蒙特卡洛法评定在线pH计示值误差的不确定度

以在线p H计为例,考察了在线酸度计示值误差不确定度的分布规律,利用蒙特卡洛法评定示值误差不确定度。对于0.01级的在线p H计,蒙特卡洛法与GUM法评定结果的差值为9.1%,小于不可靠性(20%);对于0.1级的在线p H计,蒙特卡洛法与GUM法评定结果的差值为3.8%,小于不可靠性(10%)。通过比较得出结论,采用GUM法验证了蒙特卡洛法(MCM)根据JJF 1547–2015评定在线p H计示值误差不确定度的方法是有效且适用的。尤其在测量模型非线性以及输出量的概率密度函数(PDF)较大程度地偏离正态分布或t分布等GUM法不适用的场合,蒙特卡洛法是评定在线分析监测仪器仪表示值误差不确定度的重要手段。     

Uncertainty Budget for k0-NAA

The concepts of the Guide to the expression of Uncertainties in Measurements for chemical measurements (GUM) and the recommendations of the Eurachem document "Quantifying Uncertainty in Analytical Methods" are applied to set up the uncertainty budget for k ₀-NAA. The "universally applicable spreadsheet technique", described by Kragten, is applied to the k ₀-NAA basic equations for the computation of uncertainties. The variance components — individual standard uncertainties — highlight the contribution and the importance of the different parameters to be taken into account.     

A new formulation to estimate the variance of model prediction. Application to near infrared spectroscopy calibration

Evaluation of uncertainty affecting predictions is a major trend in analytical chemistry and chemometrics. Several approximate expressions and resampling methods have been proposed for the estimation of prediction uncertainty when using multivariate calibration. This article proposes a new expression for the variance of prediction, adapted to near infrared spectroscopy specificities and particularly to the spectral error structure, induced by the high colinearity of the variables. The proposed analytical expression enables a detailed evaluation of the different contributions and components of uncertainty affecting the model. An application to real data of feedstuff near infrared spectra related to protein content has shown its advantages.     

Uncertainty estimation of anions and cations measured by ion chromatography in fine urban ambient particles (PM2.5)

The present work presents a measurement uncertainty evaluation according to Guide to the Expression of Uncertainty in Measurement (GUM) of the concentration of the cations K⁺ and Li⁺ and anions NO₃⁻² and SO₄⁻² in fine airborne particulate matter, refers to particles less than 2.5 μm in diameter (PM_2.5), as measured by ion chromatography (US-EPA 300 method). The GUM method is not typically used to report uncertainty. In general, the analytical results only report the measurement’s standard deviation under repetition as an uncertainty; thus, not all sources of uncertainty are considered. In this work, the major sources of uncertainty regarding the measurements were identified as contributions to linear least square regression lines, repeatability, precision, and trueness. The expanded uncertainty was approximately 20% for anions and cations. The largest contribution to uncertainty was found to be repeatability.     

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.     

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.     

Evaluation of measurement uncertainty in analytical assays by means of Monte-Carlo simulation

The main limitations of the Guide to the expression of Uncertainty Measurement (GUM) approach for evaluating the measurement uncertainty of analytical assays are presented and explained. The advantages of using Monte-Carlo simulation against the GUM approach are outlined and discussed and the principle of propagation of distributions is explained. The procedure of Monte-Carlo analysis is illustrated by two case studies. A first simple example quoted from the EURACHEM Guide and dealing with the preparation of a calibration standard is used to present the technique with detail in a step-by-step way. In this case the results obtained by both approaches are very similar. A second example deals with the calibration of mass according to a strong non-linear model. In this case, the Monte-Carlo analysis leads to better results.     

Uncertainty in liquid chromatographic analysis of pharmaceutical product: influence of various uncertainty sources

An ISO GUM measurement uncertainty estimation procedure was developed for a liquid-chromatographic drug quality control method-assay of simvastatin in drug formulation. In quantification of uncertainty components several practical approaches for including difficult-to-estimate uncertainty sources (such as uncertainty due to peak integration, uncertainty due to nonlinearity of the calibration curve, etc.) have been presented. Detailed analysis of contributions of the various uncertainty sources was carried out. The results were calculated based on different definitions of the measurand and it was demonstrated that unequivocal definition of the measurand is essential in order to get rigorous uncertainty estimate. Two different calibration methods - single-point (1P) and five-point (5P) - were used and the obtained uncertainties and uncertainty budgets were compared. Results calculated using 1P and 5P calibrations agree very well. The uncertainty estimate for 1P is only slightly larger than with 5P calibration.     

Implementation in MATLAB of the adaptive Monte Carlo method for the evaluation of measurement uncertainties

The ISO 98:1995 Guide to the expression of uncertainty in measurement (GUM) presents important application limitations. For its improvement, different supplements are being developed that will progressively enter into effect. The first of these supplements describes an alternative method for calculating uncertainties, the Monte Carlo method (MCM), which is not restricted to the conditions of the method described in the GUM: the linearity of the model and the application of the central limit theorem. MCM requires computer calculation systems for generating pseudo-random numbers and for evaluating the model a large number of times. There are software applications that have been specifically developed for calculating uncertainties, some of which include MCM; but they do not allow the user to control all factors in the process, particularly the result stabilization criteria. On the contrary, its implementation in a mathematical program for general purposes such as MATLAB, enables total control over the process, is simple and benefits from its calculation speed. This article details programming in MATLAB for the implementation of the adaptive MCM method.     

Estimation of the uncertainty of mass measurements from in-house calibrated analytical balances

The uncertainty evaluation of mass measurements when using “in-house” calibrated analytical balances is revisited according to the Guide to the expression of Uncertainty Measurement (GUM). The calibration of analytical balances is discussed according to the guidelines of several bodies such as ASTM, UKAS and DKD/PTB. The remainder components of uncertainty can be estimated from the balance data sheet specifications.     

Determination of phosphorus traces in platinum alloys by two-phase isotope exchange

The method of ZEMAN and KRATZER for the determination of phosphorus traces by means of two-phase isotope exchange was modified for the determination of phosphorus in pure platinum or pure platinum alloys. It was found that Pt, Rh, Ag, and As do not interfere with the determination. Among the elements usually present in platinum metal or platinum alloys, only gold interferes. It was removed by extraction from 7M HCl by MIBK and AmOAc. Hydrochloric acid also interferes but it can be removed by evaporation. The analytical procedure is given for the solution obtained by pressure decomposition of the sample (0.5 g) in a steel bomb with PTFE inlay. It is possible to determine >2 ppm P (approximate error −10%). Using a calibration dependence instead of the well known equation for isotope exchange, the content of P in the standard solution labelled with³²P need not be known.     

化学计量中不确定度评定研究进展

测量不确定度是表征合理地赋予被测量之值的分散性的参数。本文针对化学计量不确定度评定基础模型仅适用于线性模型、概率分布为正态分布或缩放位移t分布等局限,介绍了近年来不确定度评定的研究热点:蒙特卡罗方法(Monte Carlo Method,MCM),不确定度评定的来源、评定概念、评估方法及其发展过程,扩大了测量不确定度评定与表示的适用范围。     

A partial least squares based spectrum normalization method for uncertainty reduction for laser-induced breakdown spectroscopy measurements

A bottleneck of the wide commercial application of laser-induced breakdown spectroscopy (LIBS) technology is its relatively high measurement uncertainty. A partial least squares (PLS) based normalization method was proposed to improve pulse-to-pulse measurement precision for LIBS based on our previous spectrum standardization method. The proposed model utilized multi-line spectral information of the measured element and characterized the signal fluctuations due to the variation of plasma characteristic parameters (plasma temperature, electron number density, and total number density) for signal uncertainty reduction. The model was validated by the application of copper concentration prediction in 29 brass alloy samples. The results demonstrated an improvement on both measurement precision and accuracy over the generally applied normalization as well as our previously proposed simplified spectrum standardization method. The average relative standard deviation (RSD), average of the standard error (error bar), the coefficient of determination (R²), the root-mean-square error of prediction (RMSEP), and average value of the maximum relative error (MRE) were 1.80%, 0.23%, 0.992, 1.30%, and 5.23%, respectively, while those for the generally applied spectral area normalization were 3.72%, 0.71%, 0.973, 1.98%, and 14.92%, respectively.     

New Calibration Model: Combining Integrated Calibration Method and H-point Standard Addition Method to Detect and Avoid Interference Effects

A new calibration methodology based on the combination of integrated calibration method (ICM) and the H-point standard addition method (HPSAM) is presented. It allows the diagnosis and correction of errors caused in an analytical system by different kinds of interference effects. Six calibration solutions consisting of mixtures of sample, diluent, and one standard are prepared in accordance with the ICM principle to integrate the external calibration method with the standard addition method and thereby to detect and eliminate proportional interferences. Absorbance increments chosen according to the HPSAM principle are proposed to correct the errors caused by additive interferences. A set of as many as six apparent estimations of analyte concentration in a single calibration procedure is calculated for validating accuracy. As a consequence, doing calibration by the ICM-HPSAM method, it is possible to obtain the final analytical results with considerably improved accuracy. The determination of calcium in several different water samples (containing amounts between 4.9 and 127?mg?L^?1) with Arsenazo III has been chosen as an example because it is biased if the errors are not diagnosed and corrected. The results are characterized by small (not higher than 8%) relative error (RE), and good precision (RSD values smaller than 6%).     

Modelling the calibration of the industrial platinum-resistance thermometers according to GUM

According to the Guide to the Expression of Uncertainty in Measurement (GUM, JCGM 100: 2008), the calibration process and its uncertainty evaluation should be expressed in terms of mathematical function(s) of input quantities. However, in practice, expressing measurement or calibration in a way that is fully compliant with GUM might be unrealistic and require a clear definition of the calibration process itself. Depending on the applied calibration process, different modelling equations with various complexities can be written. In this paper, four different approaches are given to model the calibration process of industrial platinum-resistance thermometers.     

Correction function on biased results due to matrix effects: Application to the routine analysis of pesticide residues

A new strategy to carry out the correction of analytical results affected by systematic errors due to the matrix effect is proposed. Two types of external calibrations must be established with the purpose to estimate the matrix effect: solvent calibration (SC) and matrix-matched calibration (MC). These calibration curves are statistically compared and a correction function (CF) is proposed with the aim to simplify the resolution to the problems associated with the incidence of matrix systematic error in the analytical results. Applying this correction function to the results obtained from the solvent calibration, it is possible to make a prediction of the values that would be obtained when the matrix-matched calibration is applied. On the other hand, a rigorous study of the associated uncertainty is developed and applied to the calculated correction function. Finally, this correction function is validated by means of obtained data of recovery studies carried out by a traditional methodology. The methodology has been satisfactorily applied to the quantification of the pesticide procymidone by HPLC for assessing dermal exposure.     

Estimation of uncertainty in electrochemical amperometric measurement of dissolved oxygen concentration

A procedure for the estimation of measurement uncertainty of dissolved oxygen (DO) concentration measurement based on the ISO approach is presented. It is based on a mathematical model that involves 14 input parameters. The uncertainty of DO concentration strongly depends on changes in experimental details (temperature difference between calibration and measurement, the time interval between calibration and measurement, etc.). The relative measurement uncertainty is, however, practically independent of the DO concentration itself. The uncertainty is the lowest if the calibration and the measurement are done at the same temperature and on the same day. A calculation tool is provided (in the form of a GUM Workbench file) for practitioners that can be used for uncertainty calculation of DO concentrations at very different experimental conditions.Electronic Supplementary Material The uncertainty calculation example is available as a GUM Workbench calculation file C_O2_meas.smu (GUM Workbench ver. 1.3.3, Metrodata GmbH) together with its data file Input_values.xls (MS Excel 97). For those users who do not have GUM Workbench, the full report of the GUM Workbench calculation is available as a PDF file C_O2_meas.pdf. This material is available via the Internet at .     

Relation between prediction errors of inverse and classical calibration

The formulae for prediction errors of inverse and classical calibration derived by Centner, Massart and de Jong in the Fresenius’ Journal of Analytical Chemistry (1998) 361?:?2–9 are reconsidered. All calculations assume univariate calibration by ordinary least squares regression applied to an infinite number of data pairs. Inverse calibration gives rise to an error variance which is smaller by a certain factor than that of classical calibration. This factor amounts to unity plus the ratio of the variances of the measurement errors and of the responses used for the calibration. The root mean squared error of prediction is also smaller for inverse than for classical calibration, namely by the square root of this factor. A prediction error calculated in that way agrees well with a result obtained by Monte Carlo simulations.     

A new and consistent parameter for measuring the quality of multivariate analytical methods: Generalized analytical sensitivity

Generalized analytical sensitivity (γ) is proposed as a new figure of merit, which can be estimated from a multivariate calibration data set. It can be confidently applied to compare different calibration methodologies, and helps to solve literature inconsistencies on the relationship between classical sensitivity and prediction error. In contrast to the classical plain sensitivity, γ incorporates the noise properties in its definition, and its inverse is well correlated with root mean square errors of prediction in the presence of general noise structures. The proposal is supported by studying simulated and experimental first-order multivariate calibration systems with various models, namely multiple linear regression, principal component regression (PCR) and maximum likelihood PCR (MLPCR). The simulations included instrumental noise of different types: independently and identically distributed (iid), correlated (pink) and proportional noise, while the experimental data carried noise which is clearly non-iid.     

原子荧光光谱法测定方便米饭中砷的测量不确定度评定

介绍了原子荧光光谱法测定方便米饭中砷的测量不确定度评定方法,该法根据最小二乘法原理计算校准曲线的标准不确定度,并充分分析和识别分析过程中的不确定度来源,较为全面地评定了测量不确定度,该法对原子吸收光谱法、电感耦合等离子发射光谱法和原子荧光光谱法等测定结果的不确定度评定具有参考作用。