Comparison of ISO-GUM and Monte Carlo methods for the evaluation of measurement uncertainty: application to direct cadmium measurement in water by GFAAS

The propagation stage of uncertainty evaluation, known as the propagation of distributions, is in most cases approached by the GUM (Guide to the Expression of Uncertainty in Measurement) uncertainty framework which is based on the law of propagation of uncertainty assigned to various input quantities and the characterization of the measurand (output quantity) by a Gaussian or a t-distribution. Recently, a Supplement to the ISO-GUM was prepared by the JCGM (Joint Committee for Guides in Metrology). This Guide gives guidance on propagating probability distributions assigned to various input quantities through a numerical simulation (Monte Carlo Method) and determining a probability distribution for the measurand.In the present work the two approaches were used to estimate the uncertainty of the direct determination of cadmium in water by graphite furnace atomic absorption spectrometry (GFAAS). The expanded uncertainty results (at 95% confidence levels) obtained with the GUM Uncertainty Framework and the Monte Carlo Method at the concentration level of 3.01 μg/L were ±0.20 μg/L and ±0.18 μg/L, respectively. Thus, the GUM Uncertainty Framework slightly overestimates the overall uncertainty by 10%. Even after taking into account additional sources of uncertainty that the GUM Uncertainty Framework considers as negligible, the Monte Carlo gives again the same uncertainty result (±0.18 μg/L). The main source of this difference is the approximation used by the GUM Uncertainty Framework in estimating the standard uncertainty of the calibration curve produced by least squares regression. Although the GUM Uncertainty Framework proves to be adequate in this particular case, generally the Monte Carlo Method has features that avoid the assumptions and the limitations of the GUM Uncertainty Framework.     

New procedure of silica gel surface modification preparation of gaseous standard mixtures for calibration purposes

The new type of silica gel surface modification with using the trimethylamine as a reagent is described. The samples of chemically modified silica gel have been used for generation of gaseous standard mixtures (methyl chloride as a measurand) using the technique of thermal decomposition of the surface compound. The main aim of the research was to check the suitability of the new type of silica gel surface modification for obtaining methyl chloride as a measurand of gaseous standard mixture. The gaseous standard mixture obtained with using this technique was used for calibration of a thermal desorber-gas chromatography-flame ionization detector (TD-GC-FID) system. The homogeneity of coverage of silica gel surface with the immobilized compound has been evaluated. The full uncertainty budget of determination of liberated amount of methyl chloride has been calculated. The average amount of methyl chloride liberated from the unit sample of chemically modified silica gel is 3.59 +/- 0.13 mg g(-1). The influence of the modification way on the amount of liberated analyte has also been determined.     

Uncertainty evaluation from Monte-Carlo simulations by using Crystal-Ball software

The first Supplemental Guide to the current edition of the Guide to the expression of uncertainty measurement (GUM) deals with the propagation of distributions, and emphasizes the use of Monte-Carlo Simulation (MCS) for estimating the uncertainty of measurands. In order to carry out MCS we need computer programs for generating pseudo-random numbers and for solving numerically the integral equations arising when simulating the values of the specification variables with a given probability density function (PDF). Crystal-Ball commercial software is very suitable for performing MCS and to estimate the expanded uncertainty for the measurand. The use of Crystal-Ball is illustrated with two working examples dealing with specification models of non-linear features and with correlated variables (such as the slope and intercept of calibration straight lines), respectively.An erratum to this article can be found at     

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.     

Systematic comparison of δ13C measurements of testosterone and derivative steroids in a freeze-dried urine candidate reference material for sports drug testing by gas chromatography/combustion/isotope ratio mass spectrometry and uncertainty evaluation using four different metrological approaches

An alternative calibration procedure for use when performing carbon isotope ratio measurements by gas chromatography/combustion/isotope ratio mass spectrometry (GC/C/IRMS) has been developed. This calibration procedure does not rely on the corrections in-built in the instrument software, as the carbon isotope ratios of a sample are calculated from the measured raw peak areas. The method was developed for the certification of a urine reference material for sports drug testing, as the estimation of measurement uncertainty is greatly simplified. To ensure that the method is free from bias arising from the choice of calibration material and instrument, the carbon isotope ratios of steroids in urine extracts were measured using two different instruments in different laboratories, and three different reference materials (CU/USADA steroid standards from Brenna Laboratory, Cornell University; NIST RM8539 mineral oil; methane calibrated against NIST RM8560 natural gas). The measurements were performed at LGC and the Australian National Measurement Institute (NMI). It was found that there was no significant difference in measurement results when different instruments and reference materials were used to measure the carbon isotope ratio of the major testosterone metabolites androsterone and etiocholanolone, or the endogenous reference compounds pregnanediol, 11- ketoetiocholanolone and 11β-hydroxyandrosterone. Expanded measurement uncertainties at the 95% coverage probability ranged from 0.21‰ to 1.4‰, depending on analyte, instrument and reference material. The measurement results of this comparison were used to estimate a measurement uncertainty of δ(13)C for the certification of the urine reference material being performed on a single instrument using a single reference material at NMI.     

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.     

原子吸收光谱法测定首饰镍释放量的不确定度评定

通过对原子吸收光谱法（AAS）测定首饰中镍释放量不确定度的评定,建立了该分析过程的相应数学模型,对数学模型中各个参数进行不确定度来源分析。研究结果表明:配制标准液以及标准工作曲线拟合线性方程是不确定度的主要来源。通过计算,首饰中镍释放量的合成标准不确定度为3.02×10-3,当包含因子k=2,置信水平为95%时,扩展不确定度为 6.04×10-3 μg/(cm2·week）。     

电感耦合等离子体质谱（ICP-MS）法测定高纯氧化铟中铜含量的不确定度评定

对电感耦合等离子体质谱法（ICP-MS）测量高纯氧化铟中铜含量的测量不确定度进行评定。不确定度的来源主要包括分析过程中所用的天平、玻璃器皿、标准曲线、标准溶液、试液定容体积、样品消解及测量重复性等引入的不确定度分量。计算出各分量的不确定度,通过合成得到测量结果的合成不确定度、扩展不确定度及测试结果的报告形式。     

Acidity constants in different media (I=0 and I=0.1 M KCl) from the uncertainty perspective

Procedures for estimating the measurement uncertainty for the acidity constant Ka (or the pKa value) in different media (I=0 and I=0.1 mol L(-1) KCl), as determined by potentiometric titration, are presented. The uncertainty budgets (the relative contributions of the different input quantities to the uncertainty in the result) of the pKa (I=0) and pKa (I=0.1 mol L(-1) KCl) values are compared. Unlike the values themselves, the uncertainties and uncertainty budgets of the values are comparable. The uncertainty estimation procedures are based on mathematical models of pKa measurement and involve the identification and quantification of individual uncertainty sources according to the ISO GUM approach. The mathematical model involves 52 and 48 input parameters for pKa (I=0) and pKa (I=0.1 mol L(-1) KCl), respectively. The relative importance of each source of uncertainty is discussed. In both cases, the main contributors to the uncertainty budget are the uncertainty components due to the hydrogen ion concentration/activity measurement, which provide 63.7% (for pKa (I=0)) and 89.3% (for pKa (I=0.1 mol L(-1) KCl)) of the uncertainty. The remaining uncertainty contributions arise mostly from the limited purity of the acid. From this work, it is clear that the uncertainties of the pKa (I=0.1 mol L(-1) KCl) values tend to be lower than those of the pKa (I=0) values. The main reasons for this are that: (1) the uncertainty due to the residual liquid junction potential is nominally absent in the case of pKa (I=0.1 mol L(-1) KCl) due to the similarly high concentrations of background electrolyte in the calibration solutions and measured solution; (2) the electrode system is more stable in solutions containing the 0.1 mol L(-1) KCl background electrolyte and so the readings obtained in these solutions are more stable.     

Estimation of the quantification uncertainty from flow injection and liquid chromatography transient signals in inductively coupled plasma mass spectrometry

The quality of the quantitative results obtained from transient signals in high-performance liquid chromatography–inductively coupled plasma mass spectrometry (HPLC–ICPMS) and flow injection–inductively coupled plasma mass spectrometry (FI–ICPMS) was investigated under multielement conditions. Quantification methods were based on multiple-point calibration by simple and weighted linear regression, and double-point calibration (measurement of the baseline and one standard). An uncertainty model, which includes the main sources of uncertainty from FI–ICPMS and HPLC–ICPMS (signal measurement, sample flow rate and injection volume), was developed to estimate peak area uncertainties and statistical weights used in weighted linear regression. The behaviour of the ICPMS instrument was characterized in order to be considered in the model, concluding that the instrument works as a concentration detector when it is used to monitorize transient signals from flow injection or chromatographic separations. Proper quantification by the three calibration methods was achieved when compared to reference materials, although the double-point calibration allowed to obtain results of the same quality as the multiple-point calibration, shortening the calibration time. Relative expanded uncertainties ranged from 10–20% for concentrations around the LOQ to 5% for concentrations higher than 100 times the LOQ.     

Estimation of uncertainty in size-exclusion chromatography with a double detection system (light-scattering and refractive index)

Size-exclusion chromatography (SEC) coupled with online laser light-scattering (LS) and refractive index (RI) detection provides an excellent approach to determine the molecular weights (Mw) of proteins by the “two-detector” approach. Mw is determined only at the maximum of a peak, using either peak heights or area ratio from the two detectors. However, proper calibration of the SEC/LS/RI system is critical to obtain high precision.Today, an essential part of any analysis is to evaluate the uncertainty associated with the method. Basically, it is possible to distinguish between factors related to signal nature, precision and those due to signal processing. Given the signal of interest is the peak height or area ratio from two detectors, the signal ratio uncertainty was calculated using the random propagation of error formula. In this case, the effect of signal correlation was evaluated to avoid the uncertainty overestimation. In the second case, the sources of uncertainty affecting analytical measurement were estimated with the information from the precision assessment. For this, two designs with two-factor fully nested were followed for each method. Finally, the contributions from various uncertainty sources related with calibration are also analysed in detail. There are in fact only three main sources of measurement uncertainty: intermediate precision, calibration and repeatability. Of these, method precision is always the greatest, regardless of approach.For all proteins and peptides studied, the Mw calculated using both methods are close to the theoretical results, independently of the design, but the contributions of individual terms to combined uncertainty depend on both the design and method used. For example, the combined uncertainty varied between 223 and 813.2 Da for carbonic anhydrase, although higher values were found for human insulin and ovalbumin dimer. Other considerations that can have a significant impact on the results are discussed.The reproducibility of the two methods versus that based on ASTRA software used as reference method was performed using the concordance correlation coefficient. The methods’ reproducibility depends on the permitted losses in precision and accuracy.     

离子色谱法测定地下水中硝酸盐氮含量的不确定度评定

采用不确定度连续传递模式,讨论了不同回归方式对离子色谱法测定岩溶地下水中硝酸根分析结果不确定度评定的差异.结果表明：（1）测定结果的不确定度主要来源于标准溶液配制过程引入的不确定度、校准曲线拟合及回归过程产生的不确定度和仪器测定过程引入的不确定度三部分;（2）不同校准曲线回归方式对测定结果的不确定度评定在不同测量水平上有不同的影响,当地下水中硝酸根含量越低,差异越大.此外,对不确定度评定过程中的各个分量进行量化,通过合成得到硝酸根测定结果的不确定度评定模型.     

电感耦合等离子体质谱法测定酱油中铅和总砷含量的不确定度评定

根据实验过程的数学模型,分析了电感耦合等离子体质谱法测定酱油中铅和总砷含量的不确定度来源,对不确定度分量进行计算,并计算出合成不确定度及扩展不确定度。     

Quality Assurance of Nuclear Analytical Techniques Based on Bayesian Characteristic Limits

Based on Bayesian statistics, characteristic limits such as decision threshold, detection limit and confidence limits can be calculated taking into account all sources of experimental uncertainties. This approach separates the complete evaluation of a measurement according to the ISO Guide to the Expression of Uncertainty in Measurement from the determination of the characteristic limits. Using the principle of maximum entropy the characteristic limits are determined from the complete standard uncertainty of the measurand.     

Establishment of traceability of ammonium nitrogen determination in wastewater

A case study is presented for the establishment of traceability for ammonium nitrogen determination in wastewater in a routine laboratory in order to fulfil the requirements of ISO/IEC standard 17025. The necessary relevant information was obtained from the method validation data, the quality control data and equipment calibration certificates. The method of measurement is described together with the measurement equation, selected traceable reference standards and the associated measurement uncertainty. The major sources of uncertainty of the result of measurement were identified and the combined uncertainty was calculated. Identification of the main uncertainty sources represents the basis for target operations for reducing the measurement uncertainty of this determination.     

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.     

Validation of a method for the determination of short-chain chlorinated paraffins in soil and sediments

An alternative approach for the reliable quantification of short-chain chlorinated paraffins (SCCPs) in sediment and soil, based on the existing method of carbon skeleton gas chromatography is presented. The method is proposed to establish an operationally defined measurand. The number of analytes to be looked at is notably reduced and the calibration problems encountered with the electron capture negative ionisation detection overcome because the conversion efficiency and the response are largely independent on the chlorine content of SCCPs. The accurate quantification is facilitated by the availability of n-alkanes as pure standards for calibration. To achieve the comparable results between laboratories, this method should be standardised. The first steps of this process, in-house development and full validation in sediment and soil, are presented for the first time. The limit of detection and quantification of 1.1 and 3.5 nmol g⁻¹, respectively, repeatability of 5% and relative expanded uncertainty of 12% were achieved providing a routinely applicable method for a reliable quantification of SCCPs.     

Comparison and validation of calibration methods for in vivo SPME determinations using an artificial vein system

The success of in vivo solid phase microextraction (SPME) depends significantly on the selection of calibration method. Three kinetic in vivo SPME calibration methods are evaluated in this paper: (1) on-fibre standardization (OFS), (2) dominant pre-equilibrium desorption (DPED), and (3) the diffusion-based interface (DBI) model. These are compared in terms of precision, accuracy, and ease of experimental use by employing a flow device simulating an animal circulatory system. In addition, the kinetic calibration methods were validated against established SPME equilibrium extraction (EE) external calibration and a conventional sample preparation method involving protein precipitation. The comparison was performed using a hydrophilic drug fenoterol as the analyte of interest. Liquid chromatography-tandem mass spectrometry (LC-MS/MS) was used for the determinations. All three kinetic methods compared well with both EE extraction and the conventional method in terms of accuracy (93-119%). In terms of precision, the DBI model had the best precision in whole blood and buffered phosphate saline solution with %RSD similar to the standard techniques (9-15%). DPED had the poorest precision of %RSD (20-30%) possibly due to errors associated with uncertainty in the amount of standard loaded on-fibre and remaining on the fibre after desorption. In addition, incurred errors could result due to the greater number of fibres used in comparison to the other two calibration methods. The precision of the OFS procedure was better than for DPED primarily because the use of multiple fibres is eliminated. In terms of the ease of use for calibration, the DBI model was the simplest and most convenient as it did not require standards once it had been calibrated or the uptake constant was calculated. This research suggests the potential use of DBI model as the best kinetic calibration method for future in-vein blood SPME investigations.     

Overall calibration procedure via a statistically based matrix-comprehensive approach in the stir bar sorptive extraction-thermal desorption-gas chromatography-mass spectrometry analysis of pesticide residues in fruit-based soft drinks

Stir bar sorptive extraction (SBSE)-thermal desorption (TD) procedure combined with gas chromatography mass spectrometry (GC-MS) and the statistical variance component model (VCM) is applied to the determination of semi-volatile compounds including organochlorine and organophosphorus pesticides in various synthetic and real fruit-based soft drink matrices. When the matrix effects are corrected using isotopically labelled or non labelled internal standard, but matrix/calibration run-induced deviations are still present in the measurements, the adoption of a variance component model (VCM) in the quantitative analysis of various matrices via an overall calibration curve is successful. The method produces an overall calibration straight line for any analyte accounting for the uncertainty due to all the sources of uncertainty, namely matrix-induced deviations, calibration runs performed at different times, measurement errors. Small increases in the detection limits and in uncertainty in the concentration values obtained in the inverse regression face favourably the decrease in times and costs for routine analyses.