Shall we consider covariances?

 The impact of correlation between the reference points used in determination of a functional relationship by application of least-squares techniques is discussed. Calculations are based on an improved effective-variance approach to the general least-squares problem. From a simulation study, general conclusions about the impact of correlation are drawn. Standard addition as an example of a method using correlated data is discussed in detail. Received: 29 October 1997 · Accepted: 26 November 1997     

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).     

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     

An uncertainty evaluation for multiple measurements by GUM

An approach for uncertainty evaluation is proposed to determine the overall uncertainty by combining the uncertainties of the individual results from multiple measurements. It is accomplished by the separate combinations of the individual random and systematic components of the uncertainties of the individual results. The approach is useful when the individual results are not statistically different. It is recognized that, owing to the correlation, the uncertainty resulting from systematic effects is not reduced by multiple measurements. On the contrary, the uncertainty resulting from random effects can be reduced. Received: 3 May 2002 Accepted: 16 July 2002     

Customers' needs in relation to uncertainty and uncertainty budgets

 The general requirement of Quality Management standards to include in test reports a statement of the uncertainty of the results reflects the fact that a test result is rather useless without a knowledge of its accuracy. After an outline of the basic concepts of uncertainty, the need for uncertainty statements is illustrated for different ranges of applications. Received: 23 December 1997 · Accepted: 3 March 1998     

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     

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     

New developments in the production and use of CRMs in Romania

 A lot of effort is being made in Romania to meet the present main strategic goal – EU integration. Since the confidence in measurements is of considerable importance in almost every field of activity, the National Institute of Metrology (INM) is involved in improving its calibration and measurement capabilities to provide services in accordance with the latest European Regulation. Within this framework the assurance of the required traceability of all measurements plays a most important role. As reliable analytical measurements depend largely upon reference materials and the assurance of the traceability of amount measurements is still developing in Romania, a new approach regarding the function of Certified Reference Materials (CRMs) may be emphasized. The experience of the INM as well as new developments in Romania in preparation and certification of Reference Materials (RMs) are described. A short review of the locally available RMs and CRMs is given. Some aspects regarding the use of RMs and CRMs, especially for calibration, are discussed for their applicability for analytical measurements. Received: 31 October 2002 Accepted: 24 January 2003 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 M. Buzoianu     

Microbiological proficiency testing: a personal perspective

The author considers the fundamental differences between analyses in microbiology and those in chemistry and physics, deducing special issues for microbiological proficiency testing. He concludes that the variability and uncertainty implicit in microbiological analysis requires a broader range of proficiency scheme providers providing a broader range of services than in chemistry and physics. Received: 10 November 2000 Accepted: 3 December 2000     

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     

Influence of buffer quality on pH measurement uncertainty: prediction and experimental evaluation

Dependence of the uncertainty of a pH measurement result on the quality of buffers (i.e. the uncertainty of their certified pH values) at different levels of instrumental uncertainty (pH-meter, etc.) was simulated using the Monte Carlo method and regression analysis. The contribution of the instrumental standard uncertainty (in the studied range from 0.1 to 1 mV) to the uncertainty of the pH measurement result is negligible, if the standard uncertainties of the pH buffers exceed 0.04 pH (e. g. for in-house buffers). It is shown how the choice of pH-meter and buffers should be correlated in order to meet the required uncertainty of a pH measurement result in a sample under analysis. The results of the simulation were compared with experimental data obtained from calibrations of a pH/ion-meter with a hydrogen working electrode (Radiometer PHM-240) and with a glass electrode (Metrohm 744). Buffers of different quality (National Institute for Standards and Technology standard reference materials, certified Radiometer buffers and Merck CertiPUR buffers) were used for the calibrations. The uncertainties of the experimental results are close to the predicted ones obtained by the simulation. Received: 16 June 2002 Accepted: 19 July 2002 Presented at the 14^th International Conference of the Israel Society for Quality, 18–21 November 2002, Jerusalem, Israel Correspondence to I. Kuselman     

A framework for the application and materials in analytical chemistry

 Working group 5 of EuraChem Nederland has developed a framework for the implementation of reference materials in analytical chemistry. In this discussed paper, the framework is proposed as a tool for the development of standard operation procedures (SOPs) in laboratories. The implementation of (certified) reference materials in these SOPs is of major importance in establishing comparability and traceability in measurement results, which in turn play a crucial role in measurement in support of trade, environmental issues, and characterisation of materials. Recent developments in the field of uncertainty analysis require the application of reference materials. It is recognised that the calculation of the combined measurement uncertainty becomes almost impossible without the use of certified reference materials with a stated uncertainty. Received: 1 December 1995 Accepted: 20 December 1995     

NATA: 50 years experience with accreditation

 Laboratory accreditation is becoming increasingly accepted around the world as a means of identifying technically competent laboratories. It is also being used as a mechanism for the acceptance of test data both nationally and internationally. The concept and mechanisms of accreditation have been developed over the past 50 years. The first national laboratory accreditation system appeared in Australia in 1947. This organisation, known as the National Association of Testing Authorities (NATA), has since taken a leading role in developing accreditation practices that are now used world-wide in evaluating testing, measurement and calibration laboratories. This paper examines the development of the world's first and largest laboratory accreditation system, and looks at the difficulties and triumphs in gaining acceptance and recognition by government and industry of the benefits of laboratory accreditation. Received: 24 June 1996 Accepted: 25 June 1996     

Calibration lines passing through the origin with errors in both axes

Linear regression of calibration lines passing through the origin was investigated for three models of y-direction random errors: normally distributed errors with an invariable standard deviation (SD) and log normally and normally distributed errors with an invariable relative standard deviation (RSD). The weighted (weighting factor is x ² _i ), geometric and arithmetic means of the ratios y _i /x _i estimate the calibration slope for these models, respectively. Regression of the calibration lines with errors in both directions was also studied. The x-direction errors were assumed to be normally distributed random errors with either an invariable SD or invariable RSD, both combined with a constant relative systematic error. The random errors disperse the true, unknown x-values about the plotted, demanded x-values, which are shifted by the constant relative systematic error. The systematic error biases the slope estimate while the random errors do not. They only increase automatically the slope estimate uncertainty, in which the uncertainty component reflecting the range of the possible values of the systematic error must be additionally included. Received: 9 May 2000 Accepted: 7 March 2001     

A retrospective reliability test for numeric data sets applied by example to atomic-mass values of some nuclides

 Under favorable conditions, a retrospective test for reliability of published sets of physical property data becomes possible. The test and the necessary conditions for its use are discussed. The test is applied, by example, to well-documented, periodically republished nuclidic (atomic) masses of nine low atomic number nuclides. An index of reliability is suggested and evaluated for the example. Revised: 27 November 1995     

Statistical evaluation of stability data for assessing variability of an analytical method

 Stability assay results of a stable solid oral dosage form, designated Product X 5 mg, were subjected to a statistical analysis in view of evaluating the intra-team repeatability and the interval-to-interval reproducibility of the analytical method. Analysis of variance and analysis of method capability were performed on stability data obtained from tablets stored in four different packages over a two-year period. Replicate-to-replicate and period-to-period standard deviations of assay results of the active drug ingredient were found to vary among the packages and were up to 1.3 and 1.5% (% assay), thus leading to maximum differences between any two reported average results of up 4.7%. Analysis of method capability showed that up to 51% of the specification range (90–110%) is taken up by variations of the reported average stability results. This large but realistic method variability does not reflect the formation of low-level impurities (ca. 0.1%) required by regulatory agencies. Received: 10 December 1998 · Accepted: 25 January 1999     

Validation of the uncertainty evaluation for the determination of metals in solid samples by atomic spectrometry

 Every analytical result should be expressed with some indication of its quality. The uncertainty as defined by Eurachem ("parameter associated with the result of a measurement that characterises the dispersion of the values that could reasonably be attributed to the, . . ., quantity subjected to measurement") is a good tool to accomplish this goal in quantitative analysis. Eurachem has produced a guide to the estimation of the uncertainty attached to an analytical result. Indeed, the estimation of the total uncertainty by using uncertainty propagation laws is components-dependent. The estimation of some of those components is based on subjective criteria. The identification of the uncertainty sources and of their importance, for the same method, can vary from analyst to analyst. It is important to develop tools which will support each choice and approximation. In this work, the comparison of an estimated uncertainty with an experimentally assessed one, through a variance test, is performed. This approach is applied to the determination by atomic absorption of manganese in digested samples of lettuce leaves. The total uncertainty estimation is calculated assuming 100% digestion efficiency with negligible uncertainty. This assumption was tested. Received: 3 November 1997 · Accepted: 2 January 1998     

Evaluation of uncertainty of reference materials

 Certification of reference materials is far more than just characterisation of a selected homogeneous batch of material. From the perspective of the ISO Guide on the Expression of Uncertainty in Measurement (GUM) all uncertainty sources relevant to the user of an individual certified reference material (CRM) sample at a moment in time should be part of the CRM uncertainty. This not only includes the full uncertainty of the batch characterisation (rather than the statistical variation), but also all uncertainties related to possible between-bottle variation, instability upon long-term storage and instability during transport to the customer. Received: 21 April 1999 · Accepted: 24 September 1999     

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