Is the estimation of measurement uncertainty a viable alternative to validation?

Two examples of the use of measurement uncertainty in a development environment are presented and compared to the use of validation. It is concluded that measurement uncertainty is a good alternative to validation for chemical processes in the development stage. Some advantages of measurement uncertainty are described. The major advantages are that the estimations of measurement uncertainty are very efficient, and can be performed before analysis of the samples. The results of measurement uncertainty influence the type of analysis employed in the development process, and the measurement design can be adjusted to the need of the process.     

Uncertainty due to the quantification step in analytical methods

The quantification step is an important source of uncertainty in analytical methods, but it is frequently misunderstood and disregarded. In this paper, it is shown how this uncertainty is closely related to the linear response range of a method, and to the Pearson correlation coefficient of the calibration line. So, if there is a need for a pre-fixed quantification uncertainty, the linear response range will be affected. Some practical cases are given showing the quantification uncertainty significance. The theoretical equation giving the value of the quantification uncertainty is deduced from which new conclusions can be taken out. Because of that, the quantification uncertainty can easily be calculated and the parameters that really affect its value are shown along the paper. Some final considerations about detection limits and two-point calibration lines are also given. The paper can also be considered a reflection on uncertainty owed to calibration and on their consequences on the analytical methodology.     

Calibration, handling repeatability, and the Maximum Permissible Error of single-volume glass instruments

The influence quantities for the uncertainty of a volumetric operation with glass instruments are calibration, repeatability and temperature. In the literature, measurement uncertainty budgets can be found, which count all three quantities separately although calibration and repeatability are merged in tabulated data to the Maximum Permissible Error. We propose that this error should be handled as a rectangular distribution in order to get a standard uncertainty. For the daily use in an analytical laboratory, the combined standard uncertainty of a volumetric operation is thus calculated from the Maximum Permissible Error plus the uncertainty of the temperature influence.     

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.     

Determination of measurement uncertainty for the determination of triazines in groundwater from validation data

Laboratories are increasingly urged to submit full uncertainties of their analytical results rather than only standard deviations. The determination of measurement uncertainties in compliance with the Guide to the Expression of Uncertainty in Measurement (GUM) is demonstrated using the validation approach explicitly endorsed by the recent edition of the EURACHEM guide for the determination of measurement uncertainty. Measurement uncertainty was split into uncertainty of the sample mass, uncertainty of the concentration of the stock standard solution, uncertainty of the calibration and uncertainty connected to within- and between-series precision. Uncertainties of sample mass and of the concentration of the stock standard solution were 0.26 and 1.14% for all analytes, which is negligible compared with the contributions of precision and calibration. Uncertainty of calibration was estimated from the calibration graph. Relative uncertainty of calibration was found to be strongly concentration dependent and to be the main uncertainty contribution below 0.2 microgram L-1. Precision was split into within-series and between-series standard deviation, which dominate the combined standard uncertainty at higher concentrations. The results obtained from these calculations are compared with results for a certified reference material and with the performance in an interlaboratory comparison. It was found that all results agreed within their uncertainty with the target values, showing that the estimated uncertainties are realistic.     

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.     

Uncertainty evaluation in proficiency testing: state-of-the-art, challenges, and perspectives

The evaluation of measurement uncertainty, and that of uncertainty statements of participating laboratories will be a challenge to be met in the coming years. The publication of ISO 17025 has led to the situation that testing laboratories should, to a certain extent, meet the same requirements regarding measurement uncertainty and traceability. As a consequence, proficiency test organizers should deal with the issues measurement uncertainty and traceability as well. Two common statistical models used in proficiency testing are revisited to explore the options to include the evaluation of the measurement uncertainty of the PTRV (proficiency test reference value). Furthermore, the use of this PTRV and its uncertainty estimate for assessing the uncertainty statements of the participants for the two models will be discussed. It is concluded that in analogy to Key Comparisons it is feasible to implement proficiency tests in such a way, that the new requirements can be met. Received: 29 September 2000 Accepted: 3 December 2000     

Verification of uncertainty budgets

The quality of analytical results is expressed by their uncertainty, as it is estimated on the basis of an uncertainty budget; little effort is, however, often spent on ascertaining the quality of the uncertainty budget. The uncertainty budget is based on circumstantial or historical data, and therefore it is essential that the applicability of the overall uncertainty budget to actual measurement results be verified on the basis of current experimental data. This should be carried out by replicate analysis of samples taken in accordance with the definition of the measurand, but representing the full range of matrices and concentrations for which the budget is assumed to be valid. In this way the assumptions made in the uncertainty budget can be experimentally verified, both as regards sources of variability that are assumed negligible, and dominant uncertainty components. Agreement between observed and expected variability is tested by means of the T-test, which follows a chi-square distribution with a number of degrees of freedom determined by the number of replicates. Significant deviations between predicted and observed variability may be caused by a variety of effects, and examples will be presented; both underestimation and overestimation may occur, each leading to correcting the influence of uncertainty components according to their influence on the variability of experimental results. Some uncertainty components can be verified only with a very small number of degrees of freedom, because their influence requires samples taken at long intervals, e.g., the acquisition of a new calibrant. It is therefore recommended to include verification of the uncertainty budget in the continuous QA/QC monitoring; this will eventually lead to a test also for such rarely occurring effects.     

Estimation of measurement uncertainty in organic analysis: two practical approaches

Estimation of measurement uncertainty has become a more regularly performed part of the whole analytical process. However, there is still much on-going discussion in the scientific community about ways of building up the uncertainty budget. This study describes two approaches for estimation of measurement uncertainty in organic analysis: one which can be used for single sets of measurements and the other based on validation studies. In both cases the main contributions to the uncertainty are presented and discussed for the analysis of PCBs in mussel tissue, but the approaches can be extended to other organic pollutants in environmental/food samples. The main contributions to the uncertainty budget arise from calibration, sample preparation, and GC–MS measurements. A comparison of the relevant sources and their contributions to the expanded uncertainty is presented.     

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.     

Empirical versus modelling approaches to the estimation of measurement uncertainty caused by primary sampling

Measurement uncertainty is a vital issue within analytical science. There are strong arguments that primary sampling should be considered the first and perhaps the most influential step in the measurement process. Increasingly, analytical laboratories are required to report measurement results to clients together with estimates of the uncertainty. Furthermore, these estimates can be used when pursuing regulation enforcement to decide whether a measured analyte concentration is above a threshold value. With its recognised importance in analytical measurement, the question arises of 'what is the most appropriate method to estimate the measurement uncertainty?'. Two broad methods for uncertainty estimation are identified, the modelling method and the empirical method. In modelling, the estimation of uncertainty involves the identification, quantification and summation (as variances) of each potential source of uncertainty. This approach has been applied to purely analytical systems, but becomes increasingly problematic in identifying all of such sources when it is applied to primary sampling. Applications of this methodology to sampling often utilise long-established theoretical models of sampling and adopt the assumption that a 'correct' sampling protocol will ensure a representative sample. The empirical approach to uncertainty estimation involves replicated measurements from either inter-organisational trials and/or internal method validation and quality control. A more simple method involves duplicating sampling and analysis, by one organisation, for a small proportion of the total number of samples. This has proven to be a suitable alternative to these often expensive and time-consuming trials, in routine surveillance and one-off surveys, especially where heterogeneity is the main source of uncertainty. A case study of aflatoxins in pistachio nuts is used to broadly demonstrate the strengths and weakness of the two methods of uncertainty estimation. The estimate of sampling uncertainty made using the modelling approach (136%, at 68% confidence) is six times larger than that found using the empirical approach (22.5%). The difficulty in establishing reliable estimates for the input variable for the modelling approach is thought to be the main cause of the discrepancy. The empirical approach to uncertainty estimation, with the automatic inclusion of sampling within the uncertainty statement, is recognised as generally the most practical procedure, providing the more reliable estimates. The modelling approach is also shown to have a useful role, especially in choosing strategies to change the sampling uncertainty, when required.     

Uncertainty-based measurement quality control

According to a simple acceptance decision rule for measurement quality control, a measured value will be accepted if the expanded uncertainty of the measurements is not greater than a preset maximum permissible uncertainty. Otherwise, the measured value will be rejected. The expanded uncertainty may be calculated as the z-based uncertainty (the half-width of the z-interval) when the measurement population standard deviation σ is known or the sample size is large (30 or greater), or by a sample-based uncertainty estimator when σ is unknown and the sample size is small. The decision made based on the z-based uncertainty will be deterministic and may be assumed to be correct. However, the decision made based on a sample-based uncertainty estimator will be uncertain. This paper develops the mathematical formulations for computing the probability of acceptance for two sample-based uncertainty estimators: the t-based uncertainty (the half-width of the t-interval) and an unbiased uncertainty estimator. The risk of incorrect decision-making, in terms of the false acceptance probability and false rejection probability, is derived from the probability of acceptance. The theoretical analyses indicate that the t-based uncertainty may result in significantly high false rejection probability when the sample size is very small (especially for samples of size 2). For some applications, the unbiased uncertainty estimator may be superior to the t-based uncertainty for measurement quality control. Several examples from acoustic Doppler current profiler streamflow measurements are presented to demonstrate the performance of the t-based uncertainty and the unbiased uncertainty estimator.     

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.     

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     

Being uncertain in thin layer chromatography—Some thoughts about latent details in the retention estimation

This paper deals with some important (but often neglected) details about the uncertainty of retention measurement in thin layer chromatography, the propagation of uncertainty during computing simple and more complex values from the retention data, ending in influence of the retention uncertainty onto the regression estimates during extrapolation and lipophilicity estimation. Theoretical considerations are tested on data from previous study. It can be concluded that when TLC spots are broad and the retention uncertainty exceeds about 0.02 of R_F value, the uncertainty should be taken into the account in further computations.     

To what extent can an uncertainty calculation be general?

 It is argued that results of uncertainty calculations in chemical analysis should be taken into consideration with some caution owing to their limited generality. The issue of the uncertainty in uncertainty estimation is discussed in two aspects. The first is due to the differences between procedure-oriented and result-oriented uncertainty assessments, and the second is due to the differences between the theoretical calculation of uncertainty and its quantication using the validation (experimental) data. It is shown that the uncertainty calculation for instrumental analytical methods using a regression calibration curve is result-oriented and meaningful only until the next calibration. A scheme for evaluation of the uncertainty in uncertainty calculation by statistical analysis of experimental data is given and illustrated with examples from the author's practice. Some recommendations for the design of corresponding experiments are formulated.     

用ISO《测量不确定度表达指南》评估ICP-AES法测定不确定度

用国际通用的方法评估出ICP－AES法测定不确定度，考虑不确定度的主要来源包括仪器的精密度、标准物质标称值的不确定度以及制备溶液过程中引起的不确定度，推导出各种传播系数表达式，计算出各种不确定度分量并将其合成，并以测定钢铁中磷含量为例，提供了计算过程所需的各参数的采集和计算方法，所用的方法同样适用于以线性回归标准曲线法获得测定结果不确定度的评估。     

Using target measurement uncertainty to determine fitness for purpose

The methods an analytical laboratory uses must be validated to be fit for purpose. The fitness for purpose of a quantitative method used to determine the concentration of a substance when assessing compliance to requirements can be described by the maximum measurement uncertainty. This is called the target measurement uncertainty. Acceptance criteria for precision and bias in the method validation are then established in terms of the target measurement uncertainty. The target measurement uncertainty can be decided by following a process which involves determining the required concentration range of the measurand; determining the acceptable level of risks of incorrect decisions of compliance; developing a suitable decision rule, with guard bands if appropriate; using the probability of making an incorrect decision of compliance based on the decision rule; and assessing the impact of bias. A key participant in this process is the end user of the data, the laboratory customer. This paper presents the concepts concerning target measurement uncertainty introduced in recently published international guidelines to the practicing analytical chemist who is not generally familiar with these concepts. Three examples are used to illustrate the process.     

A simplified approach to the estimation of analytical measurement uncertainty

The present study summarizes the measurement uncertainty estimations carried out in Nestlé Research Center since 2002. These estimations cover a wide range of analyses of commercial and regulatory interests. In a first part, this study shows that method validation data (repeatability, trueness and intermediate reproducibility) can be used to provide a good estimation of measurement uncertainty.In a second part, measurement uncertainty is compared to collaborative trials data. These data can be used for measurement uncertainty estimation as far as the in-house validation performances are comparable to the method validation performances obtained in the collaborative trial.Based on these two main observations, the aim of this study is to easily estimate the measurement uncertainty using validation data.     

Protocol for uncertainty assessment of half-lives

The apparent tendency to underestimate the uncertainty of experimentally determined half-life values of radionuclides is discussed. It is argued that the uncertainty derived from a least-squares analysis of a decay curve is prone to error. As it is quite common for a series of activity measurement results to be autocorrelated, the prerequisite of randomness of data for common statistical tests to apply is not fulfilled. In this work, an alternative data analysis method is applied that leads to a more realistic uncertainty budget. The uncertainty components are being subdivided in three categories according to the relative frequency at which they occur, an appropriate uncertainty propagation formula applied and then the total uncertainty obtained from an independent sum. An attempt is made to apply the protocol to problematic cases in literature, yet it is clear that the reporting is usually incomplete for a full uncertainty analysis. Suggestions are made for a concise but more complete reporting style, for the sake of traceability.