Appropriate rather than representative sampling, based on acceptable levels of uncertainty

Appropriate sampling, that includes the estimation of measurement uncertainty, is proposed in preference to representative sampling without estimation of overall measurement quality. To fulfil this purpose the uncertainty estimate must include contribution from all sources, including the primary sampling, sample preparation and chemical analysis. It must also include contributions from systematic errors, such as sampling bias, rather than from random errors alone. Case studies are used to illustrate the feasibility of this approach and to show its advantages for improved reliability of interpretation of the measurements. Measurements with a high level of uncertainty (e.g. 50%) can be shown to be fit for some specified purposes using this approach. Once reliable estimates of the uncertainty are available, then a probabilistic interpretation of results can be made. This allows financial aspects to be considered in deciding upon what constitutes an acceptable level of uncertainty. In many practical situations ”representative” sampling is never fully achieved. This approach recognises this and instead, provides reliable estimates of the uncertainty around the concentration values that imperfect appropriate sampling causes. Received: 28 December 2001 Accepted: 25 April 2002     

Improved evaluation of measurement uncertainty from sampling by inclusion of between-sampler bias using sampling proficiency testing

A realistic estimate of the uncertainty of a measurement result is essential for its reliable interpretation. Recent methods for such estimation include the contribution to uncertainty from the sampling process, but they only include the random and not the systematic effects. Sampling Proficiency Tests (SPTs) have been used previously to assess the performance of samplers, but the results can also be used to evaluate measurement uncertainty, including the systematic effects. A new SPT conducted on the determination of moisture in fresh butter is used to exemplify how SPT results can be used not only to score samplers but also to estimate uncertainty. The comparison between uncertainty evaluated within- and between-samplers is used to demonstrate that sampling bias is causing the estimates of expanded relative uncertainty to rise by over a factor of two (from 0.39% to 0.87%) in this case. General criteria are given for the experimental design and the sampling target that are required to apply this approach to measurements on any material.     

Measurement uncertainty as a tool for evaluating the ‘grey zone’ to reduce the false negatives in immunochemical screening of blood donors for infectious diseases

The risk of misclassifying infected individuals as healthy constitutes a crucial challenge when screening blood donors by means of immunoassays. This risk is especially challenging when the numerical results are close to the clinical decision level, i.e. in the ‘grey zone’. The concept of using measurement uncertainty for evaluating the ‘grey zone’ has previously not been systematically applied in this context. This article explains methods, models and empirical (top-down) approaches for the calculation of measurement uncertainty using results from a blood bank according to the internationally accepted GUM principles, focusing on uncertainty sources in the analytical phase. Of the different approaches available, the intralaboratory empirical approaches are emphasised since modelling (bottom-up) approaches are impracticable due to the lack of reliable model equations for immunoassays. Different methods are applied to estimate the measurement uncertainty for the Abbott Prism^® HCV immunoassay. The expanded uncertainty obtained at the clinical decision level from the intralaboratory empirical approach was 36 %. The estimated uncertainty was used to set acceptance and rejection zones following the procedure set in the Eurachem guideline, emphasising the need to minimise the occurrence of false negatives.     

Uncertainty profiles for the validation of analytical methods

This article aims to expose a new global strategy for the validation of analytical methods and the estimation of measurement uncertainty. Our purpose is to allow to researchers in the field of analytical chemistry get access to a powerful tool for the evaluation of quantitative analytical procedures. Indeed, the proposed strategy facilitates analytical validation by providing a decision tool based on the uncertainty profile and the β-content tolerance interval. Equally important, this approach allows a good estimate of measurement uncertainty by using data validation and without recourse to other additional experiments.In the example below, we confirmed the applicability of this new strategy for the validation of a chromatographic bioanalytical method and the good estimate of the measurement uncertainty without referring to any extra effort and additional experiments. A comparative study with the SFSTP approach [1] showed that both strategies have selected the same calibration functions.The holistic character of the measurement uncertainty compared to the total error was influenced by our choice of profile uncertainty. Nevertheless, we think that the adoption of the uncertainty in the validation stage controls the risk of using the analytical method in routine phase.     

Response surface modelling and kinetic studies for the experimental estimation of measurement uncertainty in derivatisation

Response surface modelling is proposed as an approach to the estimation of uncertainties associated with derivatisation, and is compared with a kinetic study. Fatty acid methyl ester formation is used to illustrate the approach, and kinetic data for acid-catalysed methylation and base-catalysed transesterification are presented. Kinetic effects did not lead to significant uncertainty contributions under normal conditions for base-catalysed transesterification of triglycerides. Uncertainties for acid-catalysed methylation with BF3 approach significance, but could be reduced by extending reaction times from 3 to 5 min. Non-linearity is a common feature of response surface models for derivatisation and compromised first-order estimates of uncertainty; it was necessary to include higher order differential terms in the uncertainty estimate. Simulations were used to examine the general applicability of the approach and to study the effects of poor precision and of change of response surface model. It is concluded that reliable uncertainty estimates are available only when the model is statistically significant, robust, representative of the underlying behaviour of the system, and forms a good fit to the data; arbitrary models are not generally suitable for uncertainty estimation. Where statistically insignificant effects were included in models, they gave negligible uncertainty contributions.     

Worst case uncertainty estimates for routine instrumental analysis

A methodology for the worst case measurement uncertainty estimation for analytical methods which include an instrumental quantification step, adequate for routine determinations, is presented. Although the methodology presented should be based on a careful evaluation of the analytical method, the resulting daily calculations are very simple. The methodology is based on the estimation of the maximum value for the different sources of uncertainty and requires the definition of limiting values for certain analytical parameters. The simplification of the instrumental quantification uncertainty estimation involves the use of the standard deviation obtained from control charts relating to the concentrations estimated from the calibration curves for control standards at the highest calibration level. Three levels of simplification are suggested, as alternatives to the detailed approach, which can be selected according to the proximity of the sample results to decision limits. These approaches were applied to the determination of pesticide residues in apples (CEN, EN 12393), for which the most simplified approach showed a relative expanded uncertainty of 37.2% for a confidence level of approximately 95%.     

Uncertainty from sampling in measurements of aflatoxins in animal feedingstuffs: application of the Eurachem/CITAC guidelines

The duplicate method for estimating uncertainty from measurement including sampling is presented in the Eurachem/CITAC guide. The applicability of this method as a tool for verifying sampling plans for mycotoxins was assessed in three case studies with aflatoxin B(1) in animal feedingstuffs. Aspects considered included strategies for obtaining samples from contaminated lots, assumptions about distributions, approaches for statistical analysis, log(10)-transformation of test data and applicability of uncertainty estimates. The results showed that when duplicate aggregate samples are formed by interpenetrating sampling, repeated measurements from a lot can be assumed to approximately follow a normal or lognormal distribution. Due to the large variation in toxin concentration between sampling targets and sometimes very large uncertainty arising from sampling and sample preparation (U(rel) ≥ 50%), estimation of uncertainty from log(10)-transformed data was found to be a more generally applicable approach than application of robust ANOVA.     

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.     

A Monte Carlo approach for estimating measurement uncertainty using standard spreadsheet software

Despite the importance of stating the measurement uncertainty in chemical analysis, concepts are still not widely applied by the broader scientific community. The Guide to the expression of uncertainty in measurement approves the use of both the partial derivative approach and the Monte Carlo approach. There are two limitations to the partial derivative approach. Firstly, it involves the computation of first-order derivatives of each component of the output quantity. This requires some mathematical skills and can be tedious if the mathematical model is complex. Secondly, it is not able to predict the probability distribution of the output quantity accurately if the input quantities are not normally distributed. Knowledge of the probability distribution is essential to determine the coverage interval. The Monte Carlo approach performs random sampling from probability distributions of the input quantities; hence, there is no need to compute first-order derivatives. In addition, it gives the probability density function of the output quantity as the end result, from which the coverage interval can be determined. Here we demonstrate how the Monte Carlo approach can be easily implemented to estimate measurement uncertainty using a standard spreadsheet software program such as Microsoft Excel. It is our aim to provide the analytical community with a tool to estimate measurement uncertainty using software that is already widely available and that is so simple to apply that it can even be used by students with basic computer skills and minimal mathematical knowledge.     

塑料中镉的测定不确定度评定

建立了用实验室内精密度和偏差的数据来评定塑料中镉的测定不确定度的方法. 通过研究不同基体和不同含量水平的样品, 考察了方法的精密度和回收率, 分别计算并合并了两者的测量不确定度. 结果表明精密度和回收率的相对不确定度分量分别为0.026和0.068, 合成不确定度为0.072, 扩展不确定度为0.14. 此评定过程为实验室评定测量不确定度提供了一种新的方法, 简单、合理, 计算结果可靠.     

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     

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.     

Uncertainty in analytical results from solid materials with electrothermal atomic absorption spectrometry: a comparison of methods

The combined uncertainty in the analytical results of solid materials for two methods (ET-AAS, analysis after prior sample digestion and direct solid sampling) are derived by applying the Guide to the Expression of Uncertainty in Measurement from the International Standards Organization. For the analysis of solid materials, generally, three uncertainty components must be considered: (i) those in the calibration, (ii) those in the unknown sample measurement and (iii) those in the analytical quality control (AQC) process. The expanded uncertainty limits for the content of cadmium and lead from analytical data of biological samples are calculated with the derived statistical estimates. For both methods the expanded uncertainty intervals are generally of similar width, if all sources of uncertainty are included. The relative uncertainty limits for the determination of cadmium range from 6% to 10%, and for the determination of lead they range from 8% to 16%. However, the different uncertainty components contribute to different degrees. Though with the calibration based on reference solutions (digestion method) the respective contribution may be negligible (precision < 3%), the uncertainty from a calibration based directly on a certified reference material (CRM) (solid sampling) may contribute significantly (precision about 10%). In contrast to that, the required AQC measurement (if the calibration is based on reference solutions) contributes an additional uncertainty component, though for the CRM calibration the AQC is “built-in”. For both methods, the uncertainty in the certified content of the CRM, which is used for AQC, must be considered. The estimation of the uncertainty components is shown to be a suitable tool for the experimental design in order to obtain a small uncertainty in the analytical result.     

Estimation of uncertainty in routine pH measurement

A procedure for estimation of measurement uncertainty of routine pH measurement (pH meter with two-point calibration, with or without automatic temperature compensation, combination glass electrode) based on the ISO method is presented. It is based on a mathematical model of pH measurement that involves nine input parameters. Altogether 14 components of uncertainty are identified and quantified. No single uncertainty estimate can be ascribed to a pH measurement procedure: the uncertainty of pH strongly depends on changes in experimental details and on the pH value itself. The uncertainty is the lowest near the isopotential point and in the center of the calibration line and can increase by a factor of 2 (depending on the details of the measurement procedure) when moving from around pH 7 to around pH 2 or 11. Therefore it is necessary to estimate the uncertainty separately for each measurement. For routine pH measurement the uncertainty cannot be significantly reduced by using more accurate standard solutions than ±0.02 pH units – the uncertainty improvement is small. A major problem in estimating the uncertainty of pH is the residual junction potential, which is almost impossible to take rigorously into account in the framework of a routine pH measurement.¹ Received: 11 August 2001 Accepted: 22 February 2002     

Models to estimate overall analytical measurements uncertainty: assumptions, comparisons and applications

Evaluation of analytical results reliability is of core importance as crucial decisions are taken with them. From the various methodologies to evaluate the fitness of purpose of analytical methods, overall measurement uncertainty estimation is more and more applied. Overall measurement uncertainty allows to combine simultaneously the remaining systematic influences to the random sources of uncertainty and allows assessing the reliability of results generated by analytical methods. However there are various interpretations on how to estimate overall measurement uncertainty, and thus various models for estimating it. Each model together with its assumptions has great impacts on the risks to abusively declare that analytical methods are suitable for their intended purpose. This review paper aims at (i) summarizing the various models used to estimate overall measurement uncertainty, (ii) provide their pros and cons, (iii) review the main areas of application and (iv) as a conclusion provide some recommendations when evaluating overall measurement uncertainty.     

The uncertainty in the calculation of the amount of blocked and reactive lysine in milk products,as determined by the furosine method

The measurement uncertainty in the calculation of the amount of blocked and reactive lysine (as determined by the furosine method) was evaluated according to the procedure described in the Eurachem/CITAC guide. The analytical method involves the chromatographic determination of lysine and furosine after acid hydrolysis. The calculation of blocked and reactive lysine in the initial protein is based on known conversion factors. The estimation of the uncertainty was performed in two steps: (1) determination of the uncertainty in the chromatographic determination of lysine and furosine, and (2) determination of the uncertainty in the calculation of blocked and reactive lysine. The individual contributions to the final uncertainty were identified, quantified, and combined in uncertainty budgets. The largest contribution to the calculation of blocked lysine came from estimating the conversion factor of blocked lysine into furosine during acid hydrolysis. For the calculation of reactive lysine, the main contribution came from the chromatographic determination of lysine. The uncertainty estimates were compared to available validation data (in-house and collaborative standard deviations of reproducibility).     

Comparison of different approaches to estimate the uncertainty of a liquid chromatographic assay

A measurement result cannot be properly interpreted without knowledge about its uncertainty. Several concepts to estimate the uncertainty of a measurement result have been developed. Here, four different approaches for uncertainty estimation are compared on the example of the RP-high-performance liquid chromatography (HPLC) assay for tylosin for veterinary use: the guide to the expression of uncertainty in measurement (GUM) approach, which derives the uncertainty of a measurement result by combining the uncertainties related to the uncertainty sources of the measurement process; the top-down approach, which uses the reproducibility estimate from an inter-laboratory study as uncertainty estimate; an approach recently presented by Barwick and Ellison, which combines precision, trueness and robustness data to obtain an uncertainty estimate of the measurement result and finally a further approach, which directly estimates the measurement uncertainty from a robustness test. The comparison shows that the different approaches lead to comparable uncertainty estimates.     

A case study in the practical estimation of measurement uncertainty

This case study is written for analytical laboratories, in order to give support to the implementation of the concept of measurement uncertainty for routine measurements. The aim is to provide a practical, understandable and common way of performing measurement uncertainty calculations, based mainly on pre-existing quality control and validation data. Practical examples taken directly from environmental laboratory monitoring are presented and explained. However, the approach is very general and should be applicable to most testing laboratories in the chemical field. Following the protocol of evaluation illustrated in the case study, it is possible to ensure that most relevant uncertainty components associated with the method are covered. Contributions associated with sampling, homogenisation, sub-sampling, and so on, are, however, excluded.     

Measurement uncertainty – a reliable concept in food analysis and for the use of recovery data?

 Steps which are taken to implement the concept of measurement uncertainty in analytical chemical laboratories should take full account of existing internationally agreed protocols for analytical quality assurance and reflect the needs of particular analytical sectors. For the food sector this may mean that for official purposes the use of the term measurement uncertainty is replaced by the term measurement reliability and that a quantitative estimation of this is made based on existing collaborative trial data. In many analytical sectors, the differing strategies currently followed for the determination and use of recovery information are an important cause of the non-comparability of analytical results. Guidelines which are being prepared for the estimation and use of recovery information in analytical measurement may provide a more unified approach which includes measurement uncertainty as a key concept in the use of recovery data. Received: 4 November 1997 · Accepted: 3 February 1998