Evaluation of measurement uncertainty for analytical procedures using a linear calibration function

In the EURACHEM/CITAC draft ”Quantifying uncertainty in analytical measurement” estimations of measurement uncertainty in analytical results for linear calibration are given. In this work these estimations are compared, i.e. the uncertainty deduced from repeated observations of the sample vs. the uncertainty deduced from the standard residual deviation of the regression. As a result of this study it is shown that an uncertainty estimation based on repeated observations can give more realistic values if the condition of variance homogeneity is not correctly fulfilled in the calibration range. The complete calculation of measurement uncertainty including assessment of trueness is represented by an example concerning the determination of zinc in sediment samples using ICP-atomic emission spectrometry. Received: 9 February 2002 Accepted: 17 April 2002     

The uncertainty of a result from a linear calibration

The standard error of a result obtained from a straight line calibration is given by a well known ISO-endorsed expression. Its derivation and use are explained and the approach is extended for any function that is linear in the coefficients, with an example of a weighted quadratic calibration in ICPAES. When calculating the standard error of an estimate, if QC data is available it is recommended to use the repeatability of the instrumental response, rather than the standard error of the regression, in the equation.     

Assessment of uncertainty in calibration of a gas mass flowmeter

 A primary calibration system was set up in Rafael some years ago, based on volumetric flow rate. The primary standard measures volumetric flow by means of the volume change of a dual piston over a specific time interval. This system serves to calibrate secondary standards of the thermal mass flowmeter type. Calibration procedures were prepared and validated. The paper describes the tests and calibration procedure conducted for the uncertainty assessment, the different components contributing to the measurement uncertainties, and the formulas involved with volumetric flow fates and with thermal mass flowmeters. Received: 10 July 1999 / Accepted: 15 February 2000     

碳酸镉饱和溶液作标准用便携式AAS测定镉的研究

以CdCO3固体溶于煮沸冷却的去离子水中配制成饱和溶液,将该饱和溶液稀释成标准溶液系列用于便携式钨丝电热原子吸收光谱仪野外实时与在线分析环境水样中痕微量镉。经测定在25℃该饱和溶液中镉的浓度为272μg.L-1,与理论计算值279μg.L-1有很好的吻合。实验优化了相关的仪器条件和实验条件,在最优的条件下该方法的线性相关系数为0.9948,检出限为0.08μg.L-1。通过检测分析环境中的水样验证了该方法是可行的。     

The development of a method for the determination of trace elements in fuel alcohol by ETV-ICP-MS using isotope dilution calibration

A method for the determination of Ag, Cd, Cu, Pb and Tl in fuel alcohol by isotope dilution electrothermal vaporization inductively coupled plasma mass spectrometry (ID ETV-ICP-MS) is proposed. The analytes were separated in two groups: Ag and Cu were determined without modifier and Cd, Pb and Tl with the use of Pd as chemical modifier. The employed ETV operational conditions were pyrolysis temperature of 800 °C for Cd, Pb and Tl and of 900 °C for Ag and Cu and vaporization temperature of 2400 °C for both groups. Seven common, one with additive and one anhydrous fuel ethanol samples were analyzed. The spiked and reference isotopes were, respectively, ¹⁰⁹Ag and ¹⁰⁷Ag, ¹¹²Cd and ¹¹¹Cd, ⁶³Cu and ⁶⁵Cu, ²⁰⁶Pb and ²⁰⁸Pb and ²⁰³Tl and ²⁰⁵Tl. The added amounts of the enriched isotope material were the same for all samples: 4.6 ng of ¹⁰⁹Ag, 5 ng of ¹¹²Cd, 21.1 ng of ⁶³Cu, 9 ng of ²⁰⁶Pb and 0.21 ng of ²⁰³Tl. The blank was bi-distilled ethanol, acidified with 0.3% (v/v) nitric acid, as the samples. The limits of detection (LODs) were calculated as three times the standard deviation of the concentrations in the blank (n = 10) and were, in μg L⁻¹, for Ag: 0.02, for Cd: 0.08, for Cu: 0.1, for Pb: 0.05 and for Tl: 0.001. The obtained concentrations in the samples were in agreement with those obtained by external calibration (EC), according to the paired t-test. The isotope dilution (ID) showed to be a robust, fast and simple calibration technique for the analysis of fuel ethanol.     

Diversity-oriented synthesis of biaryl-containing medium rings using a one bead/one stock solution platform

Diversity-oriented synthesis of structurally complex and diverse small molecules can be used as the first step in a process to explore cellular and organismal pathways. The success of this process is likely going to be dependent on advances in the synthesis of small molecules having natural product-like structures in an efficient and stereoselective manner. The development, scope, and mechanism of the oxidation of organocuprates was investigated and exploited in the atropdiastereoselective synthesis of biaryl-containing medium rings (9-, 10-, and 11-membered rings). The methodology was performed on high-capacity, large polystyrene beads by metalating aryl bromides with i-PrBu(2)MgLi, followed by transmetalating with CuCN x 2LiBr and then oxidizing with 1,3-dinitrobenzene, and was used in a diversity-oriented synthesis of biaryl-containing medium rings (library total theoretical maximum 1412 members). The high capacity beads were arrayed into 384-well plates and, using a process optimized during the development of a one bead/one stock solution technology platform, converted into arrays of stock solutions, with each stock solution containing largely one compound. These stock solutions were used in numerous phenotypic and protein-binding assays. The process described outlines a pathway that we feel will contribute to a comprehensive and systematic chemical approach to exploring biology (chemical genetics).     

Uncertainty of the concentration of a copper calibration solution

The postulated uncertainty of many commercially available standard solutions is estimated on the basis of uncertainties of individual preparation steps. The declared concentration of Cu standard solution (1000 ± 2) mg/L was verified by gravimetric analysis (found (1000.7 ± 0.4) mg/L), isotope dilution with commercial and laboratory-prepared isotope-enriched solutions (found (1000.6 ± 16.8) mg/L and (1002.4 ± 3.6) mg/L, respectively), and by atomic absorption spectrometry (found (1001.4 ± 5.3) mg/L). Uncertainty budgets of all used methods are given and the procedures of uncertainty estimation are fully documented.     

A serial dilution microfluidic device using a ladder network generating logarithmic or linear concentrations

In this paper, we propose a serial dilution microfluidic chip which is able to generate logarithmic or linear step-wise concentrations. These concentrations were generated via adjustments in the flow rate of two converging fluids at the channel junctions of the ladder network. The desired dilution ratios are almost independent of the flow rate or diffusion length of molecules, as the dilution device is influenced only by the ratio of volumetric flow rates. Given a set of necessary dilution ratios, whether linear or logarithmic, a serial dilution chip can be constructed via the modification of a microfluidic resistance network. The design principle was suggested and both the logarithmic and linear dilution chips were fabricated in order to verify their performance in accordance with the fluorescence intensity. The diluted concentrations of a fluorescein solution in the microfluidic device evidenced relatively high linearity, and the cytotoxicity test of MCF-7 breast cancer cells via the logarithmic dilution chip was generally consistent with the results generated with manual dilution.     

Evaluation of the combined measurement uncertainty in isotope dilution by MC-ICP-MS

The combination of metrological weighing, the measurement of isotope amount ratios by a multicollector inductively coupled plasma mass spectrometer (MC-ICP-MS) and the use of high-purity reference materials are the cornerstones to achieve improved results for the amount content of lead in wine by the reversed isotope dilution technique. Isotope dilution mass spectrometry (IDMS) and reversed IDMS have the potential to be a so-called primary method, with which close comparability and well-stated combined measurement uncertainties can be obtained.This work describes the detailed uncertainty budget determination using the ISO-GUM approach. The traces of lead in wine were separated from the matrix by ion exchange chromatography after HNO(3)/H(2)O(2) microwave digestion. The thallium isotope amount ratio ( n((205)Tl)/ n((203)Tl)) was used to correct for mass discrimination using an exponential model approach. The corrected lead isotope amount ratio n((206)Pb)/ n((208)Pb) for the isotopic standard SRM 981 measured in our laboratory was compared with ratio values considered to be the least uncertain. The result has been compared in a so-called pilot study "lead in wine" organised by the CCQM (Comité Consultatif pour la Quantité de Matière, BIPM, Paris; the highest measurement authority for analytical chemical measurements).The result for the lead amount content k(Pb) and the corresponding expanded uncertainty U given by our laboratory was:k(Pb)=1.329 x 10-10mol g-1 (amount content of lead in wine)U[k(Pb)]=1.0 x 10-12mol g-1 (expanded uncertainty U=kxuc, k=2)The uncertainty of the main influence parameter of the combined measurement uncertainty was determined to be the isotope amount ratio R(206,B) of the blend between the enriched spike and the sample.     

Determination of As, Ge, Hg, Pb, Sb, Se and Sn in coal slurries by CVG-ETV-ICP-MS using external or isotopic dilution calibration

A method for the multi-elemental determination of As, Ge, Hg, Pb, Sb, Se and Sn in coal reference materials by slurry sampling chemical vapor generation (CVG) using external calibration and isotopic dilution (ID) calibration and detection by electrothermal vaporization inductively coupled plasma mass spectrometry (ETV-ICP-MS) is proposed. As, Ge, Sb, Se and Sn were determined using the external calibration, while, Hg, Pb, Se and Sn were determined by isotopic dilution. About 50–250 mg of sample was mixed with an acid solution, containing aqua regia and HCl, in an ultrasonic bath. For the isotopic dilution calibration, the enriched isotopes ²⁰¹Hg, ²⁰⁶Pb, ⁷⁷Se and ¹¹⁹Sn were added to the slurry in an adequate amount in order to produce an altered isotopic ratio close to 1. The vapor produced by the reaction of the sample slurry with the reducing agent was transported to the vaporizer and trapped in a Ir-treated graphite tube at 200 °C, before vaporization at 2100 °C and transportation of the vapor to the plasma. The accuracy of the method was assured by the analysis of four certified reference coal samples, using external calibration with aqueous solutions, prepared in the same medium and subjected to the same CVG and trapping procedure as the slurries and also by isotopic dilution calibration. The obtained concentrations were in agreement with the certified values, using the t-Student test for a confidence level of 95%. The detection limits (3 s; n = 5) of isotopic dilution, in ng g^− 1, were: 0.4 for Hg, 900 for Pb, 0.3 for Se and 0.2 for Sn. For external calibration, the detection limits, in ng g^− 1, were: 1.6 for As, 0.1 for Ge, 0.3 for Sb, 0.9 for Se and 7.5 for Sn. The relative standard deviations generally were lower than 14%, adequate for slurry analysis.     

Thermodynamics of stepwise dissociation of D,L-tryptophan in aqueous solution

The heat effects of the reaction of a solution of D,L-tryptophan with solutions of KOH and HNO₃ were measured by calorimetry at temperatures of 288.15, 298.15, and 308.15 K and ionic strength values of 0.25, 0.5, and 0.75 (KNO₃). The effect of the temperature and concentration of the background electrolyte on the heats of dissociation of amino acid was considered. The standard heat effects of ionization of D,L-tryptophan were determined by extrapolation to zero ionic strength. The standard thermodynamical characteristics of the stepwise dissociation of D,L-tryptophan were calculated.     

Prediction of measurement uncertainty in isotope dilution gas chromatography/mass spectrometry

An equation is theoretically derived which describes the relative standard deviation (RSD) of the amount ratios of analyte to its isotope-labeled variant in gas chromatography/mass spectrometry (GC/MS) using the stable isotope dilution method. The determination of methyltestosterone is taken as an example. The uncertainty equation proposed is justified by comparing the theoretical RSD values with the experimental RSD values obtained by replication over a wide range of analyte amount. The detection limit and quantitation limit are estimated from the continuous plot (precision profile) of the theoretical RSD against analyte amount.     

Fractal calibration in size-exclusion chromatography I. An introduction

The elution behaviour of different polymer-solvent systems in three types of organic columns for SEC has been compared and interpreted. The experimental data show that the classical universal calibration is not accomplished. Deviations from a unique curve are observed due to the binary and ternary interactions between the components of the system (solvent, polymer and gel) which results on secondary mechanisms accompanying the main pure or "ideal" SEC separation mechanism. Both, enthalpic and entropic effects are interpreted in terms of the swelling and crosslinking degrees of the gel packings, and are also related with the fractal characteristics of their surfaces, such as the fractal dimension and the available pore size. Moreover, a relationship between the fractal dimension of the pore surface and the chromatographic distribution coefficient is proposed.     

Measurement of discharge rate in a canal using radiotracer dilution technique

Measurement of discharge rates of fluids and solids is an essential requirement in industrial and environmental systems. Radiotracer techniques are widely used for measurement of fluids/solids in situations where conventional techniques cannot be applied. The present paper describes application of radiotracer dilution technique to measure the discharge rate of water in a canal with an objective to validate efficiency of the Concrete Volute Pump used for pumping water in the canal. ¹³¹I radioisotope having activity of 55.5 GBq was used as radiotracer. The discharge rate of water was measured to be 20.6 m³/s.     

Exploiting monosegmented flow analysis to perform in-line standard additions using a single stock standard solution in spectrophotometric sequential injection procedures

The robustness of sequential injection analysis (SIA) was combined with the monosegmented flow analysis (MSFA) approach, in which there is no dispersion of the reaction zone with carrier, to develop a methodology to perform in-line dilution. This approach allows one to know accurately the dilution of sample and reagent inside the monosegment, without the need for determination of dispersion coefficients. As a consequence, the methodology allowed the mechanization of procedures to perform standard additions and to construct analytical curves using a single stock standard solution, with very simple and conventional computation of the sample concentration. The method was illustrated with experiments using the bromothymol blue (BTB) dye, in which no reactions are involved, as well as with the spectrophotometric methodology for determination of Fe(II) using o-1,10-phenanthroline as chromogenic reagent. The resulting method presented a sampling frequency of 30 analyses per hour and a detection limit of 25 μg l⁻¹.     

Is the decomposition of the primary ozonide a concerted or stepwise process?

An ab initio SCF-MO calculation shows that both concerted and stepwise processes are equally probable for the cleavage of the primary ozonide, leading to the Criegee intermediate. The value of the corresponding activation energy is discussed, and the results are found in agreement with the stereochemistry of the reaction. A very facile ring opening is also predicted.     

An uncertainty evaluation for multiple measurements by GUM, III: using a correlation coefficient

After a measurement, a measured value and a measurement uncertainty are produced as a measurement result. By a repeated measurement, another measurement result is produced. Between the individual results of the two measurements, it is shown that there may be a significant correlation. A correlation coefficient can be determined when a GUM-compliant uncertainty budget for a measurement is available. Utilizing the correlations between the N individual results, an equation is derived to combine the N individual uncertainties of N measurements. Using the newly derived equation including the correlation coefficient, three measurement uncertainties of three measurement results are combined as an example. The combined uncertainty is compared with the uncertainty of a measurement which treats the three individual measurements as one process. Papers published in this section do not necessarily reflect the opinion of the editors, the editorial board, or the publisher.     

分光光度法测定金属硅中铁的线性校正与受控下的不确定度评估

用分光光度法测定金属硅中铁量,来分析讨论如何采用基本方法和控制方法技术,进行校正函数的残差齐性方差检验和有效期间的受控分析。研究结果表明,采用控制方法可以确保测量不确定度尽可能小,以达到检测的最终要求。     

Estimation of the standard uncertainty of a calibration curve: application to sulfur mass concentration determination in fuels

The construction of a calibration curve using least square linear regression is common in many analytical measurements, and it comprises an important uncertainty component of the whole analytical procedure uncertainty. In the present work, various methodologies are applied concerning the estimation of the standard uncertainty of a calibration curve used for the determination of sulfur mass concentration in fuels. The methodologies applied include the GUM uncertainty framework, the Kragten numerical method, the Monte Carlo method (MCM) as well as the approximate equation calculating the standard error of prediction. The standard uncertainty results obtained by all methodologies agree well (0.172?C0.175?ng???L^?1). Aspects of inappropriate use of the approximate equation of the standard error of prediction, which leads to overestimation or underestimation of calculated uncertainty, are discussed. Moreover, the importance of the correlation between calibration curve parameters (slope and intercept) within GUM, MCM and Kragten approaches is examined.