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.     

The determination of chromium, copper and nickel in groundwater using axial plasma inductively coupled plasma atomic emission spectrometry and proportional correction matrix effect reduction

The performance of a proportional correction matrix effect reduction procedure was investigated for an axially viewed inductively coupled plasma. It was shown that the proportional correction factor (ratio of analyte matrix effect and internal standard matrix effect) was sufficiently stable over the investigated matrix element concentration ranges (0–2000 mg/L of Na and 0–400 mg/L of Ca) for the procedure to be successful. Proportional correction results in the best correction for matrix effects compared to the classical 1 : 1 intensity ratio correction procedure or the approach without any correction, as was shown in recovery experiments using analyte spiked groundwater samples. Matrix effects as high as 18% without correction were reduced to less than 4% applying proportional correction. Received: 22 February 1997 / Revised: 28 May 1997 / Accepted: 7 June 1997     

The basis set convergence of the Hartree–Fock energy for H3 +, Li2 and N2

 By using completely optimized basis functions it is shown that the convergence of the Hartree–Fock energy for the H₃ ⁺, Li₂ and N₂ molecules is significantly better described by exponential behavior than by inverse power dependence. This is the case both with respect to the number of basis functions of a given type and with respect to the highest angular momentum function included. The Hartree–Fock limit for H₃ ⁺ is estimated to be −1.300372125 hartree. Received: 14 February 2000 / Accepted: 12 April 2000 / Published online: 18 August 2000     

Uncertainties in Determination of pH

 A statistical analysis of multi-point calibration procedure for practical measurement of pH under laboratory conditions is given. The procedure is shown to provide the necessary elements for simple assignment of an uncertainty to a pH measurement – an essential element of quality control. Performance of ordinary least squares regression for prediction of confidence limits is compared to orthogonal regression, inverse regression and Monte Carlo simulations. In case of pH measurement by multi-point calibration procedure, methods considering uncertainties in both axes are found to be statistically more satisfactory than ordinary least squares regression. By analysis of 50 pH calibration data, randomly selected from 250 5-point glass electrode calibrations, it is found that the practical differences, however, are of minor importance. The significance of uncertainty in pH is demonstrated for an example from metal ion speciation in aqueous solution. Received September 20, 1999. Revision April 19, 2000.     

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.     

Determination of low concentrations by spectrophotometry: Uranium-thiocyanate system

Errors in the determination of low concentrations by spectrophotometry are investigated with the uranium-thiocyanate system as an example. The reagent blank has significant absorption and measurements are made at 375 nm instead of the λ_max. The error in the intercept of the calibration curve is an important factor in such measurements and the errors involved in the estimation of 1 μg/ml (normal working range 4–40μg/ml) are studied. It is shown that both random and systematic errors associated with the intercept are responsible for observed errors. The two types of errors are resolved by ANOVA (analysis of variance). The error in the measurement of a single value is estimated and compared with measured values for different calibration ranges. It is seen that two factors predominantly influence the error in the measured concentration — the variance from regression and the closeness of the measured value to the mean of the calibration range.     

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     

Analysis of long-term distributions of calibration parameters and calibration intervals for an atomic absorption spectrophotometer

 A combination of "black box" and "calendar-time" methods for the determination of calibration intervals of an analytical measuring instrument is discussed. Since the methods require information on the distributions of the calibration parameters, such information is described for an atomic absorption spectrophotometer, as an example. The hypotheses on the normal distribution of the calibration parameters are tested using the ω²-criterion and accepted at 0.90–0.95 levels of confidence. Corresponding control charts are designed for indication of warning and action limits of the calibration parameters, and diagnoses of outliers in further calibrations. Control charts indicate also when the calibration should be done according to the full program of the equipment manufacturer. Received: 15 April 2000 / Accepted: 24 July 2000     

Analytical Hartree–Fock wave functions for the atoms Cs to Lr

 Analytical approximations to Hartree–Fock wave functions are constructed using Slater-type functions for the ground states of all 49 neutral atoms from Cs (Z=55) to Lr (Z=103). The current compilation is more extensive and more accurate than previous ones. The wave functions are available upon request from the authors or from the Web page http://www.unb.ca/chem/ajit/download.htm on the Internet. Received: 6 December 1999 / Accepted: 29 February 2000 / Published online: 12 May 2000     

Kinetic determination of carminic acid by its inhibition of lanthanide-sensitized luminescence

 The stopped-flow mixing technique was used to develop a simple and fast kinetic method for the determination of carminic acid based on its inhibitory effect on the fluorescence intensity of the europium(III)- diphacinone-ammonia system in the presence of Triton X-100. Analytical data can be obtained within 10 s after the reactants are mixed, which minimizes manipulation and enables the ready application of the proposed method to routine analyses for carminic acid in orange soft drinks. The dynamic range of the calibration graph was 0.5–15 μg ml^-1 and the relative standard deviation less than 4%. The analytical recoveries obtained by applying the method directly to the analysis of samples ranged from 90.0 to 111.8%. Received : 11 November 1995/Revised: 2 February 1996/Accepted: 6 February 1996     

Metrological estimation of sampling and sample preparation procedures as applied to analytical testing of technogenic origin raw material containing recoverable precious metal

 Different schemes of analytical testing including the sampling, sample preparation and sample analysis operations are considered as applied to a lot of raw material containing recoverable precious metal. The errors resulting from the step-by-step operations of the analytical testing are estimated. Sampling and sample preparation operations are found to be significant contributors to the total error of determination of the percentage and /or weight of a precious metal of interest in a lot. Some ways to diminish both the sampling error and the total error of the analytical testing procedure are recommended. Received: 28 December 1998 · Accepted: 22 February 1999     

Coil-to-globule-type transition of poly(N-isopropylacrylamide) adsorbed on colloidal silica particles

 The temperature dependence of the dimensions of poly(N-isopropylacrylamide) (PNIPAM) adsorbed on two different colloidal silica particles was studied with dynamic light scattering. The hydrodynamic diameter was measured when the temperature was varied stepwise from 10 to 60 °C. PNIPAM molecules free in solution undergo a conformational transition at the θ temperature. We have found that PNIPAM adsorbed onto silica particles also undergoes a transition below the θ temperature. When a small amount of polymer was adsorbed the coil-to-globule transition at the θ temperature did not occur. Potentiometric titrations showed that the surface charge of the silica particles was not affected by the polymer adsorption. Sodium dodecyl sulfate (SDS) (100–1200 mg/l) was added to improve the stability. The particles with a higher zeta potential required a smaller addition of SDS to prevent coagulation compared to the particles with a smaller surface potential. For low additions of SDS the transition curves of adsorbed PNIPAM were unaffected. For larger additions of SDS the collapse of PNIPAM was shifted to higher temperatures. When as much as 1200 mg/l SDS was added, two regions with weak transitions were observed before the collapse. It was also observed that the presence of SDS results in a smaller adsorption of PNIPAM onto the particles. The addition of SDS strongly increased the magnitude of the electrophoretic mobility of the polymer–particle unit. From the electrophoretic measurements an electrokinetic layer thickness was calculated and it was found to be smaller than the corresponding hydrodynamic layer thickness, as obtained by dynamic light scattering. Received: 14 December 1999/In revised form: 22 February 2000/Accepted: 6 March 2000     

Prediction of the Raman spectrum of the aqueous formate anion by a combined density functional theory and self-consistent-reaction-field study

Formate, HCOO⁻, is a small ion that can be used as a convenient model to represent general carboxylic acids as well as the terminal side chains of glutamic and aspartic amino acids in biological systems. Several ab initio techniques (Hartree–Fock and density functional theory methods) were used to study the formate anion in aqueous solution, where the solvent was treated as an electrostatic influence by means of a self-consistent-reaction-field (SCRF) method. The comparison of calculated frequencies with Raman experimental data constitutes a good test for the solvation model employed in this work. The results showed that the application of a SCRF method not only produced smaller errors but also improved the linear correlation between predicted and experimental values. This latter characteristic enables a more efficient application of a linear scaling factor, λ, which corrects the calculated frequencies. In fact, the application of λ to the values calculated for the continuum, when compared to those obtained for a vacuum, resulted in smaller root-mean-square errors of the deviations from the experimental data. Received: 15 May 2000 / Accepted: 19 June 2000 / Published online: 11 September 2000     

Spectrophotometric simultaneous determination of ceratine, creatinine, and uric acid in real samples by orthogonal signal correction–partial least squares regression

Abstract  This work describes a quantitative spectroscopic method for the analysis of ternary mixtures of ceratine (CER), creatinine (CRE), and uric acid (UA) using multivariate data models based upon ultraviolet spectroscopy. By multivariate calibration methods, such as partial least squares regression, it is possible to obtain a model adjusted to the concentration values of the mixtures used in the calibration range. In this study, the calibration model is based on absorption spectra in the 200–260 nm range for 36 different mixtures of CER, CRE, and UA. The unrelated information was removed by the orthogonal signal correction (OSC) method and the results were proved. Evaluation of the prediction errors for the prediction set reveals the OSC-treated data give substantially lower root mean square error of prediction (RMSEP) values than original data. The RMSEP for CER, CRE, and UA with OSC were 1.1686, 0.2195, and 0.3726, and without OSC were 1.9057, 0.3482, and 0.6164, respectively. This procedure allows the simultaneous determination of CER, CRE, and UA in synthetic and real samples. Graphical abstract        

The analysis of process gases: a review

 A general review of key issues involved in the analysis of process gases is presented. The reasons for such measurements – which include safety, quality, environmental and economic factors are considered. The technical issues arising from these measurements are dependent upon a variety of factors, including the overall sampling system, the type of analytical instrumentation, methods of data collection and the specified calibration protocols. The use of gas calibration cylinders as transfer standards is detailed and issues of stability and traceability to reference material discussed. Received: 1 March 2000 / Accepted: 31 March 2000     

Optimum conditions for pulse generation in diaphragm-free Karl Fischer coulometry

A flexible instrument was designed in order to investigate the influence of current magnitude, current duration and the frequency of the pulse generation on the error obtained in coulometric Karl Fischer titrations carried out in diaphragm-free cells. For a given current magnitude the lowest errors were obtained for current durations more than 60% of the total time for the pulse cycle. No significant influence of the pulse frequency (5–1000 Hz) was found independently of the pulse current duration for three different types of reagents intended for diaphragm-free coulometry. For all reagents, the errors obtained with the home-built instrument were significantly smaller than those obtained with an optimized commercial titrator based on pulsed current generation. Using optimum conditions for the former instrument, in combination with an imidazole-buffered reagent at pH 10 containing chloroform as modifier, the accuracy was close to 100%. Thus, it is now possible to achieve the same high accuracy with diaphragm-free coulometry as with the conventional diaphragm based technique. The precision of the water determinations was affected by the size of the background. Received: 16 March 2000 / Revised: 17 May 2000 / Accepted: 22 May 2000     

Optimum conditions for pulse generation in diaphragm-free Karl Fischer coulometry

A flexible instrument was designed in order to investigate the influence of current magnitude, current duration and the frequency of the pulse generation on the error obtained in coulometric Karl Fischer titrations carried out in diaphragm-free cells. For a given current magnitude the lowest errors were obtained for current durations more than 60% of the total time for the pulse cycle. No significant influence of the pulse frequency (5–1000 Hz) was found independently of the pulse current duration for three different types of reagents intended for diaphragm-free coulometry. For all reagents, the errors obtained with the home-built instrument were significantly smaller than those obtained with an optimized commercial titrator based on pulsed current generation. Using optimum conditions for the former instrument, in combination with an imidazole-buffered reagent at pH 10 containing chloroform as modifier, the accuracy was close to 100%. Thus, it is now possible to achieve the same high accuracy with diaphragm-free coulometry as with the conventional diaphragm based technique. The precision of the water determinations was affected by the size of the background. Received: 16 March 2000 / Revised: 17 May 2000 / Accepted: 22 May 2000     

Continuous dynamic-gravimetric preparation of calibration gas mixtures for air pollution measurements

 The preparation of calibration gas mixtures for air pollution measurements by the dynamic-gravimetric method was investigated using sulphur dioxide in nitrogen as a model. The target mole fraction was 200×10^–9 mol/mol, with the option of also getting smaller mole fractions. Thermal mass flow meters calibrated with reference mass flows were used to measure the dilution gas flow (nitrogen). The relative standard uncertainty of the dilution gas flows between 10 mg/s (approx. 500 ml/min) and 40 mg/s (approx. 2000 ml/min) was 0.15%. The mass flow of the target component measured as the permeation rate was determined via the quasi-continuous observation of the loss in the permeation tube mass during the measuring time. A magnetic coupling system and an adapted microbalance were used for this purpose. The results presented show permeation rates measured over the lifetime of a tubular permeation source. The measurement cycles took between 3 days and 7 h at least. The relative standard uncertainty of the mixture composition did not exceed 2%. First comparisons with gas mixtures prepared by the static-gravimetric method show compatibility. The applicability of the system is not restricted to the SO₂/N₂ mixture. It can also be used for preparing other gas mixtures in this field of application. Received: 26 April 2000 / Accepted: 12 September 2000     

A flow analysis system with an amperometric detector for the determination of hydrogen sulphide in waters

 A flow analysis system with an amperometric H₂S detector and a gas extraction unit as well as an integrated coulometric calibration unit is described, which allows an on-line determination of hydrogen sulphide in aquatic samples. By variation of different parameters (e.g. flow rate, gas injection volume, pH of solution) a wide dynamic working range of concentrations from 1 μmol/l H₂S to 750 μmol/l is accessible. The sampling rate is about 36 samples h⁻¹ using an average flow rate of 1.78 ml/min and a gas injection volume of 28 μl. The measuring system is designed as a portable device. In combination with the polyethylene-tube of a PTFE-underwater pump field-measurements on board are possible. Received: 16 February 1995/Revised: 5 April 1995/Accepted: 11 April 1995 Acknowledgements. This work was supported by the Bundesminister für Forschung und Technologie under the project “DYSMON II” (03F0123D) and by the Fonds der Chemischen Industrie zur F?rderung von Chemie und Biologischer Chemie. Correspondence to: P. Jeroschewski