z-test, a zeta test and an uncertainty outlier test is presented. This new method is compared with eight other evaluation methods (both measurement uncertainty using and measurement uncertainty ignoring) in common use and/or recommended by ISO 13528. The data set used to test the evaluation methods is real data and consists of the ⁹⁵Nb results of the National Physical Laboratory Environmental Radioactivity Proficiency Test Exercise 2007. The evaluation of 14 out of 32 results were affected by the choice of method.     

From GUM to alternative methods for measurement uncertainty evaluation

Since the advent of the Guide to the expression of Uncertainty in Measurement (GUM) in 1995 laying the principles of uncertainty evaluation numerous projects have been carried out to develop alternative practical methods that are easier to implement namely when it is impossible to model the measurement process for technical or economical aspects. In this paper, the author presents the recent evolution of measurement uncertainty evaluation methods. The evaluation of measurement uncertainty can be presented according to two axes based on intralaboratory and interlaboratory approaches. The intralaboratory approach includes “the modelling approach” (application of the procedure described in section 8 of the GUM, known as GUM uncertainty framework) and “the single laboratory validation approach”. The interlaboratory approaches are based on collaborative studies and they are respectively named “interlaboratory validation approach” and “proficiency testing approach”.     

Integration of metrological principles and performance evaluation in a proficiency testing scheme in support of the Council Directive 98/83/EC

Proficiency testing as a means of external quality assessment plays the role of independent evidence of laboratories’ performance. To enable laboratories to fulfil the requirements stated in legislation, methodology for evaluation of laboratories’ performance in proficiency testing schemes should incorporate principles of measurement results which are fit for intended use and incorporate evaluation of laboratories’ performances based on independent reference value. A proficiency testing scheme was designed to support Drinking Water Directive (98/83/EC) specifically. The methodology for performance evaluation, which takes into account a “fitness for purpose”-based standard deviation for proficiency assessment, is proposed and discussed in terms of requirements of the Drinking Water Directive. A ζ′-score, modified by application of target uncertainty was developed in a way that fulfils requirements defined in the legislation. As an illustration, results are reported for nitrate concentration in water. The approach presented can also be applied to other fields of measurements.     

Evaluation of proficiency testing results taking into account their uncertainties

A new composite score for the evaluation of performance of proficiency testing participants is proposed. The score is based on a combination of the z-score, uncertainty of a participant’s measurement result and uncertainty of the proficiency testing scheme’s assigned value. The use of such a composite score will allow evaluation not only of the participant’s ability to determine an analyte in corresponding matrix, but also their understanding of the uncertainty in the obtained analytical result. The score may be helpful for the laboratory’s quality system and for laboratory accreditation according to ISO 17025.     

Determination of uncertainty in analytical measurements from collaborative study results on the analysis of a phenoxymethylpenicillin sample

The correct interpretation of a measurement result requires knowledge about its uncertainty. Depending on the conditions under which the analyst is operating, different operational definitions of uncertainty have been proposed. They include: within-laboratory uncertainty, reproducibility uncertainty, bias-included uncertainty and absolute uncertainty. Here we consider the evaluation of the reproducibility uncertainty derived from the results obtained in an inter-laboratory experiment. Nine laboratories participated in an inter-laboratory study for the analysis of phenoxymethylpenicillin. The analyses consisted of a Karl-Fischer water determination, an acid-base titration to assay phenoxymethylpenicillin and a liquid chromatography (LC) method to determine 4-hydroxyphenoxymethylpenicillin and other impurities. The experimental set-up allowed to obtain for each determination s_r² and s_L² as estimates of the repeatability variance (σ_r²) and the between-laboratory variance (σ_L²), respectively. The reproducibility uncertainties for the different assays were then derived from these estimates.     

An error model for evaluation and interpretation of proficiency testing

Data from proficiency testing can be used to increase our knowledge of the performance of populations of laboratories, individual laboratories and different measurement methods. To support the evaluation and interpretation of results from proficiency testing an error model containing different random and systematic components is presented. From a single round of a proficiency testing scheme the total variation in a population of laboratories can be estimated. With results from several rounds the random variation can be separated into a laboratory and time component and for individual laboratories it is then also possible to evaluate stability and bias in relation to the population mean. By comparing results from laboratories using different methods systematic differences between methods may be indicated. By using results from several rounds a systematic difference can be partitioned into two components: a common systematic difference, possibly depending on the level, and a sample-specific component. It is essential to distinguish between these two components as the former may be eliminated by a correction while the latter must be treated as a random component in the evaluation of uncertainty. Received: 20 November 2000 Accepted: 3 January 2001     

Estimates of uncertainty of measurement from proficiency testing data: a case study

The results obtained by a laboratory over a number of proficiency testing/external quality assessment schemes (PT/EQAS) rounds can give information on the uncertainty of its measurements for a given test, provided that conditions such as full coverage of the routine analytical range, traceability, and small uncertainty of the assigned values (compared to the spread of the results) are met and provided that systematic deviations and any other sources of uncertainty are considered. As organisers of the Italian EQAS (ITEQAS) in occupational and environmental laboratory medicine, we tested this hypothesis using as model data from well-performing laboratories taking part in ITEQAS for lead in blood over the last 2 years. We also investigated how different PT/EQAS features (frequency of trials and number of samples) would affect a laboratory estimate of its uncertainty. Such information can be helpful in improving PT/EQAS organisation and define, for a given test: (a) the state of the art of the uncertainty of current measurement procedures, (b) identify needs for improvement of analytical methodologies and (c) set targets for acceptable uncertainty values.Presented at the Eurachem PT Workshop September 2005, Portorož, Slovenia.Papers published in this section do not necessarily reflect the opinion of the Editors, the Editorial Board and the Publisher.     

A statistical strategy for discouraging collusion in split-level proficiency testing schemes

A statistical strategy for discouraging collusion in split-level proficiency testing schemes was developed. When the samples are randomly labeled, the difference in the analyte levels in the two samples can be designed to maximize the probability of detecting collusion when it occurs, so that participants who colluded cannot easily receive satisfactory assessments. This favors providing convictive assessments of participants proficiency and giving the participants a level playing field.     

Comparability of analytical results obtained in proficiency testing based on a metrological approach

A “yes–no” type of criterion is proposed for the assessment of comparability of proficiency testing (PT) results when the PT scheme is based on a metrological approach, i.e. on the use of a reference material as the test sample, etc. The criterion tests a null hypothesis concerning the insignificance of a bias of the mean of the results from a traceable value certified in the reference material used for the PT. Reliability of such assessment is determined by the probabilities of not rejecting the null hypothesis when it is true, and rejecting it when it is false (the alternative hypothesis is true). It is shown that a number of chemical, metrological and statistical reasons should be taken into account for careful formulation of the hypotheses, enabling the avoidance of an erroneous assessment of the comparability. The criterion can be helpful for PT providers and laboratory accreditation bodies in analysis of PT results.     

Comparability and compatibility of proficiency testing results in schemes with a limited number of participants

Comparability and compatibility of proficiency testing (PT) results are discussed for schemes with a limited number of participants (less than 20–30) based on the use of reference materials (RMs) as test items. Since PT results are a kind of measurement/analysis/test result, their comparability is a property conditioned by traceability to measurement standards applied in the measurement process. At the same time, metrological traceability of the certified value of the RM (sent to PT participants as test items) is also important, since the PT results are compared with the RM certified value. The RM position in the calibration hierarchy of measurement standards sets the degree of comparability for PT results, which can be assessed in the scheme. However, this assessment is influenced by commutability (adequacy or match) of the matrix RM used for PT and routine samples. Compatibility of PT results is a characteristic of the collective (group) performance of the laboratories participating in PT that can be expressed as closeness of the distribution of the PT results to the distribution of the RM data. Achieving quality-of-measurement/analysis/test results in the framework of the concept “tested once, accepted everywhere” requires both comparability and compatibility of the test results.     

Implementation of proficiency testing schemes for a limited number of participants

A metrological background for the selection and use of proficiency testing (PT) schemes for a limited number N of laboratories-participants (less than 20–30) is discussed. The following basic scenarios are taken into account: (1) adequate matrix certified reference materials (CRM) or in-house reference materials (IHRM) with traceable property values are available for PT use as test items; (2) no appropriate matrix CRM is available, but a CRM or IHRM with traceable property values can be applied as a spike or similar; (3) only an IHRM with limited traceability is available. The discussion also considers the effect of a limited population of PT participants N _p on statistical assessment of the PT results for a given sample of N responses from this population. When N _p is finite and the sample fraction N/N _p is not negligible, a correction to the statistical parameters may be necessary. Scores suitable for laboratory performance assessment in such PT schemes are compared. Presented at the 3rd International Conference on Metrology, November 2006, Tel Aviv, Israel.     

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     

ISO/IEC 17043: the new International Standard for proficiency testing

The revision of ISO/IEC Guide 43 is well underway by CASCO Working Group 28, with the author as Convener. The ballot on the committee draft was successfully completed in June 2008. The Working Group met in September to resolve the CD comments and to recommend that the document should advance as an ISO/IEC DIS. The document is in harmony with ISO/IEC 17025 (2005), ILAC G13 (2007), and the IUPAC Harmonized Protocol (2006) for proficiency testing. Major changes from Guide 43 include considerations for inspection bodies, requirements for metrological traceability of assigned values for calibration schemes, limitations on subcontracting, requirements for reporting the uncertainty of assigned values, and for including method information and technical commentary in scheme reports. Minor changes include requirements for equipment used in the manufacture and testing of proficiency test items, considerations for handling laboratories’ reported uncertainties, and the issuance of certificates of participation. These changes have not generated any substantial objections from the CASCO membership and liaisons.     

Interlaboratory study of a liquid chromatography method for erythromycin: determination of uncertainty

Erythromycin is a mixture of macrolide antibiotics produced by Saccharopolyspora erythreas during fermentation. A new method for the analysis of erythromycin by liquid chromatography has previously been developed. It makes use of an Astec C18 polymeric column. After validation in one laboratory, the method was now validated in an interlaboratory study. Validation studies are commonly used to test the fitness of the analytical method prior to its use for routine quality testing. The data derived in the interlaboratory study can be used to make an uncertainty statement as well. The relationship between validation and uncertainty statement is not clear for many analysts and there is a need to show how the existing data, derived during validation, can be used in practice. Eight laboratories participated in this interlaboratory study. The set-up allowed the determination of the repeatability variance, s(2)r and the between-laboratory variance, s(2)L. Combination of s(2)r and s(2)L results in the reproducibility variance s(2)R. It has been shown how these data can be used in future by a single laboratory that wants to make an uncertainty statement concerning the same analysis.     

Influence of silica gel humidity on the determination of hydrocarbon types in gasoline by the ASTM D 1319 standard test method in relation to proficiency test reproducibility

The results obtained for the olefin content of gasoline with the ASTM D1319 Standard Test Method show a strong increase with the humidity of the silica gel used, while such an increase is absent for the aromatic hydrocarbon content. These results seem to suggest that the increased experimental reproducibility, compared to the value of the ASTM D1319 Standard Test Method, which is often observed for the olefin content in proficiency tests, may be due to the use of insufficiently dry silica gel.