Uncertainty calculations in the certification of reference materials. 1. Principles of analysis of variance

 The preparation and certification of reference materials is a rapidly developing area. Many innovative reference materials have limited homogeneity and stability, and, additionally, the uncertainty estimation of the property values must be brought in agreement with the principles of the “Guide to the expression of uncertainty in measurement” (GUM). The results of the homogeneity and stability studies must be included to a certain extent in the uncertainty of the property values of the reference material, in order to comply with these requirements. The basic theory needed to accomplish this is essentially the theory of analysis of variance (ANOVA). As GUM also allows alternative evaluations other than Type A evaluations, a reinterpretation of the theory of ANOVA is necessary to establish a model for the certification of reference materials that is widely applicable. For this, analysis of variance can be used as a statistical technique to derive standard uncertainties from homogeneity, stability and characterisation data. Received: 10 May 2000 / Accepted: 29 July 2000     

Uncertainty calculations in the certification of reference materials. 2. Homogeneity study

 Many reference materials undergo a batch certification, which implies that a small number of samples is taken from a batch, characterised, and these results are then assumed to be representative of all remaining samples. An important aspect in this design is the translation of the characterisation data to a single sample, as usually the laboratory will be using only one sample of the batch. This form of homogeneity is very important and can be influenced to a certain extent by well-designed sample preparation procedures. Another subsampling problem associated with many reference materials is that only a small test portion is drawn from the sample to carry out the measurement. Obviously, this test portion must be representative of the sample, otherwise the certified value is still not applicable. Both kinds of homogeneity tests are examined in the paper and evaluated using practical examples. Received: 31 May 2000 · Accepted: 29 July 2000     

Trends in the certification of reference materials

The certification of reference materials is still a rapidly developing area. Mostly driven by demands from laboratories, new reference materials are produced, and even new categories of materials are developed, such as genetically modified organism materials or materials for qualitative analysis. Even in more classical areas, such as the certification of chemicals for purity, there are important new insights, in particular in modelling the measurements and the property values. Laboratories are asking increasingly for uncertainty budgets of reference materials that are compatible with the concepts of the Guide to the expression of uncertainty in measurement, thus putting stronger demands to improve not only the quality of the materials, but also of the science and technology behind a certification. Three important issues are highlighted to exemplify these trends: the further interpretation of homogeneity and stability data, the appreciation of asymmetry due to mathematical constraints (relevant for, e.g., purity and trace analysis), and the certification of reference materials for qualitative measurement.Presented at BERM-9—9th International Symposium on Biological and Environmental Reference Materials, 15–19June 2003, Berlin, Germany     

Uncertainty calculations in the certification of reference materials

To serve as a measurement standard, a (certified) reference material must be stable. For this purpose, the material should undergo stability testing after it has been prepared. This paper looks at the statistical aspects of stability testing. Essentially, these studies can be described with analysis of variance statistics, including variant regression analysis. The latter is used in practice for both trend analysis and for the development of expressions for extrapolations. Extrapolation of stability data is briefly touched upon, as far as the combined standard uncertainty of the reference material is concerned. There are different options to validate the extrapolations made from initial stability studies, and some of them might influence the uncertainty of the reference material and/or the shelf-life. The latter is the more commonly observed consequence of what is called ’stability monitoring’. Received: 6 October 2000 Accepted: 4 December 2000     

Implementing the GUM in the certification of reference materials: the revision of ISO Guide 35

The availability of certified reference materials, certified in accordance to the GUM is an important tool for the proper estimation of measurement uncertainty in routine analysis. Many CRMs may suffer from incomplete or wrongly estimated uncertainties, mainly due to lack of guidance on how to implement the GUM in the production of CRMs. In particular the inclusion of the impact of inhomogeneity and instability in the uncertainty budget is often missing. The ongoing revision of ISO Guide 35 aims to fill this gap in providing guidance how (batch) inhomogeneity and instability can be translated into measurement uncertainty. The structure of the current ISO Guide 35 has been maintained as far as possible, but major parts underwent revision to become better aligned with GUM and ISO Guide 34 (2000). Received: 9 April 2001 Accepted: 22 October 2001     

The interpretation and use of stability data in the certification of reference materials

 Stability tests are carried out on candidate reference materials in order to ascertain that the certification values continue to be valid a reasonable time after completion of the certification analysis. These tests are also used for recommending storage conditions, as well as the duration of storage before certification values need be rechecked. BCR (Community Bureau of Reference) reference materials do not normally have an expiry date, but rely on stability monitoring throughout the lifetime of the certified material. The 1997 version of the BCR Guidelines for the production and certification of reference materials does, however, take into account the necessity of limiting the validity of a certification, when degradation of the material during storage cannot be ignored. This paper discusses an example of significant degradation taking place between the time of completion of the certification analysis and the issue of a formal certificate. Various options are presented together with an account of their influence on the certified values and their uncertainties. Received: 3 October 1997 · Accepted: 3 November 1997     

The use of certified reference materials in the Romanian traceability scheme

 For ensuring the traceability and uniformity of measurement results, the main objectives of national metrology programmes in chemistry are to calibrate and verify measuring instruments, to evaluate the uncertainty of measurement results and to intercompare the analytical results, etc. The concept of traceability has developed recently in chemical measurements, thus, an attempt to implement the principles of metrological traceability especially by appropriateness calibration using composition certified reference materials (CRMs) is underlined. Interlaboratory comparisons are also a useful response to the need for comparable results. The paper presents some aspects and practices in the field of spectrometric measurement regarding the metrological quality of the traceability by calibrating the instruments using suitable and reliable CRMs. The uncertainty of results, as a measure of the reliability that can be placed on them, has been adequately described in different documents and, as a consequence, some examples of evaluating the measurement uncertainty are described. The relationship between uncertainty and traceability, as two fundamental concepts of metrology which are intimately linked, is underlined. Received: 12 November 1999 / Accepted: 10 December 1999     

Some aspects of the evaluation of measurement uncertainty using reference materials

 In practice there are three aspects that need to be considered in order to achieve the required traceability according to its definition: the 'stated reference', the 'unbroken chain of calibrations' and the "stated uncertainty". For a certain chemical result, each of these aspects highly depends on the measurement uncertainty, both on its magnitude and how it was estimated. Therefore, the paper describes the experience of the Romanian National Institute of Metrology in estimating measurement uncertainty during the certification of reference materials (RMs), in metrological activities (calibration, pattern approval, periodical verification, etc.), as well as during the analytical measurement process. Practical examples of estimation of measurement uncertainty using RMs or certified reference materials are discussed for their applicability in spectrophotometric and turbidimetric analysis. Use of the analysis of variance to obtain some additional information on the components of measurement uncertainty and to identify the magnitude of individual random effects is described. Received: 12 November 1999 / Accepted: 25 February 2000     

Improvements in efficiency of production and traceability for certification of reference materials

Issues of current interest to certified reference material producers are addressed. Alternative strategies for certification of matrix reference materials are discussed and the benefits of adopting a flexible, cost-effective approach are described. The difficulty of undertaking homogeneity testing where certification is to be carried out with definitive techniques capable of providing very small measurement uncertainty is discussed. Methodology is described which combines conventional screening of the candidate material for homogeneity with an additional, precise assessment of homogeneity based on isotope dilution mass spectrometry measurements. A systematic procedure for evaluating the commutability (horizontal traceability or scope) of matrix reference materials has been evaluated and shows that in some circumstances matrix effects may be less pervasive than is generally believed. This offers the possibility, especially for trace analysis applications, of more efficient use of existing reference materials without compromising measurement reliability. Vertical traceability of matrix reference material data is of growing interest but is difficult to achieve with present interlaboratory certification exercises. A modification is described which attempts to address this issue. It also offers the possibility of improved identification of outliers and reduced variation of data between the participating laboratories.Presented at BERM-9—9th International Symposium on Biological and Environmental Reference Materials, 15–19June 2003, Berlin, Germany     

Homogeneity testing of reference materials

 Homogeneity testing is of the highest importance for the certification of reference materials, as it should demonstrate the validity of the certified values and their uncertainties in the analysis of individual units or portions thereof. However, the conclusions drawn from the results of these studies may often be questioned. It is proposed to improve this situation by quantifying the effect of homogeneity studies in terms of their impact on the uncertainty of certified values. Here it should be noted that the between-units variability directly affects the certified uncertainty, whereas the within-unit inhomogeneity only defines the minimum representative test portion. Received: 18 September 1997 · Accepted: 21 November 1997     

Uncertainty of chemical oxygen demand determination in wastewater samples

 The measurement uncertainty of the result of chemical oxygen demand determination in wastewater was evaluated. The major sources of uncertainty of the result of measurement were identified as the purity of reagents, volumetric operations, gravimetric operations, bias, and the repeatability of the method. Identification and evaluation of uncertainty sources was followed by combined uncertainty calculations. The combined uncertainty was compared to the experimentally determined variation and good agreement was found, indicating that the major uncertainty sources had been identified. The results show that the major sources of uncertainty arose from repeatability at high concentration level and volumetric steps at low concentration level, thus revealing the target operations for reducing the measurement uncertainty of this determination. Received: 5 August 2002 Accepted: 5 November 2002 Acknowledgements This research was supported by the Ministry of Education, Science and Sport of the Republic of Slovenia (Project Z2–3530). 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 A. Drolc     

Traceable property values of in-house reference materials

The traceability of in-house reference materials (IHRM) is discussed. It is shown that a systematic error in results of a measured value, specific to a measurement method or to a laboratory developing an IHRM, can be overcome if a comparative approach to IHRM characterization is used. A traceability chain of the value carried by the IHRM to the value carried by the reference material with higher metrological status and sufficiently similar matrix (for example, a certified reference material – CRM according to ISO Guide 30) is helpful in such a case. The chain is realized when the IHRM samples are analysed simultaneously with the CRM samples under the same conditions. This and other traceability chains necessary for the IHRM development are examined as the measurement information sources.     

Uncertainty of measurement and legislative limits

 The uncertainty affecting analytical measurements has to be taken into account when evaluating compliance of suspect matrices to legislative limits. To this aim Type 1 and 2 errors must be considered. This necessarily leads to the evaluation of the minimum detectable inadmissible signal, from which the minimum detectable inadmissible concentration can be obtained. The signal of suspect matrices thus has to be compared with the minimum detectable inadmissible signal. This paper aims to discuss practical problems involved in the comparison.     

A traceability protocol to the SI by gravimetric analysis

 An example is presented of a traceability protocol for the measurement of a single-element strontium reference material solution, executed by a "primary" method of measurement for certification. The method of measurement is briefly described together with the measurement equation and the associated calculations for the estimation of uncertainties. This is followed by a discussion and estimate of each component of uncertainty associated with the measurement, together with a final estimate of uncertainty. The final estimate of uncertainty compares well with observed uncertainties for two previous laboratory measurements of the reference material. Received: 21 February 1998 · Accepted: 17 August 1998     

Homogeneity and stability of reference materials

 Homogeneity and stability are two crucial characteristics of any certified reference material (CRM). Utmost care must be taken during preparation to create materials as homogeneous and stable as possible. Degradation can generally be minimised by reducing the water activity of the material to a level between 0.15 and 0.35. However, careful preparation by itself is not enough. Positive demonstration of homogeneity and stability is required from the perspective of implementing uncertainty calculus according to the Guide to the Expression of Uncertainty in Measurement (GUM). In many cases, homogeneity and stability studies fail to give sufficient quantitative information on homogeneity and stability, mainly because of a lack of measurement repeatability and insufficient number of replicates. In this work, some solutions to these problems and their implications are presented. Received: 25 April 2000 / Accepted: 12 September 2000     

Development and supply system of reference materials based on the Measurement Law in Japan

 Analytical instruments used for measurements of air and water pollution are calibrated by using reference materials such as standard gases and standard solutions. In Japan, since the middle of the 1970s, those reference materials which are traceable to the national standards maintained at national research institutes have been supplied to users by reference material producers. In order to establish the primary standards and to secure the traceability from the working standards to the national ones, various analytical methods such as coulometric, titrimetric and gravimetric analyses for purity determination and highly sensitive atomic spectrometry for trace analysis have been developed as the primary methods and reference methods. The Japanese Measurement Law, revised in 1992, has introduced a new traceability system in which a public organization, a "designated calibration body", can also prepare and maintain the national standards under the advice and instruction of national research institutes. The designated calibration body can provide calibration services to reference material producers (accredited calibration bodies) by using the national standards. The reference materials supplied in conformity with the traceability system include standard gases, pH standard solutions, metal standard solutions and non-metal ion standard solutions. Received: 4 October 1996 Accepted: 2 December 1996     

A pilot experiment of joint assessments by accreditation and certification bodies in clinical laboratories

When the quality system of the health care organization is certified and the laboratory accredited, two different types of assessments are also performed. To reduce the extra work caused by these different assessments the Finnish Accreditation Service FINAS and SFS-Certification have made a pilot experiment in combining the assessments. Joint assessments have been a positive experience to the laboratory as well as to the assessing bodies, and we find this operating model worth developing.     

ISO uncertainty and collaborative trial data

 The possibility of using interlaboratory study repeatability and reproducibility estimates as the basis for measurement uncertainty estimates is discussed. It is argued that collaborative trial reproducibility is an appropriate basis for estimating uncertainty in routine testing provided certain conditions are met by the laboratory. The primary shortcomings relate to establishment of traceability and consequent estimation of bias associated with the method, and quantitatively establishing the relevance to the single laboratory. Approaches to resolving both difficulties are proposed, the former via full implementation of trueness determination suggested in ISO 5725 : 1994 or by independent checks on individual accuracy and precision, the latter via a reconciliation procedure. The paper also discusses other factors including sampling and sample pre-treatment, change in sample matrix, and the influence of level of analyte. Received: 28 October 1997 · Accepted: 17 November 1997