Uncertainty of sampling in chemical analysis

 Uncertainty of sampling is the contribution from sampling errors to the combined uncertainty associated with an analytical measurement when the measurand is the concentration of the analyte in the 'target', the total bulk of material that the sample is meant to represent. Of the errors considered to contribute to uncertainty, random errors of sampling, characterised by precision, are much more accessible to investigation than those due to bias. Where an approximation to random sampling can be achieved, realistic precisions can normally be estimated. In some instances reproducibility precision is significantly greater than repeatability precision, and the contribution of between-sampler variations to sampling uncertainty must be acknowledged. However, the collaborative trial of a sampling method is an expensive and difficult exercise to execute. A system of internal quality control for routine sampling can be introduced. Fitness for purpose has been defined in terms of the required combined uncertainty of sampling and analysis. Received: 4 November 1997 · Accepted: 26 November 1997     

Human being as a part of measuring system influencing measurement results

The role of human being as a part of a measuring system in a chemical analytical laboratory is discussed. It is argued that a measuring system in chemical analysis includes not only measuring instruments and other devices, reagents and supplies, but also a sampling inspector and/or analyst performing a number of important operations. Without this human contribution, a measurement cannot be carried out. Human errors, therefore, influence the measurement result, i.e., the measurand estimate and the associated uncertainty. Consequently, chemical analytical and metrological communities should devote more attention to the topic of human errors, in particular at the design and development of a chemical analytical/test method and measurement procedure. Also, mapping human errors ought to be included in the program of validation of the measurement procedure (method). Teaching specialists in analytical chemistry and students how to reduce human errors in a chemical analytical laboratory and how to take into account the error residual risk, is important. Human errors and their metrological implications are suggested for consideration in future editions of the relevant documents, such as the International Vocabulary of Metrology (VIM) and the Guide to the Expression of Uncertainty in Measurement (GUM).     

Chemical metrology, chemistry and the uncertainty of chemical measurements

Chemical results normally involve traceability to two reference points, the specific chemical entity and the quantity of this entity. Results must also be traceable back to the original sample. As a consequence, any useful estimation of uncertainty in results must include components arising from any lack of specificity of the method, the variation between repeats of the measurement and the relationship of the result to the original sample. Chemical metrology does not yet incorporate uncertainty arising from any lack of specificity from the method selected or the traceability of the result to the original sample. These sources of uncertainty may however have much more impact on the reliability of the result than will any uncertainty associated with the repeatability of the measurement. Uncertainty associated with sampling may amount to 50–1000% of the reported result. Chemical metrology must be expanded to include estimations of uncertainty associated with lack of specificity and sampling. Received: 29 May 2001 Accepted: 17 December 2001     

Reliability of measurements of pesticide residues in food

This paper accounts for the major sources of errors associated with pesticide residue analysis and illustrates their magnitude based on the currently available information. The sampling, sample processing and analysis may significantly influence the uncertainty and accuracy of analytical data. Their combined effects should be considered in deciding on the reliability of the results. In the case of plant material, the average random sampling (coefficient of variation, CV=28–40%) and sample processing (CV up to 100%) errors are significant components of the combined uncertainty of the results. The average relative uncertainty of the analytical phase alone is about 17–25% in the usual 0.01–10 mg/kg concentration range. The major contributor to this error can be the gas-liquid chromatography (GLC) or high-performance liquid chromatography (HPLC) analysis especially close to the lowest calibrated level. The expectable minimum of the combined relative standard uncertainty of the pesticide residue analytical results is in the range of 33–49% depending on the sample size.The gross and systematic errors may be much larger than the random error. Special attention is required to obtain representative random samples and to eliminate the loss of residues during sample preparation and processing.     

The metrology of unstable measurands

 Type A statistical uncertainty in measurements is usually derived from the standard deviation of the measured data. This is correct as long as the measurand is stable over time and has a meaningful constant value. In such a case the average measurement and the standard deviations are meaningful. However, as measurement methods are refined and become more precise, we can observe that a given measurand may be unstable and change with time and the uncertainty in measurement must be redefined. This is specifically true in the metrology of time which can be measured today more precisly than any other measurand. We argue that in such a case the uncertainty in the prediction of the next measurement should be used instead of the uncertainty in measurement. Both uncertainties coincide for a stable measurand. The prediction of the next measurement is achieved by means of predictors. In this paper we describe the application of linear predictors and especially optimum linear predictors to predict in the presence of various types of instability. To illustrate the issues we use clock instabilities and clock metrology as this field is most developed. A measurand can be unstable but still predictable and thus useful. This is well known in the case of white noise about a linear drift for which the optimum predictor is a linear regression. Since the deviations from prediction of optimum prediction are of white noise, we can now use simple statistics to estimate the uncertainty of the optimum or close to optimum prediction. In this paper we present the various optimum or close to optimum linear predictors optimized for different types of instability and estimate the associated prediction uncertainties.     

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.     

Collaborative sampling trial in the context of quality assurance in the German marine monitoring programme for the North Sea and the Baltic Sea

This paper presents the assessment of a collaborative trial in sampling in the Baltic Sea in the framework of quality assurance in the German marine monitoring programme for the North Sea and the Baltic Sea. The objective of investigations was to determine the influence of sampling on analytical results for selected monitoring parameters and to harmonize the procedure for sampling of sea water to a large extent. In these studies the staff of three vessels took replicate sea water samples, 1 m below the surface and below the halocline, at two monitoring stations. Mass concentration mean values for different nutrient parameters were obtained from each sample, all in one laboratory. Data produced from the hierarchical design were treated with robust analysis of variance (ANOVA) to generate uncertainty estimates, as standard uncertainties (“u” expressed as standard deviation), for geochemical variation (s _geochem), primary sampling (s _sampling), and chemical analysis (s _analysis). Geochemical variation dominated the total variance in all cases. Sampling and analytical uncertainties contributed together up to 15% of the total variance and had a relative measurement uncertainty (u%) of less than 2% for all the parameters investigated. Thus for this study the sampling protocol and the analytical method could be regarded as fit-for-purpose. M. Gluschke was formerly affiliated to the Federal Environmental Agency, P.O. Box 33 00 22, 14191 Berlin, Germany.     

Using target measurement uncertainty to determine fitness for purpose

The methods an analytical laboratory uses must be validated to be fit for purpose. The fitness for purpose of a quantitative method used to determine the concentration of a substance when assessing compliance to requirements can be described by the maximum measurement uncertainty. This is called the target measurement uncertainty. Acceptance criteria for precision and bias in the method validation are then established in terms of the target measurement uncertainty. The target measurement uncertainty can be decided by following a process which involves determining the required concentration range of the measurand; determining the acceptable level of risks of incorrect decisions of compliance; developing a suitable decision rule, with guard bands if appropriate; using the probability of making an incorrect decision of compliance based on the decision rule; and assessing the impact of bias. A key participant in this process is the end user of the data, the laboratory customer. This paper presents the concepts concerning target measurement uncertainty introduced in recently published international guidelines to the practicing analytical chemist who is not generally familiar with these concepts. Three examples are used to illustrate the process.     

Uncertainty from sampling,in the context of fitness for purpose

Sampling is an integral part of nearly all chemical measurement and often makes a substantial or even a dominant contribution to the uncertainty of the measurement result. In contrast with analysis, however, the uncertainty contribution from sampling has usually been ignored. Indeed, far less is known about sampling uncertainty, although in some application sectors it is known to exceed the analytical uncertainty, especially when raw materials (natural or industrial) are under test. In 1995 the authors of this paper proposed a framework of concepts and procedures for studying, quantifying, and controlling the uncertainty arising from the sampling that normally precedes analysis. Many of the ideas were based on analogy with well-established procedures and considerations relating to quality of analytical measurement, ideas such as validation of the sampling protocol, sampling quality control and fitness for purpose. Since that time many of these ideas have been explored experimentally and found to be effective. This paper is a summary of progress to date. Presented at the AOAC Europe Workshop, November 2006, Limassol, Cyprus.

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Sampling Studies of Plastics and its Recycling Process Using Normal and Large Sample INAA

An inventory study was carried out of the trace element distribution in plastic products, made of new raw materials, and products made of recycled plastic scrap. Both normal and large sample INAA have been used. The uncertainty introduced by sampling a product made of new plastic pellets was found to be 1.3% for analytical portions of 200 mg, the extreme concentrations being 5% apart. In the end product of the recycling of scrap plastic this sampling uncertainty reflects the variation of trace element levels in the semi-manufactured product, and variations up to 200–300% may occur. Even larger variations can be expected between products, produced within a batch.     

Gy sampling theory in environmental studies: 2. Subsampling error estimates

Sampling can be a significant source of error in the measurement process. The characterization and cleanup of hazardous waste sites require data that meet site-specific levels of acceptable quality if scientifically supportable decisions are to be made. In support of this effort, the US Environmental Protection Agency (EPA) is investigating methods that relate sample characteristics to analytical performance. Predicted uncertainty levels allow appropriate study design decisions to be made, facilitating more timely and less expensive evaluations. Gy sampling theory can predict a significant fraction of sampling error when certain conditions are met. We report on several controlled studies of subsampling procedures to evaluate the utility of Gy sampling theory applied to laboratory subsampling practices. Several sample types were studied and both analyte and non-analyte containing particles were shown to play important roles affecting the measured uncertainty.

Gy sampling theory was useful in predicting minimum uncertainty levels provided the theoretical assumptions were met. Predicted fundamental errors ranged from 46 to 68% of the total measurement variability. The study results also showed sectorial splitting outperformed incremental sampling for simple model systems and suggested that sectorial splitters divide each size fraction independently. Under the limited conditions tested in this study, incremental sampling with a spatula produced biased results when sampling particulate matrices with grain sizes about 1 mm.     

Uncertainty of the result of TOC determination in water samples

It is becoming increasingly important to have a reliable and rapid technique for determining total organic carbon (TOC) in wastewater as procedures for wastewater purification could be better applied by knowing the amount of TOC in the wastewater. We describe here an evaluation of the uncertainties associated with TOC determinations in wastewater. TOC was determined by combustion and an infrared (IR) detection method, as described in the standard procedures of the International Organization for Standardization (1999; no. 8245). The major sources of uncertainty in the measurements were identified as being contributions from the linear least square calibration, repeatability, recovery and stability of the sample (storage conditions). A 10% relative expanded uncertainty of TOC measurement in the range of 0.2 to 500 mg L⁻¹ TOC was calculated, which also includes the uncertainty due to sampling.     

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     

The importance of precision in sampling sludges, biowastes and treated soils in a regulatory framework

As part of the European Commission (EC)'s revision of the Sewage Sludge Directive and the development of a Biowaste Directive, there was recognition of the difficulty of comparing data from Member States (MSs) because of differences in sampling and analytical procedures. The ‘HORIZONTAL' initiative, funded by the EC and MSs, seeks to address these differences in approach and to produce standardised procedures in the form of CEN standards. This article is a preliminary investigation into aspects of the sampling of biosolids, composts and soils to which there is a history of biosolid application. The article provides information on the measurement uncertainty associated with sampling from heaps, large bags and pipes and soils in the landscape under a limited set of conditions, using sampling approaches in space and time and sample numbers based on procedures widely used in the relevant industries and when sampling similar materials.These preliminary results suggest that considerably more information is required before the appropriate sample design, optimum number of samples, number of samples comprising a composite, and temporal and spatial frequency of sampling might be recommended to achieve consistent results of a high level of precision and confidence.     

From a single analyzer to multiple instruments—The GUM approach

Assessment and expression of analytical quality have become novel spotlights in medical laboratories since accreditation began in the early 1990s, in Europe. Evaluation of uncertainty of measurement by definition was launched in Finland when the Finnish Accreditation Service (FINAS) accredited the first medical laboratories in the mid 1990s. In spite of all the analytical and statistical knowledge which has been available in medical laboratories for years, evaluation of total uncertainty of measurement has not yet caught on. The concept is still unfamiliar to experts and, indeed, little guidance has been available. National and international activities, with good results, can be shown when the educational aspect is considered. The Guide to the Expression of Uncertainty in Measurement (GUM) remains the main document for uncertainty evaluation. Uncertainty of measurement together with target value of uncertainty can be used as a good measure for analytical quality in large or smaller laboratories over time, because it is a quantitative indication and the evaluation is easy to repeat as running practical tools are available.Presented at the 8th Conference on Quality in the Spotlight, 17–18 March 2003, Antwerp, Belgium     

On the use of the ‘uncertainty budget’ to detect dominant terms in the evaluation of measurement uncertainty

In the evaluation of measurement uncertainty, the uncertainty budget is usually used to identify dominant terms that contribute to the uncertainty of the output estimate. Although a feature of the GUF method, it is also recommended as a qualitative tool in MCM by using ‘nonlinear’ equivalents of uncertainty contributions and sensitivity coefficients. In this paper, the use of ‘linear’ and ‘nonlinear’ parameters is discussed. It is shown that when and only when the standard uncertainty of the output estimate is nearly equal to the square root of the sum of the squares of the individual uncertainty contributions, will the latter be a reliable tool to detect the degree of contribution of each input quantity to the measurand uncertainty.     

Soil sampling uncertainty on arable fields estimated from reference sampling and a collaborative trial

On three fields of arable land of (3–6)×10⁴ m², simple reference sampling was performed by taking up to 195 soil increments from each field applying a systematic sampling strategy. From the analytical data reference values for 15 elements were established, which should represent the average analyte mass fraction of the areas. A “point selection standard deviation” was estimated, from which a prediction of the sampling uncertainty was calculated for the application of a standard sampling protocol (X-path across the field, totally 20 increments for a composite sample). Predicted mass fractions and associated uncertainties are compared with the results of a collaborative trial of 18 experienced samplers, who had applied the standard sampling protocol on these fields. In some cases, bias between reference and collaborative values is found. Most of these biases can be explained by analyte heterogeneity across the area, in particular on one field, which was found to be highly heterogeneous for most nutrient elements. The sampling uncertainties estimated from the reference sampling were often somewhat smaller compared to those from the collaborative trial. It is suspected that the influence of sample preparation and the variation due to sampler were responsible for these differences. For the applied sampling protocol, the uncertainty contribution from sampling generally is in the same range as the uncertainty contribution from analysis. From these findings, some conclusions were drawn, especially about the consequences for a sampling protocol, if in routine sampling a demanded “certainty of trueness” for the measurement result should be met.     

Compliance decision criteria—problems encountered and actions taken in the EU and Codex

It is now recognised that there is an intimate relationship between the final analytical result and the sampling, the measurement uncertainty and the recovery factor used to obtain that result. Within the food sector in the EU this was identified by the SCOOP Task 9.1 “Preparation Of A Working Document In Support Of The Uniform Interpretation Of Legislative Standards And The Laboratory Quality Standards Prescribed Under Directive 93/99/EEC”. The recommendations from this Report have been accepted in the Food Contaminants and the Undesirable Substances in Feed Sectors. These are given in the SANCO document “Report To The Standing Committee On The Food Chain And Animal Health On The Relationship Between Analytical Results, The Measurement Uncertainty, Recovery Factors And The Provisions In EU Food And Feed Legislation With Particular Focus On The Community Legislation Concerning: (A): Contaminants In Food (Council Regulation (EEC) No 315/93 of 8 February 1993 Laying Down Community Procedures For Contaminants In Food), and (B): Undesirable Substances In Feed (Directive 2002/32/EC Of The European Parliament And Of The Council Of 7 May 2002 On Undesirable Substances In Animal Feed).” Similar considerations were identified in the Codex Alimentations Commission where the guidelines “The Use Of Analytical Results: Sampling, Relationship Between The Analytical Results, The Measurement Uncertainty, Recovery Factors And The Provisions In Codex Standards” are being progressed through the Codex system. Both of these Reports stress that before deciding whether a sample is in compliance with a legislative limit the uncertainty should be deducted and the results corrected for recovery. Thus that there is a difference between the legal specification and enforcement limit will be stressed and that this should be appreciated when specifications are being set. The rationale behind the Reports is described. Presented at AOAC Europe/Eurachem Symposium March 2005, Brussels, Belgium

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Estimation of measurement uncertainty by the budget approach for heavy metal content in soils under different land use

A reference database was used for the estimation of the standard uncertainties resulting from sampling, sample preparation, and analysis of soil samples from a target area in Switzerland. This evaluation was based on an extended reference sampling of the Comparative Evaluation of European Methods for Sampling and Sample Preparation of Soils Project. Samples were taken according to the national sampling protocols of 15 European countries and were analyzed for zinc, cadmium, copper, and lead. The combined uncertainty for all laboratories was estimated according to the ISO Guide to the Expression of Uncertainty in Measurement. It was found that the sampling uncertainty was not larger than the analytical uncertainty if more than ten sample increments were taken. The uncertainty due to variation in sampling depth and sample size reduction was only significant under unfavorable conditions. On the basis of an uncertainty budget the sampling protocols can be optimized and a ranking is possible, aimed at conditions that are fit for the specific purpose.Electronic Supplementary Material Supplementary Material is available in the online version of this article at