Estimation of the uncertainty of CRMs in accordance with GUM: application to the certification of four enzyme CRMs

Uncertainties of four enzyme-CRMs that have recently been certified in a co-operation between the IRMM and the International Federation for Clinical Chemistry were estimated. Estimation was based on the sum of the uncertainties of characterization, homogeneity and stability. Data from the certification collaborative study were used to estimate laboratory uncertainties, which form the basis for the uncertainty of characterization. Estimations for the uncertainty of homogeneity were derived from classical homogeneity studies. The estimations of uncertainty of stability caused the most difficulties. Realistic uncertainties fitting the needs of customers while being derived from measurement data based on theoretical considerations were obtained.     

Preparation and preliminary certification of two new Polish CRMs for inorganic trace analysis

Preparation and characterization of two new reference materials of biological origin, namely: Tea Leaves (INCT-TL-1) and Mixed Polish Herbs (INCT-MPH-2) is described. The raw materials were ground in an agate ball mill, sieved through a nylon sieve, collecting fraction of particle size: Æ£67 ·m, and carefully homogenized. Preliminary homogeneity testing by XRF method and final checking of homogeneity by NAA after distribution of the materials into containers revealed that they are sufficiently homogeneous at least for sample size ≥100 mg. Both materials were prepared in amounts exceeding 40 kg and certified on the basis of a worldwide interlaboratory comparison, in which 109 laboratories from 19 countries participated. The method of data evaluation leading to assignment of certified values was essentially the same as that used previously in this Laboratory, but supplemented by additional data from the analysis of a CRM which was sent to the participants and analyzed by them along with the candidate reference materials. In addition the results for a few elements by very accurate developed methods in this Laboratory were obtained and used to support the certification process. Analytical uncertainties and stability uncertainties were quantified to arrive at combined uncertainties of the certified values. So far 18 elements in INCT-TL-1 and 21 in INCT-MPH-2 could be certified.     

Estimating the uncertainty of stability for matrix CRMs

The new version of ISO Guide 34 requires producers of certified reference materials (CRMs) to include contributions of possible instability to the overall CRM uncertainty, to obtain a value for the uncertainty in compliance with the Guide to the Expression of the Uncertainty in Measurement (GUM). A pragmatic approach to estimating the uncertainty of stability is presented. It relies on regression analysis of stability data with subsequent testing of the slope of the regression line for significance. If the slope is found to be statistically insignificant, a shelf life is chosen and the uncertainty connected with this time is estimated via the standard deviation of the slope. This uncertainty is included in the overall uncertainty of the CRM. This approach is explained with examples showing its applicability to matrix CRMs. Received: 12 October 2000 / Revised: 2 January 2001 / Accepted: 3 January 2001     

Uncertainty calculations in the certification of reference materials. 1. Principles of analysis of variance

 The preparation and certification of reference materials is a rapidly developing area. Many innovative reference materials have limited homogeneity and stability, and, additionally, the uncertainty estimation of the property values must be brought in agreement with the principles of the “Guide to the expression of uncertainty in measurement” (GUM). The results of the homogeneity and stability studies must be included to a certain extent in the uncertainty of the property values of the reference material, in order to comply with these requirements. The basic theory needed to accomplish this is essentially the theory of analysis of variance (ANOVA). As GUM also allows alternative evaluations other than Type A evaluations, a reinterpretation of the theory of ANOVA is necessary to establish a model for the certification of reference materials that is widely applicable. For this, analysis of variance can be used as a statistical technique to derive standard uncertainties from homogeneity, stability and characterisation data. Received: 10 May 2000 / Accepted: 29 July 2000     

Uncertainty calculations in the certification of reference materials 4. Characterisation and certification

The main objective of the certification of a reference material is to determine its property values including their uncertainty. In the previous parts of this series, the basis for the evaluation of measurement uncertainty of the property values has been examined, including the conversion of homogeneity and stability study data into standard uncertainties. In this final part, the determination of the property values and the modelling of the certification process is discussed. It is noted that the characterisation of a reference material can be modelled in some cases using analysis of variance statistics, but a more generally applicable model can be developed based on χ²-fitting. Furthermore, it is concluded that there is an advantage in using absolute standard uncertainties instead of relative ones when modelling the certification process. Received: 14 October 2000 Accepted: 21 January 2001     

Conclusions from 13 years of stability testing of CRMs for determination of metal species

We present results of the systematic stability monitoring of certified reference materials (CRMs) for the mass fractions of metal species. Materials are tested regularly for the mass fractions of organotin, organomercury, organolead and organoarsenic species. Evaluation is based on ratios of results on samples stored under normal conditions and under even safer conditions (“reference stock”) to eliminate the effects of laboratory-to-laboratory variation. Of all results in this study, the results of organotin measurements show the highest relative standard deviations (up to 45%). Determination of methylmercury in sediment and fish is possible with much better precision (standard deviations of reproducibility below 5%). The accuracies of determinations of trimethyllead and organoarsenic species are slightly worse but still below 10%. The data confirmed stability since production (i.e. up to 13 years). However, shelf lives cannot be extended into the future based on these data, as uncertainty contributions for stability need to be included in the uncertainty budgets of CRMs to allow positive demonstration of the validity of certificates. Estimation of typical measurement uncertainties based on the data obtained from stability monitoring shows that potential degradation is negligible compared to uncertainties typical for this kind of measurement, demonstrating that the materials are still sufficiently reliable to demonstrate laboratory proficiency.     

Certified reference materials for the quality control of EDTA- and acetic acid-extractable contents of trace elements in sewage sludge amended soils (CRMs 483 and 484)

 The ecotoxicity and mobility of trace elements in soils are often evaluated through analytical results resulting from operationally-defined determinations (single and sequential extractions), e.g. based on EDTA, acetic acid etc. extractions. The significance and comparability of these results is highly dependent on the procedures used (standardized protocols or standards adopted by international bodies) and their quality control relies on the availability of reference materials certified following these strictly applied procedures. Recognizing the need to harmonize some of the extraction schemes currently used for soil analysis, the Measurements and Testing Programme (formerly BCR) has organized a series of interlaboratory studies, the first aim of which was to evaluate EDTA- and acetic acid-extraction procedures and the second objective was to certify reference materials for their extractable trace element contents. Two sewage amended soils have been prepared for this purpose, originating respectively from Scotland and Catalonia. This paper describes the preparation, homogeneity and stability studies, and gives an overview of the certification campaign. Received: 6 May 1996/Revised: 14 June 1996/Accepted: 27 June 1996     

Use of uncertainty information for estimation of certified values. Comparison of four approaches using data from a recent certification exercise

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. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Homogeneity and stability of reference materials

 Homogeneity and stability are two crucial characteristics of any certified reference material (CRM). Utmost care must be taken during preparation to create materials as homogeneous and stable as possible. Degradation can generally be minimised by reducing the water activity of the material to a level between 0.15 and 0.35. However, careful preparation by itself is not enough. Positive demonstration of homogeneity and stability is required from the perspective of implementing uncertainty calculus according to the Guide to the Expression of Uncertainty in Measurement (GUM). In many cases, homogeneity and stability studies fail to give sufficient quantitative information on homogeneity and stability, mainly because of a lack of measurement repeatability and insufficient number of replicates. In this work, some solutions to these problems and their implications are presented. Received: 25 April 2000 / Accepted: 12 September 2000     

Preparation and evaluation of sufficiently homogeneous and stable reference materials for priority hazardous substances in whole water

We have prepared and evaluated three whole water test materials containing eight polycyclic aromatic hydrocarbons (PAHs), six polybrominated diphenyl ethers (PBDEs) and tributyltin (TBT) with respect to homogeneity and short-term stability. The test materials were used as samples in two inter-laboratory comparisons. The materials were composed of natural mineral water and model suspended particulate matter (SPM) containing the target compounds at ng L^?1 levels. The expanded uncertainty of the estimated mass concentrations in the final test materials was obtained by combining contributions from the homogeneity, the stability and the model SPM characterization. The whole water materials were sufficiently homogeneous and stable at 4 °C for their intended use. In total, 12 out of 15 investigated target parameters could be assessed to be present with a relative combined expanded uncertainty below 25 %. The outcome of the two inter-laboratory comparisons confirmed the good quality of the test materials and the level of uncertainties associated with the estimated mass concentrations. These findings are an important contribution towards the development of whole water matrix reference materials certified for PAH, PBDE and TBT in support of the Water Framework Directive of the European Union.     

Estimating the uncertainty of stability for matrix CRMs.

The new version of ISO Guide 34 requires producers of certified reference materials (CRMs) to include contributions of possible instability to the overall CRM uncertainty, to obtain a value for the uncertainty in compliance with the Guide to the Expression of the Uncertainty in Measurement (GUM). A pragmatic approach to estimating the uncertainty of stability is presented. It relies on regression analysis of stability data with subsequent testing of the slope of the regression line for significance. If the slope is found to be statistically insignificant, a shelf life is chosen and the uncertainty connected with this time is estimated via the standard deviation of the slope. This uncertainty is included in the overall uncertainty of the CRM. This approach is explained with examples showing its applicability to matrix CRMs.     

Preliminary study to prepare a reference material of styrene metabolites – mandelic acid and phenylglyoxylic acid – in human urine

 A preliminary batch of the reference material was prepared by freeze-drying pooled urine samples obtained from healthy persons occupationally exposed to styrene. Tests for homogeneity and stability were performed by determining urine concentrations of mandelic (MA) and phenylglyoxylic acids (PGA). The urinary MA and PGA concentrations were followed over an 8-month period using high performance liquid chromatography (HPLC). No changes of the concentration values were found. Pure PA and PGA from Merck and Fluka, respectively, were used for traceability purposes, because certified or standard reference materials for MA and PGA do not exist. Control material ClinChek-Urine Control (Recipe) was analysed simultaneously. The mean values of MA and PGA compared well with the means of control samples and fell within the control range. The certified values and their uncertainties were evaluated from the results of interlaboratory comparisons, homogeneity (277.0 ± 7.4 mg L⁻¹ for MA and 148.0 ± 4.7 mg L⁻¹ for FGA) and stability tests. The values are unweighted arithmetical averages of accepted results and their uncertainties are combined uncertainties enlarged by coefficient k=1, evaluated from the standard uncertainties of the interlaboratory comparison, homogeneity and stability tests. Received: 17 September 2002 Accepted: 1 November 2002 Acknowledgement This work was supported by the Internal Grant Agency of Ministry of Health of the Czech Republic (Grant NJ/6784–3). 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 I. Šperlingová     

Planning and combining of isochronous stability studies of CRMs

The first part of this paper discusses some critical factors in planning and evaluation of isochronous stability studies. Recommendations on the number of time-points, number of items, and number of replicates to be measured on each unit are given. In general, more than two time-points should be used. The effect of batch heterogeneity can be eliminated by spreading the results over more units. An approach for combining two or more isochronous stability studies is developed in the second part. This approach includes a potential correction of the earlier stability study, pooling of data of the stability studies, and an uncertainty evaluation taking into consideration the uncertainty of the initial correction. The statistical basis for this approach is developed and equations for evaluation of the uncertainty of stability of the combined study are given.     

Evaluation of combined measurement uncertainty of the determination of Mn content in sediment samples

Combined uncertainties of an analysis of elemental content of sediment samples were evaluated. A monitoring system has been designed and implemented for the characterization of the environmental conditions of Lake Balaton in Hungary. Sediments samples were collected and an acidic digestion method was used to determine the concentration of elements. For the calculation of the result of each measurement three different approaches were considered, namely a.) the calculation of the result using a calibration curve and estimating the confidence limit by the Student t-distribution, b.) calculation of the combined uncertainty and c.) estimation of the sampling errors using the transport and field blanks. The latter approach gave the most reliable result since it included all the parameters which had to be considered regarding sampling and sample handling, and measurement. Determination of acid soluble Mn content in sediment samples has been chosen as an example, and the combined uncertainty is calculated using blanks for sampling. Received: 17 March 2000 Accepted: 4 October 2000     

加替沙星纯度标准物质研制

研制加替沙星纯度标准物质。采用质量平衡法和氢谱定量核磁法对加替沙星纯度标准物质候选物进行纯度定值,采用卡尔费休法和热重分析法准确测量了影响主成分纯度的水分含量,并考察了水分含量的稳定性。开展了加替沙星纯度定值、均匀性检验、稳定性考察以及不确定度评估。结果表明,加替沙星纯度标准物质的纯度值为93.1%,扩展不确定度为0.6%(k=2),水分含量为6.6%,特性量值均匀性良好,6个月稳定性可靠,被认定为国家二级标准物质,编号为GBW(E) 100476。研制的加替沙星纯度标准物质填补了国内空白,同时也为吸湿性较强的药物纯度标准物质研制过程中水分测定提供了参考与借鉴。     

Lifetime of the traceability chain in chemical measurement

Since the uncertainty of each link in the traceability chain (measuring analytical instrument, reference material or other measurement standard) changes over the course of time, the chain lifetime is limited. The lifetime in chemical analysis is dependent on the calibration intervals of the measuring equipment and the shelf-life of the certified reference materials (CRMs) used for the calibration of the equipment. It is shown that the ordinary least squares technique, used for treatment of the calibration data, is correct only when uncertainties in the certified values of the measurement standards or CRMs are negligible. If these uncertainties increase (for example, close to the end of the calibration interval or shelf-life), they are able to influence significantly the calibration and measurement results. In such cases regression analysis of the calibration data should take into account that not only the response values are subjects to errors, but also the certified values. As an end-point criterion of the traceability chain destruction, the requirement that the uncertainty of a measurement standard should be a source of less then one-third of the uncertainty in the measurement result is applicable. An example from analytical practice based on the data of interlaboratory comparisons of ethanol determination in beer is discussed. Received: 5 October 2000 Accepted: 3 December 2000     

Stochastic ensembles of thermodynamic potentials

The provision of uncertainty estimates along with measurement results or values computed thereof is metrologically mandatory. This is in particular true for observational data related to climate change, and thermodynamic properties of geophysical substances derived thereof, such as of air, seawater or ice. The recent International Thermodynamic Equation of Seawater 2010 (TEOS-10) provides such properties in a comprehensive and highly accurate way, derived from empirical thermodynamic potentials released by the International Association for the Properties of Water and Steam (IAPWS). Currently, there are no generally recognised algorithms available for a systematic and comprehensive estimation of uncertainties for arbitrary properties derived from those potentials at arbitrary input values, based on the experimental uncertainties of the laboratory data that were used originally for the correlations during the construction process. In particular, standard formulas for the uncertainty propagation which do not account for mutual uncertainty correlations between different coefficients tend to systematically and significantly overestimate the uncertainties of derived quantities, which may lead to practically useless results. In this paper, stochastic ensembles of thermodynamic potentials, derived from randomly modified input data, are considered statistically to provide analytical formulas for the computation of the covariance matrix of the related regression coefficients, from which in turn uncertainty estimates for any derived property can be computed a posteriori. For illustration purposes, simple analytical application examples of the general formalism are briefly discussed in greater detail.     

Uncertainties of mercury determinations in biological materials using an atomic absorption spectrometer – AMA 254

 The method is based on catalysed ignition of a sample portion in a flow of oxygen, capture of mercury by an amalgamator and measurement of the mercury vapour's absorbance after thermic release from the amalgamator. Three powdered food samples, a certified reference material (CRM) human hair and a reference material (RM) urine (liquid) were measured in the first range of the instrument (the possible contents determined according to our measurement procedure were 0.0003–0.5 ppm). The calibration function used was a line passing through the origin. The combined standard uncertainties of the mercury determinations were computed from uncertainty components of five quantities: absorbance of the sample, absorbance of the sample blank, slope of the calibration line, correction factor of the abscissa axis, and mass or volume of the sample. The most important uncertainty component is the uncertainty of the sample absorbance measurement which amounts to 52% of the determination uncertainty at the minimum (RM urine) and about 90% at the maximum (in our laboratory homogenized powdered food samples; analysis of variance showed their homogeneity to be insufficient). The results of the CRM and RM analyses do not indicate a significant systematic error for this determination. The relative expanded uncertainty (coefficient was 2) of the determination increases from 9 to 13% for the insufficiently homogenized samples with decreasing mercury content (range of 0.004–0.03 ppm); higher homogeneity of samples results in a decrease of the expanded uncertainty, e.g. 4.6% for the liquid sample (RM urine). Received: 26 April 1999 / Accepted: 30 August 1999     

Uncertainty analysis of correlated stability constants

Every attempt of using a computer to model reality has two main uncertainties: the conceptual uncertainty and the data uncertainty. The conceptual uncertainty deals with the choice of model selected for the simulation and the data uncertainty is about the precision and accuracy of the input data. They are often determined experimentally and may thus be encumbered by a number of uncertainties. Normally when treating uncertainties in input data these data are treated as independent variables. However, since many of these parameters are determined together they are actually correlated. This paper focuses on chemical stability constants, a most important parameter for chemical calculations based on speciation. Commonly in the literature they are at best given with an uncertainty interval. We propose to also give the covariance matrix thus giving the opportunity to really assess correlations. In addition we discuss the effect of these correlations on speciations.     

Preservation of sensitive CRMs and monitoring their stability at IRMM

Over the years, the nature of CRMs has changed considerably. Recently, more and more CRMs have been certified in their "natural" form, that is processed as little as possible, with analytes at their natural concentration level. This and the trend towards certified properties other than the concentrations of clearly defined molecules/elements have made guaranteeing stability of CRMs and estimating a shelf life an even more important issue for reference material producers than it has been before. One way to meet this challenge is to take more care in processing, storage and dispatch of CRMs. At IRMM, approximately 20 % of the RMs are stored at –20 °C or below and about 10% require cooled transportation. In addition, increased efforts for assessing stability are needed. Shelf lives are estimated using addition of an uncertainty component based on real-temperature stability studies rather than by accelerated stability studies. These pre-certification efforts are complemented by a stability-monitoring program, which at IRMM includes 80 % of the non-nuclear and non-isotopic materials. Although the costs for these efforts are high in absolute terms, they are only a minor and indispensable contribution to the total costs of CRM production.