F.X. Rius

Multivariate detection limits estimators

Abstract The theoretical development of the concept of detection limit in multicomponent systems has only begun very recently and its practical applications are limited to a few specific techniques such as emission spectrometry (ICP-OES) or high performance liquid chromatography (HPLC-DAD). This paper critically reviews the theoretical approaches advanced up to the present, describes the hypotheses and theoretical backgrounds on which they are based and discusses the advantages and limitations of the different techniques and derived estimators. The connection with the derivation of the detection limits based on the var(cun) variance associated to the predicted response of an individual observation in regression theory is introduced and finally, some suggestions as to potential areas of interest for future development are envisaged.

Multivariate detection limits with fixed probabilities of error

Abstract In this paper, a new approach to calculate multivariate detection limits (MDL) for the commonly used inverse calibration model is discussed. The derived estimator follows the latest recommendations of the International Union of Pure and Applied Chemistry (IUPAC) concerning the detection capabilities of analytical methods. Consequently, the new approach: (a) is based on the theory of hypothesis testing and takes into account the probabilities of false positive and false negative decisions, and (b) takes into account all the different sources of error, both in calibration and prediction steps, which affect the final result. The MDL is affected by the presence of other analytes in the sample to be analysed; therefore, it has a different value for each sample to be tested and so the proposed approach attempts to find whether the concentration derived from a given response can be detected or not at the fixed probabilities of error. The estimator has been validated with and applied to real samples analysed by NIR spectroscopy.

Radial basis functions applied to the classification of UV–visible spectra

Abstract This paper describes how to apply a neural network based in radial basis functions (RBFs) to classify multivariate data. The classification strategy was automatically implemented in a sequential injection analytical system. RBF neural network had some advantages over counterpropagation neural networks (CPNNs) when they are used in the same application: the classification error was reduced from 20% to 13%, the input variables (UV–visible spectra) did not have to be preprocessed and the training procedure was simpler.

Uncertainty of results in routine qualitative analysis

Abstract Uncertainty is a performance characteristic that should be estimated in both quantitative and qualitative results in order to improve knowledge of their reliability. Contrary to quantitative results, uncertainty in qualitative analysis cannot be expressed as an interval around the predicted value. The uncertainty is probabilistic in nature as it might express the probability of taking a wrong decision. In this article, we review four different ways of estimating the uncertainty of a qualitative or screening system: contingency tables; Bayes’ theorem; statistical intervals; and, performance curves. We pay particular attention to their advantages and drawbacks, and their main applications.

Selection of the Best Calibration Sample Subset for Multivariate Regression

This paper discusses a methodology for selecting the minimum number of calibration samples in principal component regression (PCR) analysis. The method uses only the instrumental responses of a large set of samples to select the optimal subset, which is then submitted to chemical analysis and calibration. The subset is selected to provide a low variance of the regression coefficients. The methodology has been applied to UV-visible spectroscopy data to determine Ca(2+) in water and near-IR spectroscopy data to determine moisture in corn. In both cases, the regression models developed with a reduced number of samples provided accurate results. As far as precision is concerned, a similar root-mean-squared error of cross-validation (RMSECV) is found when comparing the new methodology with the results of the regression models that use the complete set of calibration samples and PCR. The number of analyzed samples in the calibration set can be reduced by up to 50%, which represents a considerable reduction in costs.

Multivariate standardization techniques using UV-Vis data

Abstract Three standardization techniques, namely piecewise direct standardization (PDS), single wavelength standardization (SWS) and centering correction (CC) were applied to multivariate models developed using UV-Vis spectra. The data were obtained for the determination of Ca(II) and Mg(II) in natural waters analysed by sequential injection analysis (SIA). Unlike NIR, changes in measuring conditions are mainly reflected by changes in the sensitivity in the spectra. In all the models tested, the prediction errors in the best standardization conditions were less than one half of those in the non-corrected second conditions. Moreover, bias was not detected by the joint interval test. Of all the standardization techniques assayed, PDS gives the lowest mean squared error of prediction, probably due to the inclusion of more variability in the mapping of the spectra. The influential parameters, such as the number of standardization samples or the window size in PDS, were studied. The larger the number of samples in the standardization subsets, the more effective the techniques are, whereas the variation in window size does not greatly affect the calculations.

Multivariate Statistical Process Control Applied to SulfateDetermination by Sequential Injection Analysis

A methodology was developed for determining sulfates in water at levels up to 500 mg l -1 using a sequential injection analysis system. The multivariate calibration model avoids the need for the separation of interferents and sample pre-treatment. The trueness of the multivariate calibration model was assessed by comparing the predictions of the model with reference concentrations determined by a reference method using the joint interval test for the slope and intercept of the regression line with errors on both axes. The accuracy, evaluated by the root mean square error of prediction, reached 6.9%. Multivariate statistical process control techniques were used to check the system’s stability before developing the model and the validity of the model when it is used to predict the concentrations of unknown samples.

Figures of merit in multivariate calibration. Determination of four pesticides in water by flow injection analysis and spectrophotometric detection

Abstract The accuracy, trueness and determination limit of a flow injection analysis (FIA) method are evaluated in the simultaneous determination of the pesticides Carbaryl (RYL), Carbofurane (CBF), Propoxur (PPX) and Isoprocarb (IPC) in water by multicomponent analysis. Calibration is based both on the spectra of artificially made samples according to the experimental design theory and the spectra of pure pesticides. Prediction errors in the range 0.1–1.4 evaluated as RMSEP are obtained. The absence of bias is evaluated from the joint confidence interval test for the regression line obtained from measured and predicted concentrations taking into account errors in both axes. Multivariate determination limits were found to be between 0.03 and 1.0 ppm.

Multivariate standardization techniques on ion-selective sensor arrays

Multivariate standardization techniques [slope/bias (S/B) correction, single wavelength standardization (SWS) and piecewise direct standardization (PDS)] were used to attempt to correct changes over time in multivariate calibration models for potassium and calcium. These models were constructed with ion-selective electrode (ISE) arrays. Multivariate PDS local models which included the correlation between the sensors of the array were better than the other simple techniques. We considered the relationship between the variables (sensors) and, in the PDS treatment, we have indicated their arrangement which is taken from the loadings plot. We used the Kennard–Stone algorithm to select the standardization samples from the original responses of the samples and the partial least squares (PLS) scores of each model. These scores include information about the concentrations. The models and standardizations were validated by predictions on real samples such as natural waters. The best standardization conditions provided unbiased predictions with no loss of precision.

Expert system for the voltammetric determination of trace metals: Part I. Determination of copper, zinc, cadmium, lead and indium

Abstract An expert system for the voltammetric determination of Cu, Zn, Cd, Pb and In was developed. The system guides the user in the choice of sample treatment, the most appropriate voltammetric procedure and the identification and determination of the trace metals. The techniques implemented are differential-pulse polarography and anodic stripping voltammetry, using mercury drop electrodes. Only well known methods are recommended, with particular attention to standard methods. For the identification and resolution of overlapping peaks (Cd and In), the system may call two external programs, written in turbo BASIC. Quantification is carried out by means of the multiple standard addition method, and the quality of the calibration graph is tested by several statistical validation tests. The tool kit for the development of the expert system KES (Knowledge Engineering System) is used. Only commercially available material was used. The system is easily portable if the shell for the development of the expert system is employed.