Practical digest for evaluating the uncertainty of analytical assays from validation data according to the LGC/VAM protocol

The estimation of the measurement uncertainty of analytical assays based on the LGC/VAM protocol from validation data is fully revisited and discussed in the light of the study of precision, trueness and robustness.     

The role of the sample standard deviation in the analysis of measurement data

This paper builds on recent letters to the editor to consider different ways in which the ‘sample standard deviation’ of a set of repeated measurements might be used in the expression of accuracy or uncertainty. A distinction is made between using the sample standard deviation, s, to calculate a figure of merit for the measurement procedure and using s to express uncertainty in the estimate of a measurand. In particular, we consider whether s should be adjusted for bias. It is shown that most procedures involving s are valid without the application of any such adjustment. The paper emphasizes the importance of clear definitions and an unambiguous statement of purpose, and also emphasizes the need for a distinction in notation between a random variable and its observed value.     

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.     

Estimation of measurement uncertainty for the determination of aflatoxin M1 in milk using immunoaffinity clean-up procedures

A measurement uncertainty estimated for aflatoxin M₁ determination in milk sample has been calculated using data generated from analytical method validation studies. The protocol adopted is described in detail in document LGC/VAM/1998/088. The uncertainty budget was based on precision, trueness and ruggedness data. The individual contributions are described in detail. The expanded uncertainty for aflatoxin M ₁ at a concentration of 20 ng L⁻¹ was estimated as 2.81 ng L⁻¹. This was calculated using a coverage factor of two which gives a level of confidence of approximately 95%. Presented at AOAC Europe / Eurachem Symposium March 2005, Brussels, Belgium     

An approach to detection capabilities estimation of analytical procedures based on measurement uncertainty

Detection capabilities are important performance characteristics of analytical procedures. There are several conceptual approaches on the subject, but in most of them a level of ambiguity is presented. It is not clear which conditions of measurements should be used, and there is a relative lack of definition concerning blanks. Moreover, there are no systematic experimental studies concerning the influence of uncertainty associated with bias evaluation. A new approach based on measurement uncertainty is presented for estimating quantities that characterize capabilities of detection. It can be applied to different conditions of measurement and it is not necessary to perform an additional experiment with blanks. Starting from a modelling process of the combined uncertainty of concentration, it is possible to include in the estimated quantities the effects due to random errors and the uncertainty associated to evaluation of bias. The detection capabilities are then compared with the results obtained using some other relevant approaches. Slightly higher values were obtained with the measurement uncertainty approach due to inclusion of uncertainty associated with bias.     

Practical estimation of the uncertainty of analytical measurement standards

Nowadays, a lot of time and resources are used to determine the quality of goods and services. As a consequence, the quality of measurements themselves, e.g., the metrological traceability of the measured quantity values is essential to allow a proper evaluation of the results with regard to specifications and regulatory limits. This requires knowledge of the measurement uncertainties of all quantity values involved in the measurement procedure, including measurement standards. This study shows how the uncertainties due to the preparation, as well as the chemical and compositional stability of a chemical measurement standard, or calibrator, can be estimated. The results show that the relative standard uncertainty of the concentration value of a typical analytical measurement standard runs up to 2.8% after 1 year. Of this, 1.9% originates from the preparation of the measurement standard, while 2.0 and 0.53% originate from the chemical and compositional stability during storage at −20 °C. The monthly preparation of working calibrators stored at 4 °C and used on a weekly basis, results in an additional standard uncertainty of the analyte concentration value of 0.35% per month due to compositional stability. While the preparation procedure is the major contributor to the total measurement uncertainty, the uncertainties introduced by the stability measurements are another important contributor, and therefore, the measurement procedure to evaluate stability is important to minimize the total measurement uncertainty.     

Assessment of uncertainty in pesticide multiresidue analytical methods: main sources and estimation

The estimation of the uncertainty associated to analytical methods is necessary in order to establish the comparability of results. Multiresidue analytical methods lack very often of information about uncertainty of results with likely implications when results are compared with maximum residue levels (MRL) established by regulations. An adequate identification and estimation of each uncertainty source allows to laboratories to establish the accuracy of results and to balance with time-consuming and costs.     

Treatment of uncorrected measurement bias in uncertainty estimation for chemical measurements

Consistent treatment of measurement bias, including the question of whether or not to correct for bias, is essential for the comparability of measurement results. The case for correcting for bias is discussed, and it is shown that instances in which bias is known or suspected, but in which a specific correction cannot be justified, are comparatively common. The ISO Guide to the Expression of Uncertainty in Measurement does not provide well for this situation. It is concluded that there is a need for guidance on handling cases of uncorrected bias. Several different published approaches to the treatment of uncorrected bias and its uncertainty are critically reviewed with regard to coverage probability and simplicity of execution. On the basis of current studies, and taking into account testing laboratory needs for a simple and consistent approach with a symmetric uncertainty interval, we conclude that for most cases with large degrees of freedom, linear addition of a bias term adjusted for exact coverage ("U(e)") as described by Synek is to be preferred. This approach does, however, become more complex if degrees of freedom are low. For modest bias and low degrees of freedom, summation of bias, bias uncertainty and observed value uncertainty in quadrature ("RSSu") provides a similar interval and is simpler to adapt to reduced degrees of freedom, at the cost of a more restricted range of application if accurate coverage is desired.     

A new terminology for the approaches to the quantification of the measurement uncertainty

A new terminology for the approaches to the quantification of the measurement uncertainty is presented, with a view to a better understanding of the available methodologies for the estimation of the measurement quality and differences among them. The knowledge of the merits, disadvantages and differences in the estimation process, of the available approaches, is essential for the production of metrologically correct and fit-to-purpose uncertainty estimations. The presented terminology is based on the level of the analytical information used to estimate the measurement uncertainty (e.g., supralaboratory or intralaboratory information), instead of the direction of information flow (“bottom-up” or “top-down”) towards the level of information where the test is performed, avoiding the use of the same designation for significantly different approaches. The proposed terminology is applied to the approaches considered on 19 examples of the quantification of the measurement uncertainty presented at the Eurachem/CITAC CG4 Guide, Eurolab Technical Report 1/2002 and Nordtest Technical Report 537. Additionally, differences of magnitude in the measurement uncertainty estimated by various approaches are discussed.     

Performance of uncertainty evaluation strategies in a food proficiency scheme

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.     

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     

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     

Correlation between repeated measurements: bane and boon of the GUM approach to the uncertainty of measurement

With measurement uncertainty estimation accounting for all relevant uncertainty contributions, the results of measurements using the same procedure on different objects or samples may no longer be considered as being independent, and correlations have to be taken into account. For this purpose, a simple approximation for the estimation of covariances is derived and applied to the estimation of uncertainty for some basic combinations of two measurement results. This covariance estimate is also applied to the estimation of uncertainty for the mean value of the results of replicate measurements on the same object or sample.

A practical approach to assessment of sampling uncertainty

The paper reports the approach followed in the SOILSAMP project, funded by the National Environmental Protection Agency (ANPA)of Italy. SOILSAMP is aimed at assessing uncertainties associated with soil sampling in agricultural, semi-natural, urban, and industrial environments. The uncertainty assessment is based on a bottom-up approach, according to the Guide to the Expression of Uncertainty in Measurement published by the International Organization for Standardization (ISO). A designated agricultural area, which has been characterized in terms of elemental spatial distribution, will be used in future as a reference site for soil sampling intercomparison exercises. Received: 19 November 2001 Accepted: 6 January 2002     

Repeatability: some aspects concerning the evaluation of the measurement uncertainty

Various publications stress the importance of the repeatability (i.e. precision) of the calculation of the measurement of uncertainty. We reveal by detailing an example from production control in the pharmaceutical industry that the effect of other influence quantities should not be neglected, because their magnitude is even larger than the contribution of repeatability. We review the role of repeatability within the calculation of measurement uncertainty for several common validation and day-to-day measurement scenarios. They show that measurement models need to consider the measurement sequences of the various scenarios. Otherwise the size and effect of the repeatability might be overestimated. At the end Monte Carlo simulations were used to investigate the determination of the repeatability under certain restrictions. The simulation uncovered a significant bias toward the common formula for calculating the standard deviation when it is based on a duplicated measurement of a sample. Papers published in this section do not necessarily reflect the opinion of the Editors, the Editorial Board and the Publisher     

Low-frequency noise in analytical soil measurements

Fourier analysis of the real-time quality-control charts for colorimetric, photometric, and pH soil measurements shows 1/f ⁿ (n=1±0.05) noise intensity dependence on frequency, in correspondence to the earlier test for atomic absorption measurements. In addition, the prevailing character of the sample preparation in the general noise frequency dependence is clearly demonstrated. Some important analytical problems are addressed where knowledge of the specific character of the time variation in the analytical data sets is essential.     

Attempts to include uncorrected bias in the measurement uncertainty

In ISO Guide it is strictly recommended to correct results for the recognised significant bias, but in special cases some analysts find out practical to omit the correction and to enlarge the expanded uncertainty for the uncorrected bias instead. In this paper, four alternatively used methods computing these modified expanded uncertainties are compared according to the levels of confidence, widths and layouts of the obtained uncertainty intervals. The method, which seems to be the best, because it provides the same uncertainty intervals as in the case of the bias correction, has not been applied very much, maybe since these modified uncertainty intervals are not symmetric about the results. The three remaining investigated methods maintain their intervals symmetric, but only two of them provide intervals of the kind, that their levels of confidence reach at least the required value (95%) or a larger one. The third method defines intervals with low levels of confidence (even for small biases). It is proposed a new method, which gives symmetric intervals just with the required level of confidence. These intervals are narrower than those symmetric intervals with the sufficient level of confidence obtained by the two mentioned methods. A mathematical background of the problem and an illustrative example of calculations applying all compared methods are attached.     

Introduction of measurement uncertainty estimation into analytical instrument software: mission impossible?

In this paper we argue that introduction of ISO GUM based uncertainty estimation into analytical equipment software is a “mission possible” and is wholly realistic at this stage of development of the art. A possible general scheme of implementation of uncertainty estimation into analytical instrument software is presented based on the example of high-performance liquid chromatography (HPLC) but is also applicable to most other analytical instruments. This implementation would be very beneficial for the analysts/practitioners as the uncertainty would be handled within their everyday software environment.     

Introduction of measurement uncertainty estimation into analytical instrument software: mission impossible?

In this paper we argue that introduction of ISO GUM based uncertainty estimation into analytical equipment software is a “mission possible” and is wholly realistic at this stage of development of the art. A possible general scheme of implementation of uncertainty estimation into analytical instrument software is presented based on the example of high-performance liquid chromatography (HPLC) but is also applicable to most other analytical instruments. This implementation would be very beneficial for the analysts/practitioners as the uncertainty would be handled within their everyday software environment.