Uncertainty estimation to evaluate mass balances on a combustion system

Mass balances of ash and potassium for a fluidized bed combustor were performed incorporating measurement uncertainties. The total output mass of ash or a chemical element should be equal to the mass in the input fuel; however, this is not often achieved. A realistic estimation of recovery uncertainty can support the reliability of a mass balance. Estimation of uncertainty helps to establish a reliable evaluation of the recovery ratio of ash mass and elemental mass. This may clarify whether any apparent lack in closing the mass balance can be attributed to uncertainties. The evaluation of measurement uncertainty for different matrices, namely coal, biomass, sand and ashes from different streams was based on internal quality control data and external quality control data, namely analysis of samples from proficiency tests or use of a certified reference material. The evaluation of intermediate precision and trueness allowed the estimation of measurement uncertainty. Due to the different physic and chemical characteristics of the studied matrices, the uncertainty of precision was evaluated using R-charts of data obtained from the analysis of duplicates for the majority of samples. This allowed evaluating sample heterogeneity effects. The instrumental acceptance criterion was also considered and included in the combined uncertainty. The trueness was evaluated using data from several proficiency tests and from analysis of a certified reference material or sample spiking. Statistically significant bias was included.     

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     

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     

Uncertainty assessment in instrumental neutron activation analysis of biological materials

Summary The expression of measurement uncertainties in a standardized form is a requirement for result reliability as it imposes implications to the interpretation of analytical results. In this work, sample mass, elemental standard mass, element decay constant and sample and elemental standard activities were identified as the most important uncertainty sources for the relative method of instrumental neutron activation analysis. The contribution of these sources to the expanded standard uncertainty in the concentration of As, Co, Cr, Fe, K, Na, Se and Zn in biological materials of marine origin was assessed and sample activity was identified as the major contribution.     

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.     

电感耦合等离子体原子发射光谱法测定铜合金中锆量的不确定度评定

讨论了采用电感耦合等离子体发射光谱法测定铜合金中锆量分析结果不确定度产生的原因。建立了数学模型,对测量重复性,标准溶液,标准曲线变动,试液体积,试样称量,数字修约等引起的不确定分量进行评定,计算了合成标准不确定度和扩展不确定度,并给出铜合金中锆量测定结果的报告。评定结果表明:测量重复性,标准曲线线性回归引起的不确定度对总不确定度影响最大。所以在测定中应进行多次平行测定,特别注意标准曲线的校正和绘制校准曲线所用标准样品的选择。     

A GUM-compliant uncertainty budget for the analysis of total carbon dioxide (TCO<Subscript>2</Subscript>) in equine plasma

Samples of plasma from chosen horses are collected prior to racing for the analysis of total carbon dioxide (TCO₂). Five or six (dependent on jurisdiction) tubes of blood are taken as required for a screen, followed (if positive) by confirmation (two tubes in quadruplicate) and, further confirmation (two tubes in quadruplicate) at a second referee laboratory. The threshold limit prescribed by the rules of racing is an amount concentration of 36.0 mM, with further action ensuing if the reported concentration is greater than 37.2 mM. Using QC data and an analysis of the measurement procedure, the combined standard measurement uncertainty of a measurement result was estimated to be 0.22 mM. This leads to a conclusion that the odds of incorrectly deciding that a sample at the threshold limit exceeded the action concentration, are 13 000 000:1 against. The combined standard measurement uncertainty could be reduced to 0.20 mM by combining results from the first and referee laboratories. An allowance for uncertainty of measurement of 1.0 mM is proposed, which leads to odds of 185 000:1 against concluding a sample is over the threshold limit when, in fact, it is not.     

同位素稀释电感耦合等离子体质谱(ID-ICP-MS)测定植物与人发标准物质中的铅

建立了同位素稀释电感耦合等离子体质谱(ID-ICP-MS)测定铅的方法.考察和讨论了仪器参数对同位素比值测定的影响,优化了仪器的数据采样参数.利用内标Tl对质量歧视、系统漂移进行了校正.讨论了同位素浓缩剂加入量对最终浓度测定值的不确定度的影响.将该方法应用于植物标准物质和人发标准物质的测定,结果令人满意.     

Worst case uncertainty estimates for routine instrumental analysis

A methodology for the worst case measurement uncertainty estimation for analytical methods which include an instrumental quantification step, adequate for routine determinations, is presented. Although the methodology presented should be based on a careful evaluation of the analytical method, the resulting daily calculations are very simple. The methodology is based on the estimation of the maximum value for the different sources of uncertainty and requires the definition of limiting values for certain analytical parameters. The simplification of the instrumental quantification uncertainty estimation involves the use of the standard deviation obtained from control charts relating to the concentrations estimated from the calibration curves for control standards at the highest calibration level. Three levels of simplification are suggested, as alternatives to the detailed approach, which can be selected according to the proximity of the sample results to decision limits. These approaches were applied to the determination of pesticide residues in apples (CEN, EN 12393), for which the most simplified approach showed a relative expanded uncertainty of 37.2% for a confidence level of approximately 95%.     

Certification by the Karl Fischer method of the water content in SRM 2890, Water Saturated 1-Octanol, and the analysis of associated interlaboratory bias in the measurement process

The calibration of Karl Fischer instruments and reagents and the compensation for instrumental bias are essential to the accurate measurement of trace levels of water in organic and inorganic chemicals. A stable, nonhygroscopic standard, Water Saturated Octanol, which is compatible with the Karl Fischer reagents, has been prepared. This material, Standard Reference Material (SRM) 2890, is homogeneous and is certified to contain 39.24 +/- 0.85 mg water/mL (expanded uncertainty) of solution (47.3 +/- 1.0 mg water/g solution, expanded uncertainty) at 21.5 degrees C. The solubility of water in -octanol has been shown to be nearly constant between 10 degrees C and 30 degrees C (i.e., within 1% of the value at 21.5 degrees C). The results of an interlaboratory comparison exercise illustrate the utility of SRM 2890 in assessing the accuracy and bias of Karl Fischer instruments and measurements.     

Certification by the Karl Fischer method of the water content in SRM 2890, Water Saturated 1-Octanol, and the analysis of associated interlaboratory bias in the measurement process

The calibration of Karl Fischer instruments and reagents and the compensation for instrumental bias are essential to the accurate measurement of trace levels of water in organic and inorganic chemicals. A stable, non-hygroscopic standard, Water Saturated Octanol, which is compatible with the Karl Fischer reagents, has been prepared. This material, Standard Reference Material (SRM) 2890, is homogeneous and is certified to contain 39.24 ± 0.85 mg water/mL (expanded uncertainty) of solution (47.3 ± 1.0 mg water/g solution, expanded uncertainty) at 21.5?°C. The solubility of water in 1-octanol has been shown to be nearly constant between 10?°C and 30?°C (i.e., within 1% of the value at 21.5?°C). The results of an interlaboratory comparison exercise illustrate the utility of SRM 2890 in assessing the accuracy and bias of Karl Fischer instruments and measurements.     

Application of the combination of isotope ratio monitoring with isotope dilution mass spectrometry to the determination of glucose in serum

Isotope ratio monitoring combined with n((13)C)/n((12)C) isotope dilution mass spectrometry (IRM/IDMS) provides results of low uncertainty of the order of 0.1% if it is applied to the analysis of simple mixtures as found in organic chemistry, even if only low (13)C spike additives to the sample are used. If the method is applied to the analysis of systems that require large-scale sample preparation prior to the measurement, such as the determination of glucose in serum, the results obtained exhibit a higher uncertainty that is comparable to that of the conventional gas chromatography/isotope dilution mass spectrometry (GC/IDMS) method. The reason for this observation is that the small contribution that the IRM/IDMS method makes to the uncertainty budget of the result is superimposed on a large contribution due to the sample preparation. It appears therefore that the IRM/IDMS method has no advantage over the conventional GC/IDMS method. However, if a series of measurements is carried out, and if a suitable experimental design is chosen, the IRM/IDMS method can provide valuable additional information. The influence of sample preparation on each individual result can be quantified as its deviation from the average value of all results of the series. From these data conclusions can be drawn for an improvement in sample preparation.     

Determination of measurement uncertainty for the determination of triazines in groundwater from validation data

Laboratories are increasingly urged to submit full uncertainties of their analytical results rather than only standard deviations. The determination of measurement uncertainties in compliance with the Guide to the Expression of Uncertainty in Measurement (GUM) is demonstrated using the validation approach explicitly endorsed by the recent edition of the EURACHEM guide for the determination of measurement uncertainty. Measurement uncertainty was split into uncertainty of the sample mass, uncertainty of the concentration of the stock standard solution, uncertainty of the calibration and uncertainty connected to within- and between-series precision. Uncertainties of sample mass and of the concentration of the stock standard solution were 0.26 and 1.14% for all analytes, which is negligible compared with the contributions of precision and calibration. Uncertainty of calibration was estimated from the calibration graph. Relative uncertainty of calibration was found to be strongly concentration dependent and to be the main uncertainty contribution below 0.2 microgram L-1. Precision was split into within-series and between-series standard deviation, which dominate the combined standard uncertainty at higher concentrations. The results obtained from these calculations are compared with results for a certified reference material and with the performance in an interlaboratory comparison. It was found that all results agreed within their uncertainty with the target values, showing that the estimated uncertainties are realistic.     

A computer program for a general case evaluation of the expanded uncertainty

The ISO Guide to the Expression of Uncertainty in Measurement provides a uniform method for the evaluation of combined standard uncertainty of a measurand whose expectation and standard deviation are stable over the measurement period. However, the method provided for the evaluation of the expanded uncertainty is not complete. Particularly, it does not include the case where the contributing components are correlated. Also, the probability distribution of the combined uncertainty must be close to a Normal distribution otherwise other methods must be used. The method presented here, which is implemented in a computer program, is based on a combination of the ISO guide method and Monte-Carlo simulation.The Monte-Carlo Simulation can obtain the data needed for the evaluation of the expanded and standard uncertainties directly from the measurement equation (that defines the measurand in terms of the contributing components) or from a spreadsheet-like format. Some sample results obtained by the computer program using both methods are compared and discussed.     

Validation of multi-element isotope dilution ICPMS for the analysis of basalts

In this study we have validated a newly developed multi-element isotope dilution (ID) ICPMS method for the simultaneous analysis of up to 12 trace elements in geological samples. By evaluating the analytical uncertainty of individual components using certified reference materials we have quantified the overall analytical uncertainty of the multi-element ID ICPMS method at 1–2%. Individual components include sampling/weighing, purity of reagents, purity of spike solutions, calibration of spikes, determination of isotopic ratios, instrumental sources of error, correction of mass discrimination effect, values of constants, and operator bias. We have used the ID-determined trace elements for internal standardization to improve indirectly the analysis of 14 other (mainly mono-isotopic trace elements) by external calibration. The overall analytical uncertainty for those data is about 2–3%.In addition, we have analyzed USGS and MPI-DING geological reference materials (BHVO-1, BHVO-2, KL2-G, ML3B-G) to quantify the overall bias of the measurement procedure. Trace element analysis of geological reference materials yielded results that agree mostly within about 2–3% relative to the reference values. Since these results match the conclusions obtained by the investigation of the overall analytical uncertainty, we take this as a measure for the validity of multi-element ID ICPMS.     

气相色谱-质谱联用法测定乐果的不确定度评定

本文以测定样品中乐果的含量为例,评定了气相色谱-质谱联用法测定结果的不确定度.建立数学模型,分析各不确定度分量,将不确定度分量合成,并计算其测定结果的扩展不确定度.     

Preparation and testing of standard solutions of cadmium, copper and lead

 Solutions of Cd, Cu and Pb at concentrations of about 1000 mg/l were prepared by dissolving the pure metals in HNO₃. Their concentration was verified by complexometric titration and by gravimetric analysis (Cu with salicylaldoxime, Cd with quinaldinic acid and Pb with 8-hydroxyquinoline). The results of the two methods were very similar and the uncertainty values were equal. However, the gravimetric determination can be regarded as more reliable, because titrimetric analysis is more prone to error due to inaccurate end-point reading. The expanded uncertainty of the concentrations of Cd and Cu attained 1 mg/l, which is half the value typically obtained for similar solutions from commercial manufacturers. To achieve such precise results, the bias had to be reduced by the highest possible extent, particularly by calibrating both the balance and the volumetric glassware. In addition to the uncertainty of the basic operations (volumetric and gravimetric), the uncertainty of the atomic and molecular weights constituted an appreciable component in the combined standard uncertainty; this manifested itself in the determination of Pb, where the expanded uncertainty was 2 mg/l. Received: 24 September 1998 / Accepted: 25 January 1999     

2011年约稿： 电感耦合等离子体原子发射光谱法测定铜合金中锆量的不确定度评定

讨论了采用电感耦合等离子体发射光谱法测定铜合金中锆量分析结果不确定度产生的原因。建立了数学模型,对测量重复性,标准溶液,标准曲线变动性,试液体积,试样称量,数字修约等引起的不确定分量进行评定,计算了合成标准不确定度和扩展不确定度,并给出铜合金中锆量测定结果的报告。评定结果表明：测量重复性,标准曲线线性回归引起的不确定度对总不确定度影响最大。所以,在测定中应进行多次平行测定,特别注意标准曲线的校正和绘制校准曲线所用标准样品的选择。     

用经验模型评估环境样品测量不确定度

利用水样、土壤和沉积物标准样品定值数据,建立了评估环境样品测量结果不确定度的经验模型。讨论了判断模型质量的指标。用建立的经验模型估算了实际标样和能力验证数据不确定度,并与实测结果进行了比较。探讨了利用本模型计算的相对标准偏差允许限用于实验室内部质量管理与控制的可行性。经验模型能帮助客户判断送检样品检测结果在临界值时能否满足相关要求。     

Comparison of three strategies to evaluate uncertainty from in-house validation data. A case study: mercury determination in sediments

In the present paper, three approaches are compared for the evaluation of the combined uncertainty in the determination of mercury in aquatic sediments by an aqua regia extraction procedure. For this, the data obtained in validation studies from five certified reference materials (CRMs), covering a range of concentrations from 0.8 to 130 mg kg⁻¹ of mercury and analysed by three atomic spectroscopic techniques (cold vapour generation atomic fluorescence spectrometry, CV-AFS, cold vapour generation atomic absorption spectroscopy, and inductively coupled plasma mass spectroscopy), were considered. The combined uncertainty was firstly assessed by considering separately the data obtained for each CRM analysed (approach A). Moreover, this assessment was also performed with two other calculation approaches (B and C) based on the pooled data obtained from the validation step. The comparison of the results obtained for the different techniques showed a clear bias effect when using CV-AFS with nitric acid as a diluent. In relation to the strategies tested for the combined uncertainty assessment, approach C proved to be the easiest and friendliest method for uncertainty assessment.