A model for the evaluation of uncertainty in routine multi-element analysis

A model for calculating uncertainty in routine multi-element analysis is described. The model is constructed according to the principles of GUM/EURACHEM. Control chart results are combined with other existing data and results from the actual measurement into a concentration-dependent estimate of combined standard uncertainty. Since possible sources of bias are included in the calculation, overall bias as estimated from the data is used only as a control to identify needs for modification of the model and/or the analytical procedure. For each individual sample, uncertainty can be calculated automatically based on two pre-calculated parameters together with measured concentration and instrumental standard deviation. As an example, the model is demonstrated for inductively coupled plasma-mass spectrometry (ICP-MS) analysis of sewage sludge including laboratory sub-sampling, sample preparation, and instrumental determination.     

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.     

Estimation of the standard uncertainty of a calibration curve: application to sulfur mass concentration determination in fuels

The construction of a calibration curve using least square linear regression is common in many analytical measurements, and it comprises an important uncertainty component of the whole analytical procedure uncertainty. In the present work, various methodologies are applied concerning the estimation of the standard uncertainty of a calibration curve used for the determination of sulfur mass concentration in fuels. The methodologies applied include the GUM uncertainty framework, the Kragten numerical method, the Monte Carlo method (MCM) as well as the approximate equation calculating the standard error of prediction. The standard uncertainty results obtained by all methodologies agree well (0.172?C0.175?ng???L^?1). Aspects of inappropriate use of the approximate equation of the standard error of prediction, which leads to overestimation or underestimation of calculated uncertainty, are discussed. Moreover, the importance of the correlation between calibration curve parameters (slope and intercept) within GUM, MCM and Kragten approaches is examined.     

The application of the measurement uncertainty concept to in-process control in pharmaceutical development

 Any analytical data is used to provide information about a sample. The "possible error" of the measurement can be of extreme importance in order to have complete information. The measurement uncertainty concept is a way to achieve quantitative information about this "possible error" using an estimation procedure. On the basis of the analytical result, the chemist makes a decision on the next step of the development process. If the uncertainty is unknown, the information is not complete; therefore this decision might be impossible. The major problem for the in-process control (IPC) procedure is that not only the repeatability but also the intermediate precision (which expresses the variations within laboratories related to different days, different analysts, different equipment, etc.) has to be good enough to make a decision. Unfortunately, the statistical information achieved from one single analytical run only gives information about the repeatability. This paper shows that the estimation of the measurement uncertainty for IPC is a way to solve the problem and gives the necessary information about the quality of the procedure. An example demonstrates that an estimate of uncertainty based on the standard deviations of an analytical method gives a value similar to one based on the standard deviations obtained from a control chart. Therefore, the estimation is both a very useful and also a very cost-effective tool. Though measurement uncertainty cannot replace validation in general, it is a viable alternative to validation for all methods that will never be used routinely. Received: 24 May 1996 Accepted: 10 August 1996     

New tools: Expert systems for uncertainty budgets

An important part of quality assurance in any analytical laboratory is the production of comprehensive results integrating uncertainty measurements. Many testing laboratories face the problem that the expenditure required to evaluate small uncertainties (high precision and high accuracy) is often uneconomic. In most cases an uncertainty of high reliability has to be calculated from only a few data (one calibration, few replications, etc.). This problem can be solved by an expert system. To achieve this the analytical procedure has to be structured into a dialouge and divided into parts. The uncertainty has to be calculated for each part of the procedure. Addition of the individual uncertainties results in the combined and expanded uncertainty. During the dialouge the system should advise the analyst how to get an efficient and effective calculation of uncertainty. All calculations, mathematical and statistical procedures have to be surveyable but running the system should not be too time consuming for economic reasons. Within the scope of the EURECA-project initiated by the Eidgenössische Materialprüfungs- und Forschungsanstalt (EMPA), St. Gallen, Switzerland, expert system software is being developed in cooperation with other research institutes and manufacturers of analytical instruments. Using this software it will be possible to calculate the uncertainty for analytical procedures such as titration, atomic emission spectrometry (ICP-OES), atomic absorption spectrometry (AAS) and gas- and liquid chromatography (GC, HPLC).     

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。     

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.     

Alternative calculation of measurement uncertainty with global approach in food microbiology

Calculation of measurement uncertainty is a requirement for all laboratories accredited to ISO/IEC 17025 including those carrying out microbiological analyses. Today, calculation of measurement uncertainty in microbiological analyses using precision data according to global approach principles is widely recognized by the microbiologists due to difficulties in quantification of individual uncertainty sources. In food microbiology, precision data obtained from different samples usually show over-dispersion, and the use of over-dispersed data may result in large variance. The current ISO standard on measurement uncertainty in food microbiology proposes the use of log-transformed precision data to overcome this problem. This paper proposes an alternative procedure to calculate the measurement uncertainty in food microbiology using non-logarithmic precision data. The calculations used in this procedure based on relative range of duplicate analyses can be applied to intra-laboratory reproducibility data obtained from microbiological analyses of which duplicate results show relatively low variation.     

A computer program for a general case evaluation of the expanded uncertainty

The ISO Guide to the Expression of Uncertainty in Measurement provides a uniform method for the evaluation of combined standard uncertainty of a measurand whose expectation and standard deviation are stable over the measurement period. However, the method provided for the evaluation of the expanded uncertainty is not complete. Particularly, it does not include the case where the contributing components are correlated. Also, the probability distribution of the combined uncertainty must be close to a Normal distribution otherwise other methods must be used. The method presented here, which is implemented in a computer program, is based on a combination of the ISO guide method and Monte-Carlo simulation.The Monte-Carlo Simulation can obtain the data needed for the evaluation of the expanded and standard uncertainties directly from the measurement equation (that defines the measurand in terms of the contributing components) or from a spreadsheet-like format. Some sample results obtained by the computer program using both methods are compared and discussed.     

Determination of standard sample purity using the high-precision 1H-NMR process

This paper discusses the technique for high-precision quantification using ¹H-NMR to determine the purity of analytical standard samples. The procedure described is based on the use of internal reference samples in an ¹H NMR experiment in our laboratories. The sample preparation and all relevant NMR parameters were optimized for minimum uncertainty. The validation of accuracy and precision was performed by comparing different certified reference materials. It was shown that the high-precision measurement is applicable even for relatively small sample amounts down to 2.5 mg. The relative combined uncertainty of measurement was found to be 0.15%. Two different approaches for uncertainty calculation were compared; a complete uncertainty budget was calculated.     

Monitoring the precision of routine analyses by using duplicate determinations

To ensure the reliability of results, analytical laboratories require a continuous qualitycontrol program which must take account of both systematic and random errors. Analyses of reference materials can be used to estimate systematic errors but estimates of random errors (precision) tend to be optimistic, mainly because reference materials cannot be put through the whole analytical process (e.g., primary sampling is often a major source of error). Estimates of precision must be based on routine samples. If duplicate determinations are done on routine samples, the precision can be estimated reliably. Within the optimum concentration range of analytical method (usually starting from 5-10 times the detection limit), the relative standard deviation (s_r can be regarded as being almost constant or independent of concentration. The precision can then be estimated by first calculating the s_r value of each pair of results. Individually, these are not reliable estimates of the true s_r, but they can be regarded as independent measurements of the same s_r and so can be pooled to obtain a more reliable estimate of precision with the number of duplicates as the degrees of freedom. The applicabiilty of the method is tested on soil, rock and ore samples.     

Measurement uncertainty of food carotenoid determination

For consistent interpretation of an analytical method result it is necessary to evaluate the confidence that can be placed in it, in the form of a measurement uncertainty estimate. The Guide to the expression of Uncertainty in Measurement issued by ISO establishes rules for evaluating and expressing uncertainty. Carotenoid determination in food is a complex analytical process involving several mass transfer steps (extraction, evaporation, saponification, etc.), making difficult the application of these guidelines. The ISO guide was interpreted for analytical chemistry by EURACHEM, which includes the possibility of using intra- and interlaboratory information. Measurement uncertainty was estimated based on laboratory validation data, including precision and method performance studies, and also, based on laboratory participation in proficiency tests. These methods of uncertainty estimation were applied to analytical results of different food matrices of fruits and vegetables. Measurement uncertainty of food carotenoid determination was 10–30% of the composition value in the great majority of cases. Higher values were found for measurements near instrumental quantification limits (e.g. 75% for β-cryptoxanthin, and 99% for lutein, in pear) or when sample chromatograms presented interferences with the analyte peak (e.g. 44% for α-carotene in orange). Lower relative expanded measurement uncertainty values (3–13%) were obtained for food matrices/analytes not requiring the saponification step. Based on these results, the saponification step should be avoided if food carotenoids are not present in the ester form. Food carotenoid content should be expressed taking into account the measurement uncertainty; therefore the maximum number of significant figures of a result should be 2.     

Measurement uncertainty in analytical methods in which trueness is assessed from recovery assays

We propose a new procedure for estimating the uncertainty in quantitative routine analysis. This procedure uses the information generated when the trueness of the analytical method is assessed from recovery assays. In this paper, we assess trueness by estimating proportional bias (in terms of recovery) and constant bias separately. The advantage of the procedure is that little extra work needs to be done to estimate the measurement uncertainty associated to routine samples. This uncertainty is considered to be correct whenever the samples used in the recovery assays are representative of the future routine samples (in terms of matrix and analyte concentration). Moreover, these samples should be analysed by varying all the factors that can affect the analytical method. If they are analysed in this fashion, the precision estimates generated in the recovery assays take into account the variability of the routine samples and also all the sources of variability of the analytical method. Other terms related to the sample heterogeneity, sample pretreatments or factors not representatively varied in the recovery assays should only be subsequently included when necessary. The ideas presented are applied to calculate the uncertainty of results obtained when analysing sulphides in wine by HS-SPME-GC.     

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.     

Recognizing heterogeneous distribution of platinum group elements (PGE) in geological materials by means of the Re-Os isotope system

The identification of uncertainties caused by sample inhomogeneity, as distinct from those caused by sample preparation and measurement, is a challenging task. Use of chemometric methods to separate and estimate these contributions to the combined standard uncertainty of a measurement (uc) of an analytical result requires complex experiments. The difficulty of platinum group element measurement makes this task even more complex. But unless it can be demonstrated that sample inhomogeneity is the major contributor to the high variability of an analytical result one should be careful not to mistakenly attribute this to a nugget effect. In this contribution we are able to demonstrate in two special cases that irreproducible results (up to 90% RSD) for analysis of Os and Re in the pg g(-1) to ng g(-1) range are truly caused by a nugget effect and not by inadequacies of the analytical method.     

ICP-AES法测定油漆中总铅量不确定度的讨论

根据EURACHEM／CITAC2000中的规定计算了ICP—AES法测定油漆中总铅量的不确定度,建立了数学模型和根据在测试过程中产生不确定度的变量建立了因果图。通过转化数学模型和因果图,对油漆标准样品中含铅量的测定精密度和准确度进行试验,并计算了此方法的不确定度。结论中提出可根据在日常分析试验中所积累的数据,用B类不确定度的计算方法计算所得的测定过程的不确定度具有更高的真实可信性,并指出要不断积累测试数据,不断更新测定方法的不确定度,这样得到的不确定度更为可信合理。     

User-oriented software for determination of the precision of signal-integrating analytical methods

A software package for the determination of the uncertainty in signal-integrating analytical techniques is presented. The program can be used to calculate detection limits and to determine baseline drift properties, the influence of drift-correcting procedures and integration time, etc. Complete analytical procedures, e.g., chromatography or atomic emission spectrometry, or parts of a system can be tested. No profound theoretical knowledge is required by the user; confidence intervals are calculated where necessary. The theoretical basis and the structure of the program are evaluated.     

Implementing combined uncertainty according to GUM into a commercial gamma spectrometric software

Measurement uncertainty is an important part of a measurement result that still often is neglected. A complete combined uncertainty budget can be calculated for non-routine measurements. However, for routine measurements, this work becomes time-consuming since every measurement result requires an uncertainty analysis. By analysing the uncertainty on a measurement system level in e.g. high resolution gamma spectrometry, the uncertainty analysis will be universal for a particular measurement geometry. The problem is then reduced to implementing the combined uncertainty into measurement software. This work shows how this analysis can be done and implemented into a commercial software for gamma spectrometric measurements.     

Uncertainty in spectrophotometric analysis--"error propagation break up", a novel statistical method for uncertainty management

In this work, is given the Combined Standard Uncertainty (CSU) calculation procedure, which can be applied in spectrophotometric measurements. For the assessment of the computations, different approaches are discussed, such as the contribution to the Combined Standard Uncertainty of the reproducibility, the repeatability, the total bias, the calibration curve, and the type of the measurand. Results of inter-laboratory measurements confirmed the assumptions. For the minimization of the errors propagation a controlled experimental procedure was applied by this laboratory, called “errors propagation break-up” (ERBs). The uncertainty of sample concentration from a reference curve dominates the Combined Standard Uncertainty. The contribution of the method and the laboratory bias (total bias) to the CSU is insignificant under controlled conditions of a measurement. This work develops a simple methodology that can be utilized to evaluate the uncertainty and errors control on routine methods used both by academic researchers or the industrial sector.     

An uncertainty evaluation for multiple measurements by GUM, III: using a correlation coefficient

After a measurement, a measured value and a measurement uncertainty are produced as a measurement result. By a repeated measurement, another measurement result is produced. Between the individual results of the two measurements, it is shown that there may be a significant correlation. A correlation coefficient can be determined when a GUM-compliant uncertainty budget for a measurement is available. Utilizing the correlations between the N individual results, an equation is derived to combine the N individual uncertainties of N measurements. Using the newly derived equation including the correlation coefficient, three measurement uncertainties of three measurement results are combined as an example. The combined uncertainty is compared with the uncertainty of a measurement which treats the three individual measurements as one process. Papers published in this section do not necessarily reflect the opinion of the editors, the editorial board, or the publisher.