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Accreditation and Quality Assurance: Journal for Quality, Comparability and Reliability in Chemical Measurement (v.13, #4-5)


Lectures for chemists on statistics II. The normal distribution: a briefer on the univariate case by Günther Meinrath (pp. 179-192).
Motivated by the introduction of a supplement to the GUM suggesting Monte Carlo simulation as a method for establishing a complete measurement uncertainty budget, some properties of the normal distribution are reviewed. The normal distribution is the central distribution of parametric statistics and sampling from normal distributions is a regularly occurring activity in statistical simulation by Monte Carlo methods. Algorithms for computer generation of normal deviates, areas under the normal curve, and the error function are given to encourage practical simulation. Some critical issues, e.g. coverage and influential observations, are presented. The discussion is restricted to the univariate situation. There is no intention to provide an exhaustive presentation. Statistics is a specialised field requiring sophisticated competences. The text may serve as a golden thread to acquire a quick survey on a subject of general interest.

Keywords: Normal distribution; Empirical distribution function; Sufficiency; Theory of error; Frequentist approach


A comparison of location estimators for interlaboratory data contaminated with value and uncertainty outliers by David Lee Duewer (pp. 193-216).
While estimation of measurement uncertainty (MU) is increasingly acknowledged as an essential component of the chemical measurement process, there is little agreement on how best to use even nominally well-estimated MU. There are philosophical and practical issues involved in defining what is “best” for a given data set; however, there is remarkably little guidance on how well different MU-using estimators perform with imperfect data. This report characterizes the bias, efficiency, and robustness properties for several commonly used or recently proposed estimators of true location, μ, using “Monte Carlo” (MC) evaluation of “measurement” data sets drawn from well-defined distributions. These synthetic models address a number of issues pertinent to interlaboratory comparisons studies. While the MC results do not provide specific guidance on “which estimator is best” for any given set of real data, they do provide broad insight into the expected relative performance within broadly defined scenarios. Perhaps the broadest and most emphatic guidance from the present study is that (1) well-estimated measurement uncertainties can be used to improve the reliability of location determination and (2) some approaches to using measurement uncertainties are better than others. The traditional inverse squared uncertainty-weighted estimators perform well only in the absence of unrepresentative values (value outliers) or underestimated uncertainties (uncertainty outliers); even modest contamination by such outliers may result in relatively inaccurate estimates. In contrast, some inverse total variance-weighted-estimators and probability density function area-based estimators perform well for all scenarios evaluated, including underestimated uncertainties, extreme value outliers, and asymmetric contamination.

Keywords: Consensus value; Interlaboratory comparisons; Measurement uncertainty; Mixture models; Monte Carlo evaluation; Probability density function; Robustness; Weighting function


Proficiency testing in the light of a new rationale in metrology by Kaj Heydorn (pp. 217-222).
The novel proposed definition of measurement result in the international metrology vocabulary requires a revision of standards and guidelines for proficiency testing (PT), and a new approach to processing proficiency data is needed to test the ability of laboratories to present not only unbiased quantity values, but reliable estimates of their uncertainty. Hence, an accepted reference value with the smallest possible uncertainty is needed to ascertain the proficiency of laboratories reporting results with lower than average uncertainty. A strategy based on the T-statistic is proposed leading to an accepted reference value that fully reflects the uncertainties reported by participants in a PT scheme and permits calculation of E n numbers to distinguish whether or not measurement results are consistent with the accepted definition of the measurand. The strategy is applied to PT data from a recent international laboratory intercomparison of uranium isotopic ratios.

Keywords: Proficiency testing; E n numbers; T-statistic; Synthesis of precision; Data processing strategies


A general model for interlaboratory precision accounts for statistics from proficiency testing in food analysis by Michael Thompson; Kenneth Mathieson; Andrew P. Damant; Roger Wood (pp. 223-230).
A meta-analysis of statistics from many proficiency tests has demonstrated the wide applicability of a simple model of reproducibility (interlaboratory) standard deviation. The function has already been proposed as a model for uncertainty in an analytical system, that is, a defined method, analyte and matrix type. The function is a two-parameter model with the concentration of the analyte as the single predictor variable. In this study it is applied to statistics derived from results of an international proficiency test covering many different analytes and matrix types in the food analysis sector. In nearly all instances tested the model accounted well for the observed statistics and could be used as a compact description of the performance of the analytical system.

Keywords: Precision; Model; Characteristic function; Reproducibility; Proficiency test


Performance of uncertainty evaluation strategies in a food proficiency scheme by Stephen L. R. Ellison; Kenneth Mathieson (pp. 231-238).
A study of the performance of different uncertainty evaluation strategies among 163 voluntary respondents from food proficiency schemes is presented. Strategies included use of: single-laboratory validation data, quality control data, past proficiency testing data, reproducibility data, a measurement equation and the dispersion of replicate observations on the test material. Most performed reasonably well, but the dispersion of replicate observations underestimated uncertainty by a factor of approximately 3. Intended compliance with accreditation requirements was associated with significantly improved uncertainty evaluation performance, while intended compliance with the ISO “Guide to the expression of uncertainty in measurement” had no significant effect. Substituting estimates based on the Horwitz or Horwitz–Thompson models or on PT target standard deviation for the respondents’ own estimates of uncertainty led to a marked reduction in poor zeta scores and significant improvement in dispersion of zeta scores.

Keywords: Uncertainty evaluation; Proficiency testing; Reproducibility


Use of uncertainty information for estimation of certified values. Comparison of four approaches using data from a recent certification exercise by Thomas P. J. Linsinger; Andrée Lamberty (pp. 239-245).
Four approaches for estimation of reference values and their respective uncertainties of characterisation were compared using data from the recently finalised certified reference materials ERM-EC680k and ERM-EC681k, elements in plastics. Reference values and uncertainties of characterisation were estimated as mean of laboratory means and their respective standard deviations, using equal weights and the weighting procedure of Mandel–Paule. In addition, two approaches taking into consideration uncertainty information reported by the participants, namely the consistency check and simulation procedure proposed by Cox for CCQM Key comparisons and an approach suggested by Pauwels et al. (Accred Qual Assur 3:180–184, 2000) were used. No difference between the equally-weighted and Mandel–Paule consensus means was observed and the reference value from the Cox approach was in all cases within ±2 u char of each consensus mean. Uncertainties varied between the three approaches. Uncertainties derived from equally-weighted mean of means approach are on average 14% above uncertainties using the Mandel–Paule consensus mean, 36% above the uncertainties estimated by Pauwels et al., and 54% above the uncertainties from the Cox approach. Robustness of the uncertainty estimation against incorrect estimation of uncertainties was assessed. Assumption of a 50% uncertainty of the individual uncertainties resulted in an uncertainty of 30% of the uncertainty of characterisation. Differences between the four approaches are negligible for this dataset when combined with the uncertainty contribution from heterogeneity and stability as prescribed in ISO Guide 35.

Keywords: Uncertainty; Characterisation; CRM; Certified reference materials; Intercomparison


Evaluation of analytical reporting errors generated as described in SW-846 Method 8261A by Michael H. Hiatt (pp. 247-254).
SW-846 Method 8261A incorporates the vacuum distillation of analytes from samples, and their recoveries are characterized by internal standards. The internal standards measure recoveries with confidence intervals as functions of physical properties. The frequency these confidence intervals include true values was very close to theoretical predictions. The ruggedness of the Method’s generation of confidence intervals was tested by analyzing water samples that were altered using salt, glycerin, oil, and detergent, and by increasing sample volume. Quality-control requirements were established for identifying when results might not be normally distributed. There were 11,260 analyte results, of which 90.8% of the data passed quality controls. Their distribution about true value was near theoretical values (71.3, 95.0, and 99.2% for one, two and three sigma deviations).

Keywords: Confidence interval; Analytical error; VOCs (volatile organic compounds); Method 8261


Long-term proficiency testing for the UK Acid Waters Monitoring Network by Mike Gardner (pp. 255-260).
A series of proficiency test rounds to support the UK Acid Waters Monitoring Network has been conducted since the inception of the Network in 1988. These tests provide an illustration of the accuracy and comparability of analysis for laboratories that supply data to the Network. A summary of the tests is reported. Performance with respect to accuracy targets defined for the Network has been shown to be satisfactory for the majority of measurands of interest in studies of surface water acidification.

Keywords: Acid waters; Data quality; Proficiency test accuracy


Volume calibration of 1000 μl micropipettes. Inter-laboratory comparison by Elsa Batista; Eduarda Filipe; Bodo Mickan (pp. 261-266).
A EUROMET comparison “volume calibration of 1000 μl micropipettes”, between six national metrology institutes (NMIs), was performed during 2006 with the purpose of comparing results and uncertainty calculations. The objective of this paper is to describe the volume measure instruments, the model, the method, and to discuss the results and its associated uncertainties presented by each participating NMI.

Keywords: Micropipette; Comparison; Calibration; Uncertainty


Education and training of laboratory staff as a part of laboratory competence by Olga Štajdohar-Pađen (pp. 267-270).
Competence of laboratory staff is an important part of the technical competence of each laboratory. Because the speed at which knowledge goes out of date is increasing, maintaining laboratory staff competence at an appropriate level can be a very demanding requirement, especially for laboratories operating in a free market with little or no financial help from the state or from the larger organisation they possibly belong to. In order to manage staff competence effectively and efficiently, a laboratory must first define its services and the processes needed for realisation of these services. Responsibility for each step in these processes can then be assigned and gap analysis of current competence can be performed. This article analyses the requirements of ISO/IEC 17025 standard and gives some practical advice and solutions how to organize and manage staff competence.

Keywords: Laboratory competence; Laboratory staff; Education; Training; Life-long learning; ISO/IEC 17025 standard


How to revise the GUM? by Walter Bich (pp. 271-275).
The announcement of a revision of the Guide to the expression of uncertainty in measurement has renewed the debate about the topic of measurement uncertainty. In this paper the author, chairman of Working Group 1 of the Joint Committee for Guides in Metrology, replies to the theses given in two recent papers by Semion Rabinovich. His opinions are personal, and are not necessarily shared by the JCGM/WG1. They are to be intended as a further contribution to the present discussion.

Keywords: Metrology; Measurement; Measurement uncertainty
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