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.     

Estimating the measurement uncertainty in forensic breath-alcohol analysis

The evidentiary weight attributed to forensic breath alcohol results in drunk-driving prosecutions requires that measurement uncertainty be established and shown to be fit-for-purpose. The principal components contributing to breath alcohol measurement uncertainty include: (1) biological/sampling, (2) instrumental, (3) traceability and (4) the water/air partition coefficient for control standards. Employing duplicate breath results from over 92,000 subjects to estimate the biological/sampling component and assuming reasonable forensic values for the other components, the combined and expanded uncertainty is determined for a practical example. The combined uncertainty for an unbiased single determination breath alcohol measurement was: . Employing the expanded uncertainty (k = 2.58), the 99% confidence interval for a mean breath alcohol concentration of 0.0935 g/210 L was 0.0866 to 0.1004 g/210 L. The proportion of combined uncertainty associated with each component was determined to be: biological/sampling 73%, analytical 10%, traceability 13% and water/air partition coefficient 4%. These are forensically acceptable estimates and demonstrate fitness-for-purpose of breath alcohol measurement when employing appropriate elements of quality control.     

Estimating measurement uncertainty in high-performance liquid chromatography methods

In every measurement procedure, it is important to know the components of measurement uncertainty affecting the quality of measured result and reliability of quantified result. The procedure for recognizing measurement uncertainty is not universal but depends on the method and sample type. It has to be made according to good laboratory practice. This paper aims at showing the comparison of measurement uncertainty component estimations for three methods using the high-performance liquid chromatography techniques: determination of the type and content of aromatic hydrocarbons in diesel fuels and petroleum distillates by normal phase high-performance liquid chromatography, determination of nitrates in water samples by ion chromatography, and determination of molecular weights of polystyrene by size exclusion chromatography technique. Both similarity and differences were found during the measurement uncertainty component estimation, and conclusions about influences of certain components on the result uncertainty were made.     

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.     

Relationship between performance characteristics obtained from an interlaboratory study programme and combined measurement uncertainty: a case study

 In the interlaboratory study programme "ILS Coal Characterisation", eight interlaboratory studies were organised based on the ISO standards for coal analysis. The use of blind samples in each round allows comparability of measurement results between rounds to be assessed. Based on the results, it could be demonstrated that the vast majority of the measurement results of the laboratories were traceable to results obtained in previous rounds of this programme. The hypothesis has been formulated that the combined standard uncertainty obtained from an interlaboratory study is equal to the reproducibility standard deviation. Whether the reproducibility can be used as the basis for the certification depends on whether the interlaboratory study includes all effects to be taken into account for establishing an uncertainty statement. Received: 12 April 1998 · Accepted: 2 July 1998     

Two-stage application of the optimised uncertainty method: a practical assessment

Uncertainty estimates from routine sampling and analytical procedures can be assessed as being fit for purpose using the optimised uncertainty (OU) method. The OU method recommends an optimal level of uncertainty that should be reached in order to minimise the expected financial loss, given a misclassification of a batch as a result of the uncertainty. Sampling theory can used as a predictive tool when a change in sampling uncertainty is recommended by the OU method. The OU methodology has been applied iteratively for the first time using a case study of wholesale butter and the determination of five quality indicators (moisture, fat, solids-not-fat (SNF), peroxide value (PV) and free fatty acid (FFA)). The sampling uncertainty (s(samp)) was found to be sub-optimal for moisture and PV determination, for 3-fold composite samples. A revised sampling protocol was devised using Gy's sampling theory. It was predicted that an increase in sample mass would reduce the sampling uncertainty to the optimal level, resulting in a saving in expectation of loss of over pounds 2000 per 20 tonne batch, when compared to current methods. Application of the optimal protocol did not however, achieve the desired reduction in s(samp) due to limitations in sampling theory. The OU methodology proved to be a useful tool in identifying broad weaknesses within a routine protocol and assessing fitness for purpose. However, the successful routine application of sampling theory, as part of the optimisation process, requires substantial prior knowledge of the sampling target.     

Estimates of uncertainty of measurement from proficiency testing data: a case study

The results obtained by a laboratory over a number of proficiency testing/external quality assessment schemes (PT/EQAS) rounds can give information on the uncertainty of its measurements for a given test, provided that conditions such as full coverage of the routine analytical range, traceability, and small uncertainty of the assigned values (compared to the spread of the results) are met and provided that systematic deviations and any other sources of uncertainty are considered. As organisers of the Italian EQAS (ITEQAS) in occupational and environmental laboratory medicine, we tested this hypothesis using as model data from well-performing laboratories taking part in ITEQAS for lead in blood over the last 2 years. We also investigated how different PT/EQAS features (frequency of trials and number of samples) would affect a laboratory estimate of its uncertainty. Such information can be helpful in improving PT/EQAS organisation and define, for a given test: (a) the state of the art of the uncertainty of current measurement procedures, (b) identify needs for improvement of analytical methodologies and (c) set targets for acceptable uncertainty values.Presented at the Eurachem PT Workshop September 2005, Portorož, Slovenia.Papers published in this section do not necessarily reflect the opinion of the Editors, the Editorial Board and the Publisher.     

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.     

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     

A practical procedure for assigning a reference value and uncertainty in the frame of an interlaboratory comparison

A method is suggested for the calculation of a reference value and its uncertainty to be used in the frame of an interlaboratory comparison (ILC). It is assumed that the reference value of the measurand is determined independently from the ILC round. It is derived from a limited set of measurement results obtained from one or several expert laboratories. The procedure involves three stages: (1) check of the experimental data and possible corrections; (2) check of the consistency of data, and possibly increase of the uncertainties in order to attain internal consistency; (3) choice between fully, partially or un-weighted mean.     

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     

Evaluation of the residual liquid junction potential contribution to the uncertainty in pH measurement: A case study on low ionic strength natural waters

The residual liquid junction potential (RLJP) needs to be accounted for in pH uncertainty estimation. Attempts to do this and the currently available methods for evaluating the RLJP are critically discussed and their weak sides are pointed out. In this work an empirical approach to the problem is proposed. It is based on the use of the RLJP bias estimated on a variety of measurement conditions for a specific class of analytical objects essentially differing in ionic strength from the pH calibration buffers. The data from five independent studies, including interlaboratory comparisons, on pH measurement in low ionic strength waters were used to find the overall bias observed in the 10⁻⁴ mol dm⁻³ strong acid solution. The procedure includes quantifying the uncertainty of bias values from separate studies by combination of the relevant uncertainty components and testing the consistency of the data. The weighted mean bias in pH was found to be 0.043 ± 0.007 (k = 2). With this estimate, the pH measurement uncertainties calculated according to the previously suggested procedure (I. Leito, L. Strauss, E. Koort, V. Pihl, Accredit. Qual. Assur. 7 (2002) 242-249.) can be enlarged to take the uncorrected bias into account. The resulting uncertainties on the level of 0.10-0.14 (k = 2) are obtained in this way for pH measurement in water and poorly buffered aqueous solutions in the range of pH 7.5-3.5.     

Calculation of measurement uncertainty in quantitative analysis of genetically modified organisms using intermediate precision--a practical approach

Quantitative characterization of nucleic acids is becoming a frequently used method in routine analysis of biological samples, one use being the detection of genetically modified organisms (GMOs). Measurement uncertainty is an important factor to be considered in these analyses, especially where precise thresholds are set in regulations. Intermediate precision, defined as a measure between repeatability and reproducibility, is a parameter describing the real situation in laboratories dealing with quantitative aspects of molecular biology methods. In this paper, we describe the top-down approach to calculating measurement uncertainty, using intermediate precision, in routine GMO testing of food and feed samples. We illustrate its practicability in defining compliance of results with regulations. The method described is also applicable to other molecular methods for a variety of laboratory diagnostics where quantitative characterization of nucleic acids is needed.     

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     

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.     

An estimation of the measurement uncertainty for an optical emission spectrometric method

 A validation procedure based on the ISO/IEC 17025 standard was used to demonstrate the long-term stability of a calibration process and to assess the measurement uncertainty of a standard test method for optical emission vacuum spectrometric analysis of carbon and low-alloy steel (ASTM E 415–99a). The validation was used to provide documented evidence that the selected method fulfils the requirements and that the method is ”fit for purpose”. A test for drift was applied to determine statistically whether the analytical results vary systematically with time. The accuracy and traceability of the optimised method were tested by an analysis of closely matched matrix certified reference materials (CRMs). The measurement uncertainty estimations took account of the precision study, the bias and its uncertainty, and the qualification of uncertainties not considered in the overall performance studies. Received: 2 November 2002 Accepted: 2 January 2003 Acknowledgement The author expresses gratitude to Dr. Aleš Fajgelj for helpful discussions during the 3rd Central European Conference on Reference Materials and Measurements. 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 T. Drglin     

Baseline noise and measurement uncertainty in liquid chromatography.

The stochastic properties of baseline noise in HPLC systems with a UV photo-diode array, photo-multiplier and gamma-ray detector were examined by dividing the noise into auto-correlated random process (Markov process) and an independent process (white noise). The present work focused on the effect of the stochastic noise properties on a theoretical estimation of the standard deviation (SD) of area measurements in instrumental analyses. An estimation theory, called FUMI theory (Function of Mutual Information), was taken as an example. A computer simulation of noise was also used. It was shown that the reliability (confidence intervals) of theoretical SD estimates mainly depends on the following factors: the ratio of the white noise and Markov process occurring in the baselines; the number of data points used for the estimation; the width of a target peak for which the SD is estimated.     

Measurement uncertainty in the pH measurement procedure

A measured value without even an approximate knowledge of the uncertainty is worthless. The uncertainty is part of every measured value and specification of the uncertainty is part of every analytical procedure. The uncertainty makes the value independent of its origin. The basis for estimation of the uncertainty is the "Guide to the Expression of Uncertainty in Measurement ". For some procedures, however, for example pH measurement, several problems arise in practice. This article describes a practical and inexpensive way of calculating the uncertainty of pH values.     

基于自适应蒙特卡洛法评定测量不确定度程序开发与应用

进行了基于自适应蒙特卡洛法评定测量不确定度的程序开发与应用。基于Python语言,设计开发自适应蒙特卡洛法评定测量不确定度程序,包含评定过程框架、自定义变量名称模块、过程参数关联计算模块以及蒙特卡洛法采样计算模块。程序界面简洁,操作简单,计算准确,适用于任意多个独立变量、任意多个过程参数及单一被测量的数学模型,为利用自适应蒙特卡洛法评定测量不确定度提供了方便。