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This chapter aims to explain the main frauds in milk and dairy products and the different multivariate analytical solutions to evaluate the quality and the authenticity of them, followed by a brief explanation of current state of the art and the future prospects of the application of machine learning methods in this field. The application of the nontargeted approach (fingerprinting methodology) as analytical solution is discussed. In addition, an overview of the applications of machine learning methods reported in the literature, such as artificial neural network, support vector machine, and random forest, to ensure the quality and authenticity of dairy products and milk is presented.

Using two statistical models, based on the two-level full factorial designs and sequential experimental Doehlert designs, a simultaneous determination of cadmium and zinc by solid-phase derivative spectrophotometry has been proposed. These chemometric techniques have been used for the optimization of the instrumental and experimental variables of the system. The complexes formed between cadmium and zinc with 4-(2-pyridylazo) resorcinol, in the presence of potassium iodide, were fixed on a dextran-type anion-exchange gel, at pH 8.7. The absorbance spectra of the gel, packed in a 1-mm cell, were recorded directly. The performance characteristics of the proposed method have been established. The method was applied to the simultaneous determination of both analytes in synthetic mixtures and natural water samples.

A general procedure based on variation of experimental design for checking robustness in the validation of analytical methods is presented. This procedure, which is easy to apply, consists in estimating the main total effects, in detecting outliers, checking the curvature and in determining the main side effects. Two methodologies based on the analysis of a) the residuals from the reduced model and b) the replicates from the reconstructed design were employed for the detection of outliers. In further studies, general experimental design principles were applied using two- and three-level factorial designs. In some cases, a dummy variable was introduced in order not to modify the structure of the designs utilized.

Using Response Surface Methodology (RSM) and based on sequential experimental Doehlert designs, a Solid-Phase Spectrophotometric determination of cadmium, at μg/l level, with 4-(2-pyridylazo)resorcinol in the presence of potassium iodide, has been established. The method has been characterized and validated by obtaining the performance characteristics. The IUPAC detection limit is 1.5 μg/l and reproducibility (RSD) in the determination of 76.0 μg/l is 3.4%. Robustness was established using two-level saturated fractional factorial designs. Selectivity was studied and trueness was confirmed with house reference materials.

The optimization of experimental variables may be correctly performed by the use of an appropriate experimental design from which the optimum values of such variables are simultaneously obtained. Three level designs allow us to fit experimental data to 2nd grade polynomial functions, and a suitable study of such functions makes it possible to find the optimum region from relatively few iterations. The Doehlert designs possess a suitable structure for this purpose, and thus from a single design one can locate the optimum region with reasonable accuracy, and if greater exactitude is required, it is only necessary to employ a second design in the previously located region. Another consideration is that these designs comprehend a great capacity for displacement across the variables' experimental domain, which means that a substantial quantity of data from one design can be used for the following experiment. With the application of the Doehlert designs in solid phase spectrophotometry, the optimization of variables can be performed simply, quickly and with greater efficiency compared to traditional methodology.

A simple and specific method was developed for the determination of sulfite in rainwater based on solid-phase spectrophotometry (SPS). Rainwater was collected on morpholine, sulfite was stabilized by forming an adduct that reacted with pararosanil-ine and formaldehyde, and the reaction product was fixed on Dowex 1-X8 resin. The absorbance of the solid phase was measured directly at 565 and 700 nm. The calibration curve was linear in the concentration range of 1-50 μg/L in solution (relative standard deviation = 1.7%); the International Union of Pure and Applied Chemistry detection limit was 0.8 μg/L. In simulated rainwater, the values of the calibration curve slopes were similar to that of the standard calibration curve slope, and recoveries for 40-497 μg/L sulfite ranged from 97 to 105%. Linearity, analytical sensitivity, and precision were better for the SPS method than the solution method, and the detection and quantitation limit values were lower for the SPS method than the solution method based on the similar reaction. The SPS method was subsequently used to determine sulfite in real rainwater.

In this paper the use of Doehlert's designs for the optimization of analytical methods is proposed. The use of Doehlert's designs makes it possible to create sequential designs, and enables the use of blocks and the detection of lack of fit in the calculated model. Similarly, it permits the estimation of the terms of the quadratic models with a small number of experiments.The application of the Lagrange criterion to the estimated response function leads to specific conclusion: either the existence of a maximum that permits the calculation of the optimum values of the variables, or the necessity to make a new design covering the zone previously indicated by the intersection of the straight lines traced in the direction of the maximum variation of the analytical signal.

The proposal of a new analytical method implies two important steps: the optimization of the experimental variables and the validation of the proposed method. The first one involves the selection of the values of the factors which have an influence on the analytical signal and produce the best results in the analytical process. To develop the optimization of analytical methods, two different strategies can be used. In the traditional “oneat-a-time” operation, all the values of the different factors except one are constant, and this one is the object of the survey. The alternative to this strategy is the Experimental Design; in this case the whole set of the factors comprising the system is simultaneously modified, making it possible to identify the factors which modify the analytical response. The latter strategy allows us to understand circumstances which are not explained by the traditional mode, such as those in which the analytical response is a multimodal function of the independent variables or when the effects of the variables are not additive and there is interaction