Comments to EURACHEM/CITAC guide “Measurement uncertainty arising from sampling”

The EURACHEM/CITAC Guide “Measurement uncertainty arising from sampling” deals with the design and analysis of experiments for the evaluation of the sampling and analytical standard deviation when a defined sampling and analytical method is used for the determination of the concentration, expressed as mass fraction (mg/kg), of an analyte in a specified material. The Guide recommends reporting the relative expanded uncertainty and using it directly, i.e. it implicitly assumes that the standard deviation is proportional to the mass fraction even in case the experimental data do not support this assumption. Example A1 (and some of the other examples of the Guide) demonstrates that this can result in extreme levels of underestimation or overestimation of the uncertainty of measurement results. Hence, such recommendations should be avoided!     

Estimation of limits of detection and determination in X-ray fluorescence analysis by the dependence of the relative standard deviation on analyte concentration

An experimental dependence of the relative standard deviation on analyte concentration of hyperbolic type, characterizing the precision of quantitative chemical analysis, was used to estimate the limits of detection and determination in the X-ray fluorescence analysis. A method is proposed for the determination of their values using the approximation of the experimental dependence of the relative standard deviation on the analyte concentration by a power function. The choice of the values of the relative standard deviation, being criteria for the estimation of these limits, is substantiated. A concept of the limits of detection and determination of an analytical procedure is formulated, according to which the limit of detection of an analytical procedure is an objective value depending only on the precision of determinations, and the limit of determination of an analytical procedure is a subjective value depending not only on the precision of determinations but also on the requirements to their limiting (admissible) accuracy. The limits of detection and determinations of an analytical procedure found by this approach completely characterize the possibilities of an analytical procedure in determining low concentrations of analytes. The proposed approach can be used for the estimation of the limits of detection and determination of analytical procedures and in other methods of chemical analysis with the hyperbolic dependence of the relative standard deviation on the analyte concentration.     

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.     

Determination of plutonium by isotopic dilution mass spectrometry following TTA-extraction

Isotopic dilution mass spectrometry has been applied to assess the plutonium concentration in samples such as those obtained from the dissolution of irradiated uranium fuels in a reprocessing plant. Prior to the analysis, plutonium is taken through a redox cycle and is separated from uranium and fission products by extraction into TTA-xylene. The extraction procedure, the standardization of the spike solution and the mass assay of the plutonium are described; typical results under plant conditions are given. The overall precision of a single measurement of the plutonium concentration is 0.6%, expressed as relative standard deviation, including the plant sampling error, dilution error and analytical error.     

Uncertainty in sample mass for small numbers of particles from granular materials.

The standard deviation of sample mass was quantitatively related to the number of particles in the sample, individual particle masses and the fractions of the numbers of different types of particles in the mixture. The theory was verified by sampling of cereal grain mixtures with a spinning riffler and Monte Carlo computer simulation. The theory is applicable to random sampling of well-mixed populations containing two or more types of particles.     

Considerations of particle vaporization and analyte diffusion in single-particle inductively coupled plasma-mass spectrometry

The intensity of individual gold nanoparticles with nominal diameters of 80, 100, 150, and 200 nm was measured using single-particle inductively coupled plasma-mass spectrometry (ICP-MS). Since the particles are not perfectly monodisperse, a distribution of ICP-MS intensity was obtained for each nominal diameter. The distribution of particle mass was determined from the transmission electron microscopy (TEM) image of the particles. The distribution of ICP-MS intensity and the distribution of particle mass for each nominal diameter were correlated to give a calibration curve. The calibration curves are linear, but the slope decreases as the nominal diameter increases. The reduced slope is probably due to a smaller degree of vaporization of the large particles.In addition to the degree of particle vaporization, the rate of analyte diffusion in the ICP is an important factor that determines the measured ICP-MS intensity. Simulated ICP-MS intensity versus particle size was calculated using a simple computer program that accounts for the vaporization rate of the gold nanoparticles and the diffusion rate and degree of ionization of the gold atoms. The curvature of the simulated calibration curves changes with sampling depth because the effects of particle vaporization and analyte diffusion on the ICP-MS intensity are dependent on the residence time of the particle in the ICP. Calibration curves of four hypothetical particles representing the four combinations of high and low boiling points (2000 and 4000 K) and high and low analyte diffusion rates (atomic masses of 10 and 200 Da) were calculated to further illustrate the relative effects of particle vaporization and analyte diffusion. The simulated calibration curves show that the sensitivity of single-particle ICP-MS is smaller than that of the ICP-MS measurement of continuous flow of standard solutions by a factor of 2 or more. Calibration using continuous flow of standard solution is semi-quantitative at best.An empirical equation is formulated for the estimation of the position of complete vaporization of a particle in the ICP. The equation takes into account the particle properties (diameter, density, boiling point, and molecular weight of the constituents of the particle) and the ICP operating parameters (ICP forward power and central channel gas flow rate). The proportional constant and exponents of the variables in the equation were solved using literature values of ICP operating conditions for single-particle inductively coupled plasma-mass spectrometry (ICP-MS) and inductively coupled plasma-atomic emission spectrometry (ICP-AES) measurements of 6 kinds of particles in 12 studies. The calculated position is a useful guide for the selection of sampling depth or observation height for ICP-MS and ICP-AES measurements of single particles as well as discrete particles in a flow, such as laser-ablated materials and airborne particulates.     

The use of internal standards in ICP-MS

Careful study of the matrix effect in ICP-MS showed that, in all cases studied, the magnitude of the signal suppression or enhancement depends in a regular way on the mass number. Hence, accurate correction for non-spectral interferences is only possible using an internal standard with mass number close to that of the analyte element(s). It is also shown that using an internal standard with mass number close to that of the analyte improves the precision. For both cases, the ionization energy of the internal standard seems to be of no or only secondary importance. To obtain optimal precision and accuracy, the internal standard should be selected as close in mass number as possible to that of the analyte element(s). When a number of elements over a considerable mass range are to be determined, several internal standards have to be used.     

探讨二元颗粒混合物取样误差的新的数学模型

采用新的数学模型研究二元颗粒混合物的取样误差,首次提出了取样的逻辑质量单元的理论,探讨了逻辑质量单元的物理意义,建立了按质量取样的标准偏差的计算公式.应用颗粒药品二元混合物的取样实验,证实了该公式的正确性.     

取样方差估计值的精度与样本数目之间的关系

通过数学推导建立了取样方差估计值的精度与样本数目之间的定量关系。实验也证明,取样方差估计值的标准偏差与样本数目的平方根之积可近似为一常数。应用蒙特卡罗技术模拟随机取样,对该关系式进行了验证,并探讨了取样方差估计值的分布规律,表明其规律对于组分含量服从正态分布,均匀随机分布及多项分布总体是相似的。     

Determination of selected trace elements in marine biota samples with the application of fast temperature programs and solid sampling continuous source high resolution atomic absorption spectroscopy: method validation

Analytical procedure for the determination of As, Cd, Cu, Ni, Co and Cr in marine biota samples using solid sampling high-resolution continuum source atomic absorption spectrometry (HR CS AAS) and accelerated fast temperature programmes has been developed. Calibration technique based on the use of solid certified reference materials similar to the nature of the analysed sample and statistics of regression analysis were applied. A validation approach in line with the requirements of ISO 17025 standard and Eurachem guidelines was followed. Accordingly, blanks, selectivity, calibration, linearity, working range, trueness, repeatability and reproducibility, limits of detection and quantification and expanded uncertainty for all investigated elements were assessed. The major contributors to the combined uncertainty of the analyte mass fractions were found to be the homogeneity of the samples and the microbalance precision. Traceability to the SI system of units of the obtained with the proposed analytical procedure results was also demonstrated. The potential of the proposed analytical procedure based on solid sampling HR CS AAS technique was demonstrated by direct analysis of marine reference biota samples. Overall, the use of solid sampling HR CS AAS permits obtaining significant advantages for the determination of selected trace elements in marine biota samples, such as straightforward calibration, a high sample throughput, sufficient precision, a suitable limit of detection and reduced risk of analyte loss and contamination.     

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.     

Comparison of quantification strategies for one-point standard addition calibration: The homoscedastic case

Two quantification strategies for one-point standard addition calibration have been compared mathematically. One strategy involved the extrapolation of measurement points to their intercept with the x-axis to determine the analyte content in the unknown sample, and the other strategy is based upon direct calculation of the analyte content in the unknown sample using the instrumental responses obtained during measurement. The cases of both conventional standard addition calibration (C-SAC) and sequential standard addition calibration (S-SAC) have been considered. The homoscedastic situation has been considered, where the absolute precision of the instrumental response is constant. It has been determined that the precision ratio of the two strategies is dependent on surprisingly simple parameters: such as the sample to standard mass ratio (for C-SAC) and the analyte content ratio (for S-SAC).     

Development of an electrothermal vaporization ICP–MS method and assessment of its applicability to studies of the homogeneity of reference materials

A method has been developed for measurement of the homogeneity of analyte distribution in powdered materials by use of electrothermal vaporization with inductively coupled plasma mass spectrometric (ETV–ICP–MS) detection. The method enabled the simultaneous determination of As, Cd, Cu, Fe, Mn, Pb, and Zn in milligram amounts of samples of biological origin. The optimized conditions comprised a high plasma power of 1500 W, reduced aerosol transport flow, and heating ramps below 300?°C s^–1. A temperature ramp to 550?°C ensured effective pyrolysis of approximately 70% of the organic compounds without losses of analyte. An additional hold stage at 700?°C led to separation of most of the analyte signals from the evaporation of carbonaceous matrix compounds. The effect of time resolution of signal acquisition on the precision of the ETV measurements was investigated. An increase in the number of masses monitored up to 20 is possible with not more than 1% additional relative standard deviation of results caused by limited temporal resolution of the transient signals. Recording of signals from the nebulization of aqueous standards in each sample run enabled correction for drift of the sensitivity of the ETV–ICP–MS instrument. The applicability of the developed method to homogeneity studies was assessed by use of four certified reference materials. According to the best repeatability observed in these sample runs, the maximum contribution of the method to the standard deviation is approximately 5% to 6% for all the elements investigated.     

Construction of an automated gas chromatography/mass spectrometry system for the analysis of ambient volatile organic compounds with on-line internal standard calibration

An automated sampling and enrichment apparatus coupled with a gas chromatography/mass spectrometry (GC/MS) technique was constructed for the analysis of ambient volatile organic compounds (VOCs). A sorbent trap was built within the system to perform on-line enrichment and thermal desorption of VOCs onto GC/MS. In order to improve analytical precision, calibration accuracy, and to safe-guard the long-term stability of this system, a mechanism to allow on-line internal standard (I.S.) addition to the air sample stream was configured within the sampling and enrichment apparatus. A sub-ppm (v/v) level standard gas mixture containing 1,4-fluorobenzene, chloropentafluorobenzene, 1-bromo-4-fluorobenzene was prepared from their pure forms. A minute amount of this I.S. gas was volumetrically mixed into the sample stream at the time of on-line enrichment of the air sample to compensate for measurement uncertainties. To assess the performance of this VOC GC/MS system, a gas mixture containing numerous VOCs at sub-ppb (v/v) level served as the ambient air sample. Various internal standard methods based on total ion count (TIC) and selective ion monitoring (SIM) modes were attempted to assess the improvement in analytical precision and accuracy. Precision was improved from 7-8% RSD without I.S. to 2-3% with I.S. for the 14 target VOCs. Uncertainties in the calibration curves were also improved with the adoption of I.S. by reducing the relative standard deviation of the slope (Sm%) by an average a factor of 4, and intercept (Sb%) by a factor of 2 for the 14 target VOCs.     

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     

Determination of palladium by flame atomic absorption spectrometry combined on-line with flow injection preconcentration using a micro-column packed with activated carbon fibre

The versatility of flow injection as a procedure for enhancing the performance of atomic spectrometry is demonstrated by the on-line separation and preconcentration of analyte ions of interest for methods employing atomic spectrometric measurements. In this paper, a sensitive method for the determination of palladium by flame atomic absorption spectrometry associated on-line with the flow injection technique has been developed. A flow system comprising a micro-column packed with activated carbon fibre was used for the concentration of palladium. In order to further enhance the performance of the analysis a new manifold with an additional column has been designed to increase the sensitivity by doubling the analytical signals. The method is sensitive and easily operating with a sampling rate of 15-20/h. The detection limit of this method is 0.3 ng/ml in standard solution and the precision is 3.9% relative standard deviation at 50 ng/ml. Recoveries of palladium in spiked solutions are 103-107%.     

Origin and impact of particle-to-particle variations in composition measurements with the nano-aerosol mass spectrometer

In the nano-aerosol mass spectrometer, individual particles in the 10–30 nm size range are trapped and irradiated with a high pulse energy laser beam. The laser pulse generates a plasma that disintegrates the particle into atomic ions, from which the elemental composition is determined. Particle-to-particle variations among the mass spectra are shown to arise from plasma energetics: Low ionization energy species are enhanced in some spectra while high ionization energy species are enhanced in others. These variations also limit the accuracy and precision of elemental analysis, with higher deviations generally observed when low ionization energy species are dominant in the mass spectrum. For standard datasets generated from nominally identical particles, it is shown that that the error associated with composition measurement is random and that averaging the spectra from a few tens of particles is sufficient for measuring the mole fractions of common elements to within about 10 % of the expected value. Averaging a greater number of particles offers limited improvement of the measurement precision but has the deleterious effect of degrading the measurement time-resolution, which is given by the time needed to obtain the required number of particle spectra for averaging. An internally mixed ambient particle dataset was found to give a similar result to the standard datasets, that is, the measured elemental composition converged to the average value after a few tens of particles were averaged.     

Development of an electrothermal vaporization ICP-MS method and assessment of its applicability to studies of the homogeneity of reference materials

A method has been developed for measurement of the homogeneity of analyte distribution in powdered materials by use of electrothermal vaporization with inductively coupled plasma mass spectrometric (ETV-ICP-MS) detection. The method enabled the simultaneous determination of As, Cd, Cu, Fe, Mn, Pb, and Zn in milligram amounts of samples of biological origin. The optimized conditions comprised a high plasma power of 1,500 W, reduced aerosol transport flow, and heating ramps below 300 degrees C s(-1). A temperature ramp to 550 degrees C ensured effective pyrolysis of approximately 70% of the organic compounds without losses of analyte. An additional hold stage at 700 degrees C led to separation of most of the analyte signals from the evaporation of carbonaceous matrix compounds. The effect of time resolution of signal acquisition on the precision of the ETV measurements was investigated. An increase in the number of masses monitored up to 20 is possible with not more than 1% additional relative standard deviation of results caused by limited temporal resolution of the transient signals. Recording of signals from the nebulization of aqueous standards in each sample run enabled correction for drift of the sensitivity of the ETV-ICP-MS instrument. The applicability of the developed method to homogeneity studies was assessed by use of four certified reference materials. According to the best repeatability observed in these sample runs, the maximum contribution of the method to the standard deviation is approximately 5% to 6% for all the elements investigated.     

The Horwitz ratio (HorRat): A useful index of method performance with respect to precision

The Horwitz ratio (HorRat) is a normalized performance parameter indicating the acceptability of methods of analysis with respect to among-laboratory precision (reproducibility). It is the ratio of the observed relative standard deviation among laboratories calculated from the actual performance data, RSDR (%), to the corresponding predicted relative standard deviation calculated from the Horwitz equation PRSDR (%) = 2C(-0.15), where C is the concentration found or added, expressed as a mass fraction. It is more or less independent of analyte, matrix, method, and time of publication (as a surrogate for the state of the art of analytical chemistry). It is now one of the acceptability criteria for many of the recently adopted chemical methods of analysis of AOAC INTERNATIONAL, the European Union, and other European organizations dealing with food analysis (e.g., European Committee for Standardization and Nordic Analytical Committee). The origin and applications of the formula are described. Consistent deviations from the ratio on the low side (values <0.5) may indicate unreported averaging or excellent training and experience; consistent deviations on the high side (values >2) may indicate inhomogeneity of the test samples, need for further method optimization or training, operating below the limit of determination, or an unsatisfactory method.     

Systematic error arising from ‘sequential’ standard addition calibrations. 2. Determination of analyte mass fraction in blank solutions

The use of a sequential standard addition calibration (S-SAC) can introduce systematic errors into measurements results. Whilst this error for the determination of blank-corrected solutions has previously been described, no similar treatment has been available for the quantification of analyte mass fraction in blank solutions - a crucial first step in any analytical procedure. This paper presents the theory describing the measurement of blank solutions using S-SAC, derives the correction that needs to be applied following analysis, and demonstrates the systematic error that occurs if this correction is not applied. The relative magnitudes of this bias and the precision of extrapolated measurements values are also considered.