Development and Analytical Validation of RobustNear-Infrared Multivariate Calibration Modelsfor the Quality Inspection Control of Mozzarella Cheese

Bruno G. Botelho & Bruna A. P. Mendes & Marcelo M. Sena

Received: 3 July 2012 /Accepted: 24 August 2012 /Published online: 5 September 2012# Springer Science+Business Media, LLC 2012

Abstract This paper proposed and validated robust diffusereflectance near-infrared methods for the direct determina-tion of fat and moisture in cow mozzarella cheeses usingpartial least squares regression. They were developed underthe realistic conditions of routine analysis in a state labora-tory of quality inspection control and were used for analyz-ing a great variety of mozzarella samples manufactured bydifferent manufacturing procedures and originating from thewhole state of Minas Gerais, Brazil (more than 100 differentproducers). A robust methodology was implemented, in-cluding the detection of outliers and the harmonization ofthe multivariate concepts with the traditional univariateguidelines. The models were constructed in the ranges from38.7 to 58.0 % w/w on dry basis for fat and from 41.5 to55.1 % w/w for moisture, providing root mean square errorsof prediction of 2.1 and 0.9 %, respectively. Both methodswere validated through the estimation of figures of merit,such as linearity, trueness, precision, analytical sensitivity,ruggedness, bias, and residual prediction deviation. Oncethe methods were adopted, their performances were moni-tored for approximately 1 year through control charts andwere considered satisfactorily stable with prediction errorswithin the established limits. Beyond these specific

methods, it was also pursued to present a complete method-ology for multivariate analytical validation, an importantaspect for the implementation of near-infrared spectroscopymethods in the routine of food quality inspection.

Keywords Quality control . NIR . PLS .Multivariateanalytical validation . Dairy analysis

Abbreviations and SymbolsBF Brown–Forsythe testCLS Classical least squaresDW Durbin–Watson testFOM Figures of meritIMA Instituto Mineiro de AgropecuáriaLV Latent variablesMLR Multiple linear regressionNAS Net analyte signalNIRS Near-infrared spectroscopyPCR Principal components regressionPLS Partial least squaresRJ Ryan–Joiner testRMSEC Root mean square error of calibrationRMSECV Root mean square error of cross-validationRMSEP Root mean square error of predictionRPD Relative prediction deviationRSD Relative standard deviationSD Standard deviationSDsd Standard deviation of the successive

differencesSDV Standard deviation of validation errorsSEL SelectivitySEN Sensitivityγ Analytical sensitivityε Instrumental noise

B. G. Botelho :M. M. Sena (*)Departamento de Química, ICEx, Universidade Federal de MinasGerais,31270-901, Belo Horizonte, MG, Brazile-mail: marcsen@ufmg.br

B. A. P. MendesInstituto Mineiro de Agropecuária (IMA),BR 040, Km 527,32145-900, Contagem, MG, Brazil

M. M. SenaInstituto Nacional de Ciência e Tecnologia em Bioanalítica (INCTBio),13083-970, Campinas, SP, Brazil

Food Anal. Methods (2013) 6:881–891DOI 10.1007/s12161-012-9498-z

Introduction

Mozzarella is a cheese made from pasteurized and partlyskimmed cow milk, widely found around the world, andoriginated from Campania region in Southern Italy. Alsocalled pizza cheese, it is the most consumed cheese in theUSA, Brazil, and other countries, mainly due to its use inpizzas, sandwiches, and snacks (Harbutt 2009). The State ofMinas Gerais, the second most populous in Brazil, withabout 20,000,000 inhabitants and an area of 586,528 km2,is the largest national cheese producer, with about half of theproduction (215,000 tons/year). From this total, 24 % cor-responds to mozzarella cheese (Teixeira et al. 2007). Themozzarella production in Brazil is regulated by the guide-lines of the Ministry of Agriculture, Livestock and FoodSupply (MAPA for its initials in Portuguese), which estab-lishes limits for fat, a minimum of 35 % w/w on dry weightbasis, and moisture, a maximum of 60 % w/w (MAPA1997). For this quality inspection, nitrate content and phos-phatase assay are also required, unlike other parameters,such as protein and pH. According to this regulation, thefat determination is carried out by acid hydrolysis (Gerber’smethod). This method is based on the use of a butyrometer,which presents several disadvantages. The determinationcannot be automated and involves a certain risk in handlinghighly concentrated sulfuric acid. In addition, handling thebutyrometer requires practical skills, which has a negativeeffect on the robustness and precision of the method(Badertscher et al. 2007). The moisture determination iscarried out by the oven-drying gravimetric method, a simplebut slow method, since each analysis spends from 3 to 6 h(Bradley and Vanderwarn 2001). In general, the traditionalanalytical methods of major food components, such as fatand moisture, are slow, relatively expensive, and demandhighly qualified staff. These classical methods are not effec-tive enough to cover the growing demand and low costsrequired in the quality control of industries or quality in-spection of public agencies (Rodriguez-Otero et al. 1997).

A promising alternative to overcome the drawbacks ofthe classical methods of food analysis is the joint use ofnear-infrared spectroscopy (NIRS) and multivariate calibra-tion. This combination provides methods that are rapid,nondestructive, environmentally friendly, and solvent-free,with no or low residue generation. Besides, these methodsrequire the use of minimum of sample pretreatment andhave sufficient accuracy and sensitivity with less humanintervention. The first paper that suggested the NIRS meth-od for quantification in dairy products was published by BenGera and Norris (1968), who have studied the influence offat content in milk using multiple linear regression (MLR).But, in general, the widespread use of the NIRS method hasonly emerged in the late 1980s, when the more accurate androbust multivariate calibration models partial least squares

(PLS) and principal component regression (PCR) replacedMLR in most of practical applications. Pierce and Wehling(1994) have published the first method using NIRS and PLSto determine components of cheddar cheese. Since then,several articles have been published using NIRS and multi-variate calibration for predicting quality parameters, such asfat, protein, moisture, and others, of different types ofcheese (fresh, Danbo, Emmental, and cheddar) and deriva-tives (Wittrup and Norgaard 1998; Blazquez et al. 2004;Karoui et al. 2006; Lucas et al. 2008; Pi et al. 2009; NtsameAffane et al. 2011). Specifically, no paper has been pub-lished using NIRS and multivariate calibration for determ-ing parameters of mozzarella cheese.

Some calibration models based on NIRS are not reliableand stable enough when used practically for routine analy-sis. It is necessary to improve and assure the reliability ofthese models (Huang et al. 2008). Most of the papers citedin the last paragraph have not incorporated sufficient vari-ance in their models for a wider and robust use in qualitycontrol inspection, analyzing cheese samples obtained froma small number of producers. None of these models havebeen applied in real routine analysis or have their reliabilityassessed in this context. Moreover, none of these papershave performed an analytical validation. A problem relatedto this validation is the traditional guidelines in food analy-sis that have been conceived in a univariate way and need tobe harmonized in order to encompass the specific aspects ofNIRS technology related to multivariate methods. This isthe case of the Brazilian regulations (MAPA 2009) and mostof the international guidelines at which it is based on (ICH1995, 1997; FAO 1998; Thompson et al. 2002; EC 2002).None of these guidelines have at least mentioned the word“multivariate.” Examples of conceptions that need to changemay be cited. The requirement of total selectivity of theanalytic signal does not make sense for multivariate meth-ods, since they are precisely useful when a selective wave-length does not exist. It is also not possible to obtain thetraditional calibration curves (signal as a function of con-centration) in multivariate calibration. In the past few years,the advances in multivariate theory have also brought theconcept of net analyte signal (NAS), which allows extract-ing the specific information of the analyte from the wholesignal and can be used for estimating some figures of merit(FOM). Discussions about how to harmonize univariateguidelines with multivariate methods have been the subjectof recent papers, in general (Olivieri et al. 2006; Valderramaet al. 2009) or in specific areas, such as in the analysis ofpharmaceuticals (Silva et al. 2012; Ferreira et al. 2012) andagricultural products (Valderrama et al. 2007).

The aim of this paper was to develop two simpler, robust,and rapid methods for directly determining fat and moisturein cow mozzarella cheeses, which originated from differentorigins and manufactured by different manufacturing

882 Food Anal. Methods (2013) 6:881–891

procedures (more than 100 producers), by using NIRS andPLS. These methods should be used for the quality inspec-tion control of these cheeses in Instituto Mineiro deAgropecuária (IMA), the official laboratory of the State ofMinas Gerais, in the city of Contagem, Brazil. Models fornitrate and phosphatase were not possible to build becausealmost no sample present results above the limits of quan-titation of the respective reference methods. This work alsosearched for performing the analyses under the realisticenvironment of the quality inspection control, carrying outa full analytical validation, and assessing permanently theperformance of the methods through a post-model stabilitymonitoring.

Materials and Methods

Instruments and Software

The spectra were recorded on a Perkin Elmer Spectrum 400FTIR spectrophotometer (Waltham, MA, USA), equippedwith a diffuse reflectance accessory. Data were handled usingthe MATLAB software, version 7.13 (The MathWorks,Natick, MA, USA). The PLS routine came from the PLSToolbox, version 6.5 (Eigenvector Technologies, Manson,WA, USA), and a homemade routine was also employed forthe detection of outliers.

Reagents and Samples

All the reagents and materials, sulfuric acid, isoamyl alco-hol, and purified sand, were of analytical grade, purchasedfrom certified suppliers, and used without further purifica-tion. One hundred twenty-three mozzarella cheese samplesmanufactured by different manufacturing procedures andoriginating from more than 100 different producers fromall over the state of Minas Gerais, Brazil were collectedand analyzed in 2009 and 2010. The cheese samples weretransported to the laboratory under refrigeration at 4 °C, leftfor 30 minutes until thermal equilibrium, and analyzedimmediately after opening the sample. The slices wereobtained from the internal part of the cheese samples, avoid-ing their external surface, which can be subjected todegradation.

Procedures

The cheese samples were sliced, milled with an industrialmixer, and transferred to a Perkin Elmer® plate in a suffi-cient amount to cover the bottom of the plate (about 40 g).Then, the reflectance module was pressed against the sam-ple surface. The spectra were collected as an average of 32scans, from 1,000 to 2,500 nm with 2 nm steps, with a

resolution of 8 cm−1. Ten replicate spectra of the emptyplate were also recorded in the same conditions in order toestimate the instrumental noise. During all these measure-ments, the temperature of the room was controlled at 22±1 °C. The analyses by the reference methods were performedaccording to the standard literature (Pomeranz and Meloan1994) without replicates. Fat determination was carried outwith Gerber’s method. One gram of a cheese sample wasaccurately weighed in the butyrometer, in which 10 ml of asulfuric acid solution (d01.605 gcm−3) and 1 ml of isoamylalcohol were added; then, the filler opening was sealed andthe butyrometer was shaken and tempered for 15 min in a65 °C water bath; the shaking and heating were repeateduntil total dissolution of the sample; finally, the fat columnwas adjusted to the zero point and the absolute fat contentwas read off from the lower end of the meniscus. Moisturedetermination was carried out by the oven-drying gravimet-ric method. Three grams of a cheese sample was placedin a plate and spread with the same amount of predriedfine sand. The sand aids in more rapid and efficientdrying of the sample. This mixture was homogenizedand oven-dried at 105 °C until it reached a constant weight,taking 3–6 h.

Multivariate Analytical Validation

Detection of Outliers

Outliers are samples that are very different from the rest ofthe data set and their detection is crucial when developingmultivariate NIRS models. This detection can be performedin several ways, and this paper adopted a robust methodol-ogy for detecting samples with extreme leverages, largeresiduals in the X block (spectral data) or large residuals inthe Y block (property values) (ASTM 2012; Valderrama etal. 2007). If a sample presents a leverage, it means, ameasure of the influence of each sample on the PLS model,larger than a limit value, it is considered an outlier. Outlierswith large residuals in X are detected by comparison of thetotal standard deviation, s(e), of the unmodeled spectral datawith the respective standard deviation of each sample, s(ei).If a sample presents s(ei)>2.5s(e), it is deleted at the 99 %confidence level. Outliers with large residuals in Y can bedetected by comparing the root mean square error of cali-bration (RMSEC) with the prediction errors. If a sample hasan error of prediction larger than three times the RMSECvalue, it is deleted. A full description of this methodologyincluding the equations used can be found elsewhere(Valderrama et al. 2007; Silva et al. 2012). Outliers in thevalidation set were also detected by the jackknife (externallystudentized) residuals test, according to the appropriate ref-erence (Souza and Junqueira 2005).

Food Anal. Methods (2013) 6:881–891 883

Net Analyte Signal

The NAS can be defined as the part of the analytic signalthat is uniquely related to the analyte/property of interestand orthogonal to the space spanned by the interferences

(Lorber et al. 1997). The NAS vector, x̂NASA;i , can be defined

for each sample i by the following equation:

bxNASA;i ¼ I� bXT

A;�kbXT

A;�k

� �þ� �bxA;i ¼ PNAS;kbxA;i ð1Þ

where I is the identity matrix, bXA;�k is the matrix containingexclusively the information from the interferences (except theanalyte k), the superscripted plus sign indicates the Moore–Penrose pseudoinverse matrix, and PNAS,k is a matrix whichprojects a given vector onto the NAS space. In some situa-

tions, it is not possible to estimate X̂A;�k , since the spacespanned by the interferences cannot be modeled (e.g., it isnot practical to obtain a cheese without fat). In these cases, analternative estimation of NAS is more useful, from the regres-sion vector of a PLS model with A latent variables (LV), b:

bxNASA;i ¼ b bTb� ��1

bTxi ð2Þ

The norm of each vector provides a scalar NÂSi for eachsample, which is intuitively analogous to a selective univar-iate analyte signal. The NAS can be employed in multivar-iate calibration for estimating some FOM, such as selectivityand limits of detection and quantitation.

Figures of Merit

The analytical validation was performed in order to harmo-nize univariate and multivariate concepts, searching foradapting the requirements of the Brazilian (MAPA 2009)and international guidelines (ICH 1995, 1997; FAO 1998;Thompson et al. 2002; EC 2002) to the state of the art ofhow to estimate FOM in multivariate calibration (Olivieri etal. 2006; Valderrama et al. 2009). Thus, the following FOMwere estimated: trueness, precision, linearity, workingrange, selectivity, sensitivity, analytical sensitivity, rugged-ness, bias, and residual prediction deviation (RPD). Thelimits of detection and quantitation could be calculatedbased on NAS, but they were not estimated in this workbecause they are not needed in calibration methods formajor food components at high concentrations, such as fatand moisture in cheese.

Trueness and precision can be estimated in a similar wayfor both univariate and multivariate methods. Trueness wasevaluated through the relative errors of prediction for eachsample. Nevertheless, the trueness of multivariate methodsis rather established through more specific parameters notmentioned in the traditional guidelines of food analysis,

such as RMSEC and root mean square error of prediction(RMSEP). RMSEP is more robust than RMSEC, since it isestimated from external validation samples. Precision wasassessed at two levels, repeatability and intermediary precision.Repeatability was obtained by the same analyst determining inthe same day three samples at different content levels, in sixreplicates for each one. Intermediary precision was estimatedby three different analysts determining the same three samplessix times, in different days. Since there is no calibration curvesfor multivariate models, the linearity used to be estimatedthrough the correlation coefficient (r) of a plot of referenceversus predicted values. But an r value close to 1 cannot besolely considered appropriate to assure the linearity of themethod (Thompson et al. 2002). It is essential to verify previ-ously the random behavior of the residuals of this fit. This isoften performed by visual inspection of a plot of the residuals,which may sometimes be considered quite subjective. In orderto adopt more objective criteria to assess linearity, this workadapted the methodology used by Souza and Junqueira (2005)for the univariate ordinary least squares method. Thus, therandom behavior was verified by applying the tests of Ryan–Joiner (RJ), Brown–Forsythe (BF), and Durbin–Watson (DW)to the model residuals, in order to evaluate their normality,homoscedasticity, and independency, respectively. The maintest is DW (Durbin and Watson 1951), used to check theabsence of autocorrelation, in which the standard deviation ofthe ordered residual data (SD) is compared with the standarddeviation of the successive differences (SDsd) of the same data.If the data are randomly and normally distributed and homo-scedastic, there should be no statistical difference between SDand SDsd. On the other hand, the parameters of the previouslymentioned pseudounivariate calibration curve could also beused to express linearity. The working range of the methodcan be established by confirming that the method providesacceptable degrees of linearity, trueness, and precision.

For multivariate calibration methods, the selectivity (SEL)is calculated as the ratio between the norm of each NASvector, NASij jj j , and the norm of the respective spectrum,xij jj j. It should be stressed that this definition is only useful

within a certain group of samples of similar qualitative com-position. As each sample has a different SEL, an averagevalue is used to characterize the method. Since multivariatemethods do not require signal resolution, it is also important tostress that SEL is not useful for quality control purposes. Itonly shows how much of the analytic signal is used in themultivariate model. The sensitivity (SEN) of inverse methods,such as PLS and PCR, can be calculated from:

SEN ¼ 1 bk k= ð3Þ

Since SEN is dependent on the analytical techniqueemployed, a more comparable FOM is the analytical sensitivity(γ), which is calculated as the ratio between SEN and the

884 Food Anal. Methods (2013) 6:881–891

instrumental noise (ε). In the case of diffuse reflectancemeasure-ments, ε can be estimated through the pooled standard deviationof a certain number of replicate spectra of the empty cell.

g ¼ SEN "= ð4ÞThe inverse of γ (γ−1) provides an estimation of the mini-

mum concentration difference that is distinguishable by themethod considering the random experimental noise as the onlysource of error, regardless of the specific technique employed.

Ruggedness evaluates the susceptibility of an analyticalmethod to deliberateminor changes in experimental conditions.In this work, it was assessed by varying two factors at twolevels, according to a 22 experimental design: the cheese sam-ple pretreatment (only sliced or sliced, milled, and pressed) andthe type of cell used to obtain the reflectance measurements(the plate from the spectrophotometer manufacturer or a simplePetri dish). The bias is an FOM that evaluates the presence ofsystematic errors in the model and is calculated only for thevalidation set, as follows (ASTM 2012):

bias ¼Xnvi¼1

yrefi � byi� �nv

ð5Þ

whereyrefi andbyiare the reference and predicted property values,respectively, and nv is the number of samples in the validationset. The standard deviation of validation errors (SDV) is alsoestimated and used in a Student’s t test to determine if thevalidation estimates present a statistically significant bias. Thecalculated t value is then compared to the critical t value withthe appropriate number of degrees of freedom, which is equalto nv.

SDV ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP

yrefi � byið Þ � bias½ �nv � 1

2s

ð6Þ

Another FOM appropriate for assessing the predictiveability of the calibration models is the RPD, also known asrelative predictive determinant (Williams 2001). The RPD isthe ratio of natural variation in the calibration or validationsamples to the size of probable errors occurring during theprediction, and it is more useful for comparing models ondifferent data sets or in absolute terms. It is calculated for thecalibration and validation sets according to the Eqs. 7 and 8,where RMSECV is the root mean square error of crossvalidation and SDcal and SDval are the standard deviationsof the reference values for the calibration and validationsets, respectively.

RPDcal ¼ SDcal RMSECV= ð7Þ

RPDval ¼ SDval RMSEP= ð8Þ

Post-Model Monitoring

Once the NIRS methods were established and validated,they were implemented as a replacement for the traditionalones in IMA for the routine quality control inspection ofmozzarella cheeses. During the year 2011, 53 cheese sam-ples (about 10 % of the total number of mozzarella samplesanalyzed) were randomly and equally temporarily spacedanalyzed for both the reference and NIRS methods, in orderto monitor the performance of the developed models. Thetrueness of these determinations was evaluated according tothe Brazilian regulations (MAPA 2009). These results werealso plotted in control charts and their normal and indepen-dent distribution assessed through the RJ, BF, and DW tests.

Results and Discussion

PLS Model Development

The NIR spectra of the 123 analyzed samples of mozzarellacheeses are shown in Fig. 1. By observing these spectra, itwas possible to attribute the most intense and broad bandscentered at 1,454 and 1,936 nm to vibrations of water,corresponding to the first overtone of the O–H stretch andto the combination of the stretching and bending modes ofO–H, respectively. Other observed peaks can be related tothe fat content of the cheeses and to the vibrations of thelipid molecules, such as the band centered at 1,210 nm thatis attributed to the second overtone of C–H stretch; thepeaks at 1,730 and 1,763 nm, related to the first overtoneof C–H stretch; and the peaks at 2,308 and 2,348 nm,attributed to the combination bands arising from the C–Hstretch and deformation in a CH2 group (Lucas et al. 2008;Pi et al. 2009).

The samples were split into 82 for the calibration set and41 for the validation set by using the Kennard–Stone algo-rithm, which assured the presence of the most representativesamples in the calibration set through a uniform scanning ofthe spectral data (Kennard and Stone 1969). In Fig. 1, thepresence of nonlinear baseline deviations, typical of diffusereflectance measurements and caused by the multiplicativelight scattering, can also be noted. Thus, the data werepreprocessed by multiplicative scatter correction in orderto overcome this problem (Isaksson and Naes 1988), previ-ously to the mean centering.

The number of LVs in each model was chosen by con-tiguous block (with nine splits) cross-validation, based onthe lower values of RMSECV. The best models were initial-ly selected with four and seven LVs for moisture and fat,respectively. Interval PLS models (with 10 intervals) werealso tried, but all the results were worse than the PLSmodels using the whole spectra. The regression coefficients

Food Anal. Methods (2013) 6:881–891 885

of the PLS models for fat and moisture determinations areshown in Fig. 2. By observing Fig. 2a, it was possible toidentify the spectral regions that most contributed to the fatprediction. As it was expected, the highest coefficients wererelated to second and first overtones of lipid C–H stretch(around 1,210, 1,730, and 1,763 nm). Nevertheless, it isinteresting to note that the most intense contribution camefrom the region between 1,870 and 1,890 nm, which can beattributed to the combination band of C–O and O–H

vibrations of carboxylic acids (Workman and Weyer2008), which are present in mozzarella cheeses at lowercontents. In Fig. 2b, the regions that most contribute to themoisture predictions can be indicated; the most positivecoefficients are between 1,850 and 1,910 nm, correspondingto the combination band of O–H of water. On the otherhand, the most negative coefficients were related to lipidC–H vibrations, since there is an inverse relation betweenwater and fat contents in cheeses. The peaks were observed

Fig. 1 NIR spectra of 123samples of mozzarella cheeses

Fig. 2 Regression coefficientsof the PLS models for a fat andb moisture determination

886 Food Anal. Methods (2013) 6:881–891

around 1,440 nm and between 1,690 and 1,780 nm, attrib-uted to the first overtone combination of C–H and to the firstovertone of C–H stretch, respectively.

Optimization of the Models Through the Detectionof Outliers

After the PLS models were constructed, they were opti-mized by using the procedure for the detection of outliers.The outliers were detected at 99 % confidence level, and theresults were summarized in Table 1. The outliers can beremoved within a limit of 2 out of 9 (22.2 %) of the totalnumber of samples, as established by Brazilian (MAPA2009) and international guidelines (Horwitz 1995; Souzaand Junqueira 2005). The optimization of the validationset was only performed after finishing the optimization ofthe calibration set. Besides, no more than three rounds ofoutlier detection (four models) should be performed, inorder to avoid the “snowballing effect,” when repetitiverounds continue to identify outliers (Valderrama et al.2007). As can be seen from Table 1, for the fat model, eightoutliers were detected in the calibration set (correspondingto 9.8 % of the samples) and four in the validation set (also9.8 %). From these 12 outliers, 3 and 9 were detected basedon high leverage and high Y residuals, respectively. For themoisture model, 9 outliers were identified in the calibrationset (11.0 %) and 6 in the validation set (14.6 %); from these15 outliers, 3, 1, and 11 were detected based on highleverage, high X residuals, and high Y residuals, respective-ly. Therefore, the optimized PLS model for fat determina-tion was built with 74 calibration and 37 validation samples,used 8 LVs, and accounted for 99.1 % of the variance in Xand 89.8 % in Y. The optimized model for moisture deter-mination was built with 73 calibration and 35 validation

samples, used 6 LVs, and accounted for 98.2 % of thevariance in X and 94.1 % in Y.

Analytical Validation

Table 2 summarizes the parameters estimated for evaluatingthe FOM for the proposed methods. In the following sub-sections, they are specifically discussed.

Linearity

As previously discussed, the linearity was estimated throughthe fit of the reference versus predicted values. The residualsfor the fat and moisture models are shown in Fig. 3. In mostchemometrics literature, these residuals used to be plotted as afunction of the reference values, which is not strictly cor-rected. The residuals should have been plotted as a functionof the predicted values, since they were not correlated withthem. If the data is ordered using the reference values, theywill always present some correlation, with r equals 1 minusthe r of the calibration curve (Draper and Smith 1998). As can

Table 1 Results for the optimization of the PLS models (in italics forthe final ones) through the detection of outliers

Model 1st 2nd 3rd 4th

Fat

Number of calibration samples 82 77 74 –

Number of validation samples 41 41 37 –

Number of LV 7 8 8 –

RMSEC (%) 3.1 2.1 1.8 –

RMSEP (%) 3.2 3.0 2.1 –

Moisture

Number of calibration samples 82 77 74 73

Number of validation samples 41 41 41 35

Number of LV 4 8 8 6

RMSEC (%) 1.8 1.0 0.8 0.6

RMSEP (%) 2.2 1.8 1.7 0.9

Table 2 Parameters for evaluating the main FOM of the developedNIRS methods for the determination of fat and moisture in cheese

FOM Parameter Fat Moisture

Value

Trueness Relative errors(max/min)

−8.7/8.1 % −5.3/4.0 %

Precision RSDrepeatabilitya

0.7 % 0.5 %

0.2 % 0.4 %

0.3 % 0.4 %

RSD intermediate 3.2 % 1.4 %

precisiona 8.4 % 2.6 %

4.0 % 1.2 %

Linearity DW test 1.80 1.91

Slopeb 1.00±0.02 1.00±0.03

Interceptb 0.01±2.70 0.00±1.40

Correlationcoefficientb

0.9442 0.9702

Working range 38.7 to 58.0 % 41.5 to 55.1 %

Selectivity 0.07 0.11

Sensitivity 0.009c 0.012c

Analyticalsensitivity (γ)

1.8 %−1 2.4 %−1

γ−1 0.6 % 0.4 %

Bias 0.775±1.942 % −0.001±0.933 %

RPD RPD calibration 2.1 2.9

RPD validation 2.0 2.4

a Results for three samples at three different content levelsb Values for the line fitted to the calibration samplesc Values expressed as the ratio between log (1/R) and percent

Food Anal. Methods (2013) 6:881–891 887

be observed in Fig. 3, no systematic trend was apparent in theresidual distributions. Nevertheless, the randombehavior of theseresiduals was confirmed by appropriate statistical tests (Souzaand Junqueira 2005). At 95 % confidence level, the residuals ofthe two models were considered normally distributed and homo-scedastic according to the RJ and BF tests, respectively. Inaddition, their independency was certified by the values of theDW test (Table 2), whichwere within the limits of the acceptancerange, between 1.50 and 2.50. Once the linear models wereconsidered valid assumptions, the parameters of the fit of thereference versus predicted values can be seen in Table 2.

Trueness, Precision, and Working Range

The trueness of the methods can be evaluated through theRMSEP (absolute) values of 2.1 and 0.9 % for fat andmoisture, respectively (Table 1). It can also be evaluatedbased on the observed relative errors, between −8.7 and8.1 % for fat determination and between −5.5 and 4.0 %for moisture determination. All of these values were inaccordance with the Brazilian guidelines (ICH 1997), whichestablished acceptance limits for relative errors between −20and +10 %. The precision was evaluated through the relativestandard deviation (RSD). For both methods, these values

varied between 0.2 and 0.7 % at the level of repeatability andbetween 1.2 and 8.4 % at the level of intermediary precision(Table 2). All of these results were also in accordance with theBrazilian guidelines (MAPA 2009), which prescribes a max-imum RSD of 4 % for repeatability and 10 % for intermediateprecision, considering the level of the concentration of theanalytes (above 100 gkg−1). The results of trueness and pre-cision allow assuring that both methods were consideredaccurate (EC 2002). Considering the linearity and accuracystudies, the working ranges of the methods were establishedfrom 38.7 to 58.0 % w/w for fat and from 41.5 to 55.1 % w/w for moisture. It is important to realize that these ranges arenot necessarily identical to the useful ranges of the calibration.While the calibration may cover a wide concentration range,the remainder of the validation will cover a more restrictedrange (Thompson et al. 2002).

Selectivity and Analytical Sensitivity

As previously discussed, the SEL values have no practicalinterest for quality control. The obtained results just indicatedthat 7 and 11 % of the analytic signal were used for predictingfat and moisture, respectively. Since the SEN values are notappropriate for comparison with other methods, the γ of the

Fig. 3 Residuals for thecalibration (triangles) andvalidation (circles) samples.PLS models for a fat and bmoisture determination

888 Food Anal. Methods (2013) 6:881–891

methods (Table 2) was also calculated based on the estimatedε of 0.005. The inverse of γ indicated that the methods wereable to discriminate minimum concentration differences of0.6 % for fat and 0.4 % for moisture, considering the randominstrumental noise as the only source of errors.

Ruggedness

Two factors of practical interest were chosen for theruggedness evaluation. The objective was to know if itwould be possible to replace the plates from the instru-mental manufacturer by less expensive Petri dishes forthe reflectance measurements. And also, if a simplersample pretreatment, without milling, would providethe same results. A 22 full factorial design in triplicateindicated that the two studied factors had no significant

effect on the results at 95 % confidence level. As canbe seen in Table 3, all the estimated effects were withinthe confidence intervals of ±1.79 and ±0.92 % for fatand moisture, respectively, both calculated (Bruns et al.2006) as the product of the error of the effect estimationand the appropriate t value (2.31, with 8 degrees offreedom and at 95 % confidence level).

Bias and RPD

The bias was calculated based only on the validationsamples and its estimation for both models, as shown inTable 2. From the values of bias and SDV, t00.005 wasestimated for the moisture model, which was below thecritical t of 2.026 with 37 degrees of freedom and at95 % confidence level. For the fat model, t02.426 wasestimated, which can indicate the absence of a statisti-cally significant bias only at 98 % confidence level(tcrit02.431). RPD values higher than 2.4 are considereddesirable for good calibration equations, whereas equa-tions with RPD less than 1.5 are considered unusable(Williams 2001; Patil et al. 2010). Thus, the RPD val-ues for the moisture model were considered good,whereas the RPD values for the fat model were consid-ered satisfactory (Table 2).

Table 3 Results for the ruggedness evaluation, according to a 22 fullfactorial design

Effect Fat (%) Moisture (%)

Plate 0.17 0.23

Pretreatment −1.49 −0.32

Plate × pretreatment 0.39 −0.18

Fig. 4 Control charts formonitoring the stability of theNIRS models: a fat and bmoisture. The sample numberon the x axis corresponds to ahomogeneous sampling fromJanuary to December 2011

Food Anal. Methods (2013) 6:881–891 889

Post-Model Monitoring

Once the methods were validated and adopted for thequality control inspection, they were monitored in orderto assess their stabilities. The results are shown ascontrol charts in Fig. 4. The limits marked in thesecontrol charts are based on the Brazilian guidelines(MAPA 2009), which established for monitoring thestability of quantitative methods that two thirds of thesamples should have relative errors within ±15 % (alertlimits), while one third can present maximum allowableerrors of ±33 % (action limits). Since only three sam-ples (5.6 % of the total) for the fat model and onesample (1.9 %) for the moisture model present relativeerrors above 15 % and below 33 %, both models wereconsidered satisfactorily stable. In addition, the randombehavior of these errors was also analyzed by statisticaltests. The fat model (Fig. 4a) presented a DW value of1.60, confirming the random distribution of their errors.On the other hand, the moisture model (Fig. 4b) pre-sented a DW value of 0.99, indicating the presence ofsystematic trend. In spite of this, this model is stillbeing used since it is in accordance with the adoptedguidelines (MAPA 2009).

Conclusions

This paper developed and validated two robust multi-variate diffuse reflectance NIRS methods for determin-ing fat and moisture in cow mozzarella cheese. Thesemethods have been developed under real conditions ofroutine analysis in a state laboratory of food qualityinspection control. They present several advantages overthe current methods, such as low cost, simplified pro-cedure, no need for reagents, and no chemical wastegeneration. Their main advantage is the rapidity of theanalyses, since only about 3 min is spent per determi-nation. Thus, the NIRS method is about 30 times fasterthan the Gerber’s method for fat determination and 80times faster than the gravimetric method for moisturedetermination. Both methods have been validated inaccordance with Brazilian and international guidelines,being considered linear, accurate, sensitive, and rugged.In addition, once the methods were adopted, their per-formances were monitored for approximately 1 yearthrough control charts, demonstrating that they continueto provide acceptable predictions. Finally, more thanthese specific methods, we have aimed to present acomplete and robust multivariate methodology. Thismethodology harmonizes the traditional univariate vali-dation with the requirements of multivariate calibration,

which is essential for the implementation of new NIRSmethods in the routine analysis of food quality control.

Acknowledgments B.G.B thanks CAPES and CNPq for fellowships.

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