Statistical and probabilistic approaches to confidence intervals of linear calibration in liquid chromatography.

The aim of this paper is to compare the reliability of two approaches to estimate the 95% confidence intervals of linear calibration in real situations. One is the statistical approach, which is well known in statistics, and the other is the probabilistic approach, which is based on a theory to predict the precision of instrumental analyses mainly from signal and noise, called FUMI (Function of Mutual Information) theory. The high-performance liquid chromatographic determination of quisalofop and maltose is taken as an example. Calibration lines obtained under the same experimental conditions are superimposed on the 95% confidence intervals to investigate whether the resulting confidence intervals can include all the calibration lines reasonably. A pair of 95% confidence intervals (upper and lower limits) can be calculated from each calibration line, but varies from calibration line to calibration line, although obtained under the same experimental conditions. The variability and reliability of the 95% intervals are also examined.     

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。     

Confidence intervals for calibration with neural networks

Based on neural network calibration the confidence intervals of aromaticity determination from infrared reflectance spectra of raw brown coals were estimated by means of the bootstrap method, a simplified Monte Carlo Simulation. The standard deviations and the confidence intervals were estimated to characterise the analysis error.It is shown that confidence intervals of non-linear analysis methods like Back Propagation Neural Networks (BPNN) can be estimated by the bootstrap method. The estimated confidence intervals of the calibration confirm the analysis by BPNN.     

X-ray fluorescence determination of total sulfur in fly ash

Standard addition, double dilution and standard calibration were used for x-ray fluorescence (XRF) determinations of sulfur in fly ashes. Samples were analysed as pellets prepared by mixing with acrylate copolymer or with microcrystalline cellulose (in the case of the double dilution method). Lithium sulfate was used for the standard addition method and also as standard with known sulfur content for the double dilution method. Fly ashes analysed by optical emission spectrometry with an inductively coupled plasma (ICP-OES) were used as standards for the standard calibration XRF method. Sulfur was determined in the range of ca. 10^–1–10⁰ % S. For the fly ashes from the North-Bohemian brown coals, the differences between the XRF determinations and the ICP-OES determinations ranged from ca. 1.4 to 10% rel. and precision (repeatability) was better than 10% (RSD). The standard calibration method is suitable for routine analyses of real samples of similar nature. The methods of standard addition and double dilution are rather laborious in sample preparation compared with the standard calibration. Received: 27 October 1998 / Revised: 5 March 1999 / Accepted: 11 March 1999     

Preparation of Creatinine Standard Stock Solution

Abstract

The liquid chromatography isotope dilution mass spectrometry (LC/ID‐MS) has recently been used for the certification of organic reference materials. We are developing a new definitive method of LC‐ID/MS as to determination creatinine in serum. We prepared a stock standard solution of creatinine in 10 mmol/l of acetic acid at a concentration of 8.84 mmol/l. With this acetic acid concentration, creatinine dissolved completely in a few minutes. This stock standard solution was stable at least for 1 year and has widely applications (such as GC‐MS, LC‐MS, LC, colorimetric method, etc).     

Non-linear and non-constant variance calibration curves in analysis of volatile organic compounds for testing of water by the purge-and-trap method coupled with gas chromatography/mass spectrometry

Currently used operating conditions for analysing volatile organic compounds (VOCs) by purge-and-trap gas chromatography/mass spectrometry (GC/MS) produced non-linear calibration curves with non-uniform variance. Second-order polynomial models therefore had to be used in weighted regression analysis of measurements of replicates spiked at various concentrations. A transparent procedure based on a reported method of very low computational complexity allowed calculation of the parameters of second-order models, confidence bands of regression lines, prediction bands, and confidence intervals of discriminated analyte concentrations. Tolerance intervals were introduced for this last purpose. Critical, detection and quantification levels drawn from the calibration curves were compared with those calculated by the EPA method.     

Precision and accuracy of laser ablation-ICP-MS analysis of rare earth elements with external calibration

Solid sample introduction into an ICP-MS by laser ablation is an effective method for the total analysis of rare earth elements (REEs) in soils because no digestion is needed. A problem of the method, however, is the difference of the ablated mass for each laser shot. Therefore, internal standard for the compensation of signal instability, sample preparation, and the calibration method have to be carefully chosen.The analyzed sample was a certified standard provided by IAEA (SOIL-7). The sample was mixed with an internal standard solution and polyethylene (PE), dried, homogenized in a ball-mixer/mill, and pressed to a pellet. For the calibration 5 external standards with increasing REEs concentrations (0.4–20 g/g) as well as a blank were prepared in the same way.The analysis of the pellets was performed on a VG PlasmaQuad II + with a LaserLab unit. The laser ablation-cell was modified to improve the sample particle transportation characteristics and to allow a quicker sample-exchange. The pellets were ablated from six different spots for 60 s each with a laser-repetition rate of 4 Hz.The correlation coefficients of the calibration curves based on 5 standards, were better than 0.995. The concentrations c_A of the 15 REEs in the soil sample were determined with an average relative confidence interval 100(CI)/c_A of 6.95%, as a figure for the precision. This good precision have been obtained with a new laser ablation cell, which will be described in detail.With 2 exceptions (Ce and La) the measured concentrations were within the confidence intervals (CI) of the certified values. Therefore, with respect to accuracy and precision, the presented method offers a convenient way to analyze homogeneous and powdered soil samples for REE's without digestion. Since a good calibration for the REE determination may be obtained, the laser sampling variance (within the sample) is less significant than the analytical variance. Automation of the method is possible by construction of an autosampler based on the modified laser cell.Presented in part at the 1993 European Winter Conference on Plasma Spectrochemistry, Granada, Spain     

微波消解-ICP-OES标准加入法测定钽炉灰中的钽

以氢氟酸和硝酸为溶剂通过微波消解对钽炉灰进行溶解,经分取、稀释后制得样品溶液. 对样品溶液进行半定量分析,保证校准溶液加入合适的钽量,制得系列校准溶液. 选择 Ta 240. 063 nm 为分析谱线,采用标准加入法消除测定过程中的基体效应,在电感耦合等离子体发射光谱（ ICP-OES）上对钽炉灰中的钽含量进行测定. 结果显示,绘制的工作曲线线性相关系数均在 0. 999 以上,测定结果的相对标准偏差（ n = 7）小于 0. 50%,加标回收率在94. 6% ~ 107. 9%之间.     

Transport processes through track-etch membrane filters in a reagent delivery cell

A reagent delivery cell with a track-etch membrane filter for on-line dilution of concentrated salt solutions is described. The influence of several system parameters such as concentration of the stock solution, temperature. transmembrane pressure and the dependence on the diffusion coefficients of several salt components on the dilution was evaluated. As an application example, the use of the reagent delivery cell for on-line calibration of an atomic absorption spectrometer was studied. Fluxes through the membrane filter of 10 to 50 nL mm(-2) min(-1) with relative standard deviations of 0.8% within a day and 1.9% from day to day were achieved. The permeation experiments with the track-etch membrane filter for the dilution of aqueous solutions of several chlorides and sodium salts confirm a diffusion process. Flux rates can be estimated mathematically using Fick's first law with an agreement between measured and calculated dilution factors within 86 to 113%.     

S_2OF_(10)气体标准样品制备方法和测定方法研究

提出了一系列的安全、方便、可靠、在线和可连续操作的热解吸／色谱分析柱制备Ｓ２ＯＦ１０纯品、指数稀释法配制Ｓ２ＯＦ１０标准样品、应用定量校正系数测定样品中痕量Ｓ２ＯＦ１０的方法和技术。分别采用气相色谱、红外光谱、气相色谱／质谱等方法对色谱制备的Ｓ２ＯＦ１０纯品进行了纯度分析和测定。配制Ｓ２ＯＦ１０标准气体的体积分数范围为８．０×１０－７～２．６×１０－４。气相色谱测定Ｓ２ＯＦ１０的定量校正系数为０．１９７,测定方法的相对误差范围为１．８％～２０％。     

Assessment of quality performance parameters for straight line calibration curves related to the spread of the abscissa values around their mean

In validation of quantitative analysis methods, knowledge of the response function is essential as it describes, within the range of application, the existing relationship between the response (the measurement signal) and the concentration or quantity of the analyte in the sample. The most common response function used is obtained by simple linear regression, estimating the regression parameters slope and intercept by the least squares method as general fitting method. The assumption in this fitting is that the response variance is a constant, whatever the concentrations within the range examined.The straight calibration line may perform unacceptably due to the presence of outliers or unexpected curvature of the line. Checking the suitability of calibration lines might be performed by calculation of a well-defined quality coefficient based on a constant standard deviation.The concentration value for a test sample calculated by interpolation from the least squares line is of little value unless it is accompanied by an estimate of its random variation expressed by a confidence interval. This confidence interval results from the uncertainty in the measurement signal, combined with the confidence interval for the regression line at that measurement signal and is characterized by a standard deviation s_x0 calculated by an approximate equation. This approximate equation is only valid when the mathematical function, calculating a characteristic value g from specific regression line parameters as the slope, the standard error of the estimate and the spread of the abscissa values around their mean, is below a critical value as described in literature.It is mathematically demonstrated that with respect to this critical limit value for g, the proposed value for the quality coefficient applied as a suitability check for the linear regression line as calibration function, depends only on the number of calibration points and the spread of the abscissa values around their mean.     

间接原子吸收光谱法测定药物制剂中的西米替丁

本文提出了流动注射原子吸收光谱法间接测定西米替丁的新方法。基于西米替丁与Ag（I）反应可以生成白色的沉淀，经流动注射在线过滤稀释，以原子吸收光谱法测定反应剩余银离子的量来间接测定西米替丁的量。在优化条件下西米替丁浓度在2～80mg／L范围内与吸光度呈良好的线性关系，回收率为97．0％～104．3％。方法用于片剂西米替丁的测定，结果满意。     

Determination of ultra-trace amounts of Fe in AgNO<Subscript>3</Subscript> solutions by means of isotope dilution analysis applying an inductively coupled plasma mass spectrometer equipped with a dynamic reaction cell

The development of an ICP-MS method for the determination of ultra-trace amounts of Fe in AgNO₃ solutions using isotope dilution for calibration is described. AgNO₃ solutions are used as raw materials in the production of traditional photographic materials, and it is known that contamination with metal traces can influence the quality of the films thus produced. After adding an appropriate amount of an ⁵⁴Fe-enriched spike and permitting isotopic equilibration to take place, Ag was selectively removed from the solutions by precipitation as AgBr. Although to some extent, co-precipitation of Fe is possible under the given circumstances, an incomplete recovery of the analyte element did not affect the accuracy of the results, owing to the use of isotope dilution for calibration. NH₃ was used as a reaction gas in a quadrupole-based ICP-MS instrument, equipped with a dynamic reaction cell (DRC), providing interference-free measurement of the ⁵⁴Fe/⁵⁶Fe ratio. The limit of detection (LOD) obtained using this procedure was approximately 0.01 µg g^-1. This is an excellent value in comparison with the detection limit obtained with the more traditional approach: sample dilution and external calibration with a Fe standard solution (LOD ~1 µg g^-1). To validate the method, recovery experiments were carried out. In all instances, a quantitative recovery was established. Finally, the method was applied to the analysis of AgNO₃ solutions. A large variation in Fe concentration was observed. Depending on the Fe content in the samples, relative standard deviations typically ranged between 1 and 14%.     

Measurement of peak areas in energy-dispersive x-ray fluorescence spectrometry

An algorithm is outlined for the measurement of peak areas in spectra obtained by energy-dispersive x-ray fluorescence techniques. Each fluorescence line is assumed to be a pure Gaussian function. Initially, a calibration equation relating the full width at half maximum (FWHM) to the centre of the peak is set up. Then, in an unknown spectrum, the Gauss function parameters are found by a stepwise procedure making a non-linear minimization procedure redundant. First, the background is estimated and subtracted; then the peak centres are found, and the FWHM is given by the calibration equation, which relates FWHM to the position of the peak centre. Finally, the amplitudes are estimated from a set of linear equations. The reliability of the proposed algorithm was proved for a variety of samples. The method was compared with a non-linear x² minimization routine. Quantitative analysis of two standard reference alloys was accurate. Below 20 keV, a suitable FWHM calibration is obtained from a set of K_α lines. Above 20 keV, a set of K_β1,3 lines is recommended.     

Standard dilution analysis of beverages by microwave-induced plasma optical emission spectrometry

In this work, standard dilution analysis (SDA) is combined with microwave-induced plasma optical emission spectrometry (MIP OES) to determine seven elements in coffee, green tea, energy drink, beer, whiskey and cachaça (Brazilian hard liquor). No sample preparation other than simple dilution in HNO₃ 1% v v⁻¹ is required. Due to relatively low plasma temperatures, matrix effects may compromise accuracies in MIP OES analyzes of complex samples. The method of standard additions (SA) offers enhanced accuracies, but is time-consuming and labor intensive. SDA offers a simpler, faster approach, with improved accuracies for complex matrices. In this work, SDA's efficiency is evaluated by spike experiments, and the results are compared to the traditional methods of external calibration (EC), internal standard (IS), and standard additions (SA). SDA is comparable to the traditional calibration methods, and it provides superior accuracies for applications involving ethanol-containing beverage samples. The SDA-MIP OES procedure is effective. Using only two calibration solutions, it may be easily automated for accurate and high sample throughput routine applications.     

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.     

Decomposition of multicomponent mass spectra using Bayesian probability theory

We present a method for the decomposition of the mass spectra of mixed gases using Bayesian probability theory. The method works without any calibration measurement and therefore applies also to the analysis of spectra containing unstable species. For the example of mixtures of three different hydrocarbon gases the algorithm provides concentrations and cracking coefficients of each mixture component and also their confidence intervals. The amount of information needed to obtain reliable results and its relation to the accuracy of our analysis are discussed.     

Taking into account both preparation and injection in high-performance liquid chromatography linearity studies

As mentioned in International Conference on Harmonisation publications, linearity is a principal parameter in method validation. The most popular statistical tool used is linear least-squares regression. Contrary to what is still very often practiced, the correlation coefficient can in no way be considered as an indicator of the fit quality. There is in fact a test called the "lack-of-fit test" that enables one to answer the question, "Is the linear model adapted to the calibration curve?". However, this test can give erroneous conclusions when, at each level, several sources of variation for the response are influent. It often occurs in high-performance liquid chromatography, as shown in a following example, where the calibration curve is obtained from repeated injections of repeated dilutions of a parent solution. The lack-of-fit test rejected linearity, although it was at least questionable. In fact, the reason for a discrepancy of this kind lies in the presence of a double source of variation: injection and dilution. It is possible to overcome the problem by mixing a nested ANOVA with the standard least-square linear regression. As shown in an example, implementing this methodology for data processing allows one not only to carry out an unbiased lack-of-fit test but also give estimates of the dispersion introduced respectively by the preparation and the injection.     

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.     

Determination of phosphorus by electrothermal atomic absorption spectrometry with a phosphorus hollow-cathode lamp as light source

Graphite tubes are pre-heated with a 10% (w/v) zirconium solution, and a 1% (w/v) zirconium solution is injected prior to each phosphorus sample solution. The calibration graph is linear up to ca. 100 ng P, and the detection limit is 5 ng. Phosphorus in water-soluble organic and inorganic compounds can be determined directly by the proposed method, which is also suitable for the determination of phosphorus in NBS standard reference plant materials and in green tea leaves.