Calibration uncertainty

Methods recommended by the International Standardization Organisation and Eurachem are not satisfactory for the correct estimation of calibration uncertainty. A novel approach is introduced and tested on actual calibration data for the determination of Pb by ICP-AES. The improved calibration uncertainty was verified from independent measurements of the same sample by demonstrating statistical control of analytical results and the absence of bias. The proposed method takes into account uncertainties of the measurement, as well as of the amount of calibrant. It is applicable to all types of calibration data, including cases where linearity can be assumed only over a limited range. Received: 25 August 2001 Accepted: 21 December 2001     

Introducing the concept of uncertainty of measurement in testing in association with the application of the standard ISO/IEC 17025

ISO/IEC 17025 requests laboratories to estimate the overall uncertainty associated with a test result. In many cases this means a new requirement to laboratories. It is essential to understand the importance of the knowledge of the uncertainty of measurements as well as the principle that not always the smallest possible uncertainty is needed, but fitness for purpose has to be achieved. The paper suggests a policy on the implementation of the concept of uncertainty and guidance on how to proceed, taking into account the present state of the art of understanding the problem.     

Traceability in routine chemical measurements: an example of application in the determination of CO2 at atmospheric concentration

In routine chemical measurements traceability can be achieved by using analytical instruments calibrated against primary reference materials. In the present work the calibration of a CO₂ non-dispersive infrared (NDIR) analyzer with measuring range 0–2000 μmol/mol of CO₂ and a resolution of 5 μmol/mol is reported. A procedure with working reference gas mixtures (WRMs) has been adopted, which requires seven calibration points. Primary reference gas mixtures (PRMs) are used to validate WRMs in a narrower range around the average atmospheric CO₂ concentration value. In this range the relative uncertainty reached is of the order of some parts in 10³ and the corrections are between 1 μmol/mol and 5 μmol/mol. Received: 16 March 2000 Accepted: 27 November 2000     

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     

Uncertainty calculation and implementation of the static volumetric method for the preparation of NO and SO2 standard gas mixtures

 The European Reference Laboratory of Air Pollution implements the static volumetric method for the preparation of nitrogen monoxide and sulphur dioxide reference standard gas mixtures. According to the new ISO guide for the expression of uncertainty, the uncertainty of these standards is up to 0.8% for nitrogen monoxide in the range 100 to 600 ppbv, and up to 0.4% for sulphur dioxide in the range 200 to 400 ppbv. The values presented in the present paper suggest that there is a 95% probability of the true value lying within the interval specified. To attain such low uncertainty values, the standard procedure for the implementation of the static volumetric method must be rigorously followed, and instruments must be carefully maintained. Received: 26 June 1997 · Accepted: 23 August 1997     

Assessment of uncertainty in calibration of a gas mass flowmeter

 A primary calibration system was set up in Rafael some years ago, based on volumetric flow rate. The primary standard measures volumetric flow by means of the volume change of a dual piston over a specific time interval. This system serves to calibrate secondary standards of the thermal mass flowmeter type. Calibration procedures were prepared and validated. The paper describes the tests and calibration procedure conducted for the uncertainty assessment, the different components contributing to the measurement uncertainties, and the formulas involved with volumetric flow fates and with thermal mass flowmeters. Received: 10 July 1999 / Accepted: 15 February 2000     

Global trends in quality specifications: a report from the Stockholm Conference

 In Stockholm a conference entitled: "Strategies to Set Global Quality Specifications in Laboratory Medicine" was held in April 1999. The primary aim in organizing the Conference was to provide a vehicle for reaching consensus on global quality specifications in laboratory medicine. This objective was achieved and a lively constructive debate, after the presentations were complete, led to agreement on the principles laid down in the Consensus Statement. The International Federation of Clinical Chemistry (IFCC), the International Union of Pure and Applied Chemistry (IUPAC) and the World Health Organization (WHO) kindly sponsored the Conference but it must be noted that the Consensus Statement reflects the views of the presenters and registrants who participated in the Conference and does not necessarily represent those of the sponsoring bodies. This paper reports on the standardization efforts so far, the Stockholm Consensus Conference, the ISO uncertainty concept and the consensus reality. A hierarchy of quality specifications in laboratory medicine was defined and agreed on. Received: 15 April 2000 · Accepted: 15 April 2000     

The definition of primary method of measurement (PMM) of the ’highest metrological quality’: a challenge in understanding and communication

Problems with understanding, explaining and communication of the present definition of primary method of measurement are described and amendments put forward for discussion. The conclusion is drawn that in many cases more attention should be given to the measurement result and its uncertainty statement, rather than to a method. Some cases are discussed where methods might have a fundamental characteristic that other methods do not have, a condition for the epitheton ’primary’. Received: 23 December 2000 Accepted: 13 November 2000     

Should non-significant bias be included in the uncertainty budget?

The bias of an analytical procedure is calculated in the assessment of trueness. If this experimental bias is not significant, we assume that the procedure is unbiased and, consequently, the results obtained with this procedure are not corrected for this bias. However, when assessing trueness there is always a probability of incorrectly concluding that the experimental bias is not significant. Therefore, non-significant experimental bias should be included as a component of uncertainty. In this paper, we have studied if it is always necessary to include this term and which is the best approach to include this bias in the uncertainty budget. To answer these questions, we have used the Monte-Carlo method to simulate the assessment of trueness of biased procedures and the future results these procedures provide. The results show that non-significant experimental bias should be included as a component of uncertainty when the uncertainty of this bias represents at least a 30% of the overall uncertainty. Received: 29 May 2001 Accepted: 10 December 2001     

Traceability of measurement results of the effective acquisition time in gamma-ray spectrometry implemented by the pulser method

Measurement of the effective acquisition time of a spectrum by the pulser method is described. The measurement results were verified up to count rates of 12000 s^–1 at various settings of the pulse processing electronics and spectral shapes. Systematic effects of up to 2% were observed. The clocks in the spectrometers were calibrated by counting pulses generated by the DCF 77 signal with the frequency of 1 Hz. In 1-day measurements at low count rates a relative uncertainty of about 0.5 10^–3 of the effective acquisition time was obtained. At counting losses up to 30% the relative uncertainty remained below 1.5 10^–2. Received: 2 March 2002 Accepted: 26 July 2002 Correspondence to M. Korun     

Accreditation: worth the trouble?

 Since the late 1980s, much attention has been paid to the usefulness of ISO-9000 certification. At present more than 45000 companies and institutions worldwide have been granted an ISO-9000 certificate. In the field of quality assurance, however, the ISO-9000 series does not completely cover the aspect of traceability. Demonstrable traceability is a particular problem in quality assurance of products by chemical analysis. In this paper realisation of demonstrable traceability is discussed, using the field of gas analysis as an example. Attention is focused on the usefulness of accreditation for laboratories performing quality assurance analyses. The basic question is asked whether and, if so, when accreditation is worth the trouble in cases where demonstrable traceability is required. Received: 15 February 1996 Accepted: 6 March 1996     

Uncertainties of mercury determinations in biological materials using an atomic absorption spectrometer – AMA 254

 The method is based on catalysed ignition of a sample portion in a flow of oxygen, capture of mercury by an amalgamator and measurement of the mercury vapour's absorbance after thermic release from the amalgamator. Three powdered food samples, a certified reference material (CRM) human hair and a reference material (RM) urine (liquid) were measured in the first range of the instrument (the possible contents determined according to our measurement procedure were 0.0003–0.5 ppm). The calibration function used was a line passing through the origin. The combined standard uncertainties of the mercury determinations were computed from uncertainty components of five quantities: absorbance of the sample, absorbance of the sample blank, slope of the calibration line, correction factor of the abscissa axis, and mass or volume of the sample. The most important uncertainty component is the uncertainty of the sample absorbance measurement which amounts to 52% of the determination uncertainty at the minimum (RM urine) and about 90% at the maximum (in our laboratory homogenized powdered food samples; analysis of variance showed their homogeneity to be insufficient). The results of the CRM and RM analyses do not indicate a significant systematic error for this determination. The relative expanded uncertainty (coefficient was 2) of the determination increases from 9 to 13% for the insufficiently homogenized samples with decreasing mercury content (range of 0.004–0.03 ppm); higher homogeneity of samples results in a decrease of the expanded uncertainty, e.g. 4.6% for the liquid sample (RM urine). Received: 26 April 1999 / Accepted: 30 August 1999     

Evaluation of uncertainty utilising the component by component approach

 This paper reviews the so-called "component by component approach" of evaluating measurement uncertainty. An overview of the evaluation process is given followed by an in-depth discussion of some of the differences between this approach and the approach of utilising validation data. Some of the advantages and disadvantages of using the component by component approach are outlined at the end. Received: 4 August 1999 · Accepted: 11 November 1999     

The Japanese traceability system and the role of uncertainty evaluation in measurement

 The new traceability system of measurement standards based on the Japanese Measurement Law has been established since November 1993. Some reference materials such as metal standard solutions, pH standard solutions and standard gas mixtures are included in the system together with relevant physical quantities. In this system, primary measurement standard instruments or primary reference materials are designated by the regulation for each quantity. For the practical dissemination of each quantity, accreditation of calibration bodies is recognized by the steering committee under the supervision of the government. In the course of assessment of a candidate calibration body, the concepts of ISO/IEC Guide 25 and ISO/IEC Guide 58 are effectively introduced. For the estimation of reliability, the concept of how to introduce the statistical approach is effectively considered. The method of uncertainty evaluation described in the ISO document entitled "Guide to the expression of uncertainty in measurement" is adopted.     

On the assessment of compliance with legal limits Part 1: signal and concentration domains

Taking into account the uncertainty of measurement when assessing compliance of a given sample with compositional specifications or statutory limits is an open question. Rigorous assessment should be performed within the signal domain, and by considering both α and β errors. Working within the concentration domain through a calibration function, which is affected by additional experimental uncertainties, involves a different degree of uncertainty and can sometimes lead to unreliable verdicts. The matter is discussed, and illustrated with the aid of some worked examples, each using multiple simulated data sets, obtained by adding an arbitrarily chosen Gaussian noise to representative response/concentration functional relationships. Received: 12 October 2000 Accepted: 12 July 2001     

Study of the uncertainty in gravimetric analysis of the Ba ion

The determination of barium by the gravimetric method, in which the precipitation of BaSO₄ was formed and weighed, coupled with instrumental measurement of trace constituents was studied. The analyte’s remaining in the filtrate and washes, mechanical loss, contaminants in the precipitate are the main influencing factors of uncertainty. A series of condition tests have been done, to reduce the effect of the factors mentioned above and the optimum test condition was found. The determination was carried out with a strictly defined operational procedure. The trace amounts of barium in the filtrate, washes and mechanical loss were determined by ICP-AES, the chloride occluded in the precipitate was determined by ion chromatography (IC), calculated as BaCl₂ and barium, and sodium by FAAS, calculated as Na₂SO₄. The average mass of barium in the filtrate contributes about 0.06% relative to that of the total barium, in washes about 0.09%, mechanical loss about 0.06%, contaminants of BaCl₂ about 0.08% and Na₂SO₄ about 0.05%. All the trace constituents were determined and corrected on a sample-by-sample basis. Sources of uncertainty were assessed thoroughly. The uncertainty of this combined gravimetric-instrumental method was improved remarkably compared with that of gravimetric method alone. The expanded uncertainty (k =2) is 0.08%. Received: 15 June 2000 Accepted: 25 December 2001     

Quality assurance system for a decomposition method as demonstrated for the Wickbold combustion technique

 A five-step model for a quality assurance system is developed for an internal quality control check. It includes the quality control of the decomposition method and the detection method as steps belonging together. The Wickbold combustion technique as decomposition method in combination with atomic absorption spectrometry was chosen. The vaporization of the elements mercury, arsenic, lead, antimony and selenium is based on combustion in an oxyhydrogen flame. To check the efficiency of the analytical system, the uncertainty of results was calculated on the basis of the "Guide to the Expression of Uncertainty in Measurement". Received: 13 January 1997 · Accepted: 29 March 1997     

Estimation of uncertainties for the application of electrochemical sensors in clinical analysis

 The influence of the selection of type of electrochemical sensor, its design and calibration, data processing and sample history on the uncertainty of measurements in clinical analysis is discussed. Special requirements for in vivo analysis that may minimize the value of uncertainty of measurements are given. Received: 4 March 2002 Accepted: 1 November 2002 Correspondence to R. I. Stefan     

The traceability scheme in chemical measurement

 Traceability is an essential property of a measurement result. However, it is recognized that the results of chemical measurements can be lacking in this property. In this paper we try to show how to understand and establish traceability in chemical measurement. The traceability connotation and the necessity of tracing back to SI units are described by means of comparability well-known. The roles and interrelationships of quality assurance, accreditation, calibration, reference material, analytical method, comparison and uncertainty in establishing traceability are explained with the aid of a block diagram. The paper also includes diagrams illustrating the Chinese situation and experience of establishing traceability for chemical measurement in China.     

Consideration of the uncertainty in the CRM value with the analysis of solid materials using atomic spectrometry

 The principles of the ISO "Guide to the expression of uncertainty in measurement" are applied to the analysis of solid materials by graphite furnace atomic absorption spectrometry. Assessment of trueness is achieved by the analysis of a certified reference material (CRM) under fixed instrumental conditions. For the evaluation of the method's uncertainty (as part of the validation) a model equation is derived, considering all significant contributions, including the uncertainty in the CRM value and the uncertainty in the CRM analysis. A concrete example is presented and discussed (soya flour as an unknown sample and CRM BCR rye grass). For routine analysis a pooled estimate from the validation experiment can be used, leading to an acceptable small uncertainty range even in the case of "duplicate determination". The test for trueness (acceptance) of the result of the CRM analysis is applied and the correction for detected bias is discussed. Received: 28 June 1998 · Accepted: 13 July 1998