Assessment of uncertainty in pesticide multiresidue analytical methods: main sources and estimation

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1 Analytica Chimica Acta 454 (2002) Assessment of uncertainty in pesticide multiresidue analytical methods: main sources and estimation L. Cuadros-Rodríguez a, M.E. Hernández Torres b, E. Almansa López a, F.J. Egea González c, F.J. Arrebola Liébanas c, J.L. Martínez Vidal c, a Department of Analytical Chemistry, School of Qualimetrics, University of Granada, Granada, Spain b Centro Universitario Analítico Municipal (CUAM), El Ejido, Almería, Spain c Department of Analytical Chemistry, University of Almería, Almería, Spain Received 26 June 2001; received in revised form 1 November 2001; accepted 15 November 2001 Abstract The estimation of the uncertainty associated to analytical methods is necessary in order to establish the comparability of results. Multiresidue analytical methods lack very often of information about uncertainty of results with likely implications when results are compared with maximum residue levels (MRL) established by regulations. An adequate identification and estimation of each uncertainty source allows to laboratories to establish the accuracy of results and to balance with time-consuming and costs Elsevier Science B.V. All rights reserved. Keywords: Uncertainty; Gas chromatography; Pesticide analysis 1. Introduction The analytical properties are classified among other ways [1] in capital, basic, and accessory. A capital one is the accuracy [2], as a conjunction of the basics precision, trueness and inertia, related with such properties we find meteorological properties, such as traceability and uncertainty. These are intimately linked, having into account the formal definitions of traceability and uncertainty [], we could state that uncertainty characterises the strength of the links in the chain of traceability and the agreement to be expected between measurements. Uncertainty takes into account either random as systematic errors and gives information Corresponding author. Tel.: ; fax: address: jlmartin@ual.es (J.L. Martínez Vidal). about the range in which a result can be expected. The error cannot be determined in most of analytical methods unless the true value is stated, but the uncertainty can be estimated from the analytical method, which should be described in a detailed operating procedure. This point of view, addresses the uncertainty as a probabilistic estimation of the maximum error of a measurement. Three approaches are already proposed: bottom-up [4,5], top-down [6] and in-house validation [7,8] for the expression of uncertainty. The first approach considers the division of the analytical method into its steps and the identification, quantification and combination of all uncertainty sources. The International Standards Organisation (ISO) produced a guide for the harmonisation of the expression of results with uncertainty, which was adapted by Eurachem to the analytical problem. The second approach includes the use /02/$ see front matter 2002 Elsevier Science B.V. All rights reserved. PII: S (01)01546-X

2 298 L. Cuadros-Rodríguez et al. / Analytica Chimica Acta 454 (2002) of interlaboratory information and the third approach involves the information obtained from repeated analyses derived from in-house validation of analytical methods. In this context it seems sense for a given pesticide residues laboratory, to use the bottom-up approach in conjunction with in-house validation data for estimating the uncertainty derived from each step of the analytical method [9 11]. All this information should be considered in the frame of the analytical problem: pesticide residue analysis in vegetables has the lack in certified reference materials, CRMs, consider a wide range of analytes, which should be determined at very different concentration levels established by the maximum residue levels (MRLs), and finally there is a wide range of commodities with different matrix effect in the determination of the analytes. On other hand, the definition of uncertainty [], indicates that results should be given without systematic errors. In pesticide residue analysis, the situation is that recovery factors of most of analytes are different than 100%, so that, in a first consideration, a correction of this recovery should be necessary for the reliability of results [12]. Nevertheless, having into account again the diversity of concentration ranges and the large number of analytes, it make difficult to estimate a correction factor for each combination, adopting the accepted criteria that no correction is better than a wrong correction. The European Commission [1] considers acceptable recovery factors within %, supporting the establishment of MRLs on this basis. However a couple of questions remain: the first one is the case in which a pesticide is found in a sample at a concentration close to its MRL or even slightly greater. In a practical sense, if such limit is in the concentration range defined by the measurement and its uncertainty, the result should be considered as negative, in fact, only when the MRL is minor than the amount found minus its uncertainty, the result should be stated as positive. The other question is the case of results obtained in different laboratories, the uncertainty can led to consider them as concordant or discrepant depending on the inclusion of the allowed limit in the intervals given by the uncertainty of results in each laboratory. So that, should uncertainties be considered in the legislation for a better comparison of results? Is the above statement about the correction of recovery factors scientifically supported? Having into account that methods should be validated for a range of analytes in a range of representative commodities, allowing to estimate recovery factors for each analyte and each commodity. This paper presents a methodology for estimating the uncertainty associated to a multiresidue analytical method in cucumber matrix, through the bottom-up approach and on the basis of in-house validation data. All data appearing in this paper were obtained with the multiresidue method (MRM) proposed, which meet compliance with EN45001 requirements, since it was implemented in a pesticide residue analysis laboratory as a routine method and accredited. The uncertainty of each step is estimated identifying which of them are relevant in the global uncertainty, finally the significance of recovery factors is statistically calculated including the estimation of the results with and without correction. 2. Experimental 2.1. Chemicals The solvents used were n-hexane, acetone, cyclohexane and dichloromethane (residue analysis grade, Panreac, Barcelona, Spain). Anhydrous sodium sulphate for residue analysis was purchased from Panreac. All pesticide standard reference materials were obtained from Dr. Ehrenstorfer (Augsburg, Germany). The purity of these standard pesticides is given in Table 1. The following pesticides were tested. (a) Pesticides determined by GC NPD: Dichlorvos, methamidofos, acephate, heptenophos, ethoprophos, dimethoate, diazinon, etrimfos, parathionmethyl, chlorpyrifos-methyl, pirimiphos-methyl, malathion, parathion-ethyl, chlorpyrifos, chlorfenvinphos, triadimenol, fenamiphos, myclobutanil, buprofezin, cyproconazole, ethion and carbophenothion. (b) Pesticides determined by GC ECD: -HCH, chlorothalonil, vinclozolin, dichlofluanid, triadimefon, chlozolinate, procymidone, endosulfan-, endosulfan-, endosulfan-sulphato, nuarimol, iprodione, bromopropylate, tetradifon and acrinathrin.

3 L. Cuadros-Rodríguez et al. / Analytica Chimica Acta 454 (2002) Table 1 Relevant data for calculating the uncertainty associated to standard preparation Pesticide Purity (%) Tolerance (%) Mass (m) a (mg) VP 1 ( l) b ECD -HCH Chlorothalonil Vinclozolin Dichlofluanid Triadimefon Chlozolinate Procymidone Endosulfan Endosulfan Endosulfan-s Nuarimol Iprodione Bromopropylate Tetradifon Acrinathrin NPD Dichlorvos Methamidofos Acephate Heptenophos Ethoprophos Dimetoate Diazinon Parathion-methyl Chlorpyrifos-methyl Pirimiphos-methyl Malathion Parathion-ethyl Chlorpyrifos Chlorfenvinphos Triadimenol Fenamiphos Myclobutanil Buprofezin Cyproconazole Ethion Carbophenothion a The volume of the primary standard solutions was 50 ml in all cases excepting achrinathrin (10 ml). b VP 1 is the volume of primary standard solution measured for preparing the secondary standard solution. The final volume of this solution was 50 ml Equipment Three gas chromatographs were used: a Perkin-Elmer model 8500 equipped with an electron capture detector (ECD, 6 Ni); a Fisons model 8000 equipped with an nitrogen-phosphorus detector (NPD) and an injector AS Fisons and a Saturn 2000 ion trap mass spectrometer from Varian Instruments (Sunnyvale, CA, USA) equipped with an autosampler 8200, and a split/splitless programmed temperature injector SPI/1078 operated in the splitless mode. GC ECD operating conditions: injector temperature, 250 C; detector temperature, 50 C; initial oven temperature, 180 C for 5 min, raised at C/min to 250 C, and then held at 250 C for 2 min. The carrier gas was nitrogen at 10 ml/min. A fused silica semicapillary (HP-1) column containing 100% methylpolysiloxane as stationary phase (25 m length, 0.5 mm internal diameter (i.d.) and 1.0 mm film thickness) was used for the separation. GC NPD operating conditions: injector temperature, 250 C; detector temperature, 00 C; splitless time, 2 min; initial oven temperature, 90 C for 1 min, raised at 15 C/min to 170 C for 0 min, raised at 2 C/min to 220 C for 0 min, raised at 10 C/min to 255 C, and then held at 255 C for 5 min. The carrier gas was nitrogen at 1 ml/min. A fused silica capillary (HP-1) column containing 100% methylpolysiloxane as stationary phase (60 m length, 0.25 mm i.d. and 0.25 m film thickness) was used for the separation in the GC. GC MS operating conditions were: initial column temperature, 60 C (2.9 min), increased at 40 C/min to 150 C and finally increased at 5 C/min to 275 C (held for 10 min); initial injector temperature, 60 C (0. min) and increased at 100 C/min to 280 C (held 0 min); manifold, transfer-line and trap temperatures were 45, 260 and 200 C, respectively; flow-rate, 1 l/s and injection volume, 5 l. A DB5-MS column (0 m, 0.25 mm i.d. and 0.25 m film thickness) was employed. The ion trap mass spectrometer was operated in the electron ionisation (EI) mode and the MS/MS option was used. The computer, which controlled the system, had an EI MS/MS library specially created for the target analytes in our experimental conditions. In addition, other EI MS libraries were available. The carrier gas used was helium (purity %). Mass spectrometer settings: solvent delay, 4.5 min; 70 ev of electron impact energy and scan rate, 0.6 scans/s. For GC MS/MS, the sample was injected under the gas chromatographic conditions described for GC MS.

4 00 L. Cuadros-Rodríguez et al. / Analytica Chimica Acta 454 (2002) Analytical procedures Standards preparation A stock solution of each pesticide (primary standard solutions) was prepared dissolving pure standard in acetone (for pesticides analysed by GC NPD) and in n-hexane (for pesticides analysed by GC ECD). Working standard solutions containing a mixture of the analytes (secondary standard solutions) were prepared from the above by appropriate solvent dilutions, using automatic pipettes and glass volumetric flasks (A class). They were stored in a refrigerator at 4 C. Table 1 shows the amount of each solid standard taken for preparing the primary standard solution, and the volumes taken for preparing the secondary standard solutions. Finally, calibration curves were prepared at the concentration ranges given in Table 2, pippeting 50, 100, and 200 l of the secondary Table 2 Data calibration and parameters calibrations a Compound Concentration (mg/l) b a s b s resid Repeatability (%) Intermediate precision (%) ECD -HCH Chlorothalonil Vinclozolin Dichlofluanid Triadimefon Chlozolinate Procymidone Endosulfan Endosulfan Endosulfan-s Nuarimol Iprodione Bromopropylate Tetradifon Acrinathrin NPD Dichlorvos Methamidofos Acephate Heptenophos Ethoprophos Dimetoate Diazinon Parathion-methyl Chlorpyrifos-methyl Pirimiphos-methyl Malathion Parathion-ethyl Chlorpyrifos Chlorfenvinphos Triadimenol Fenamiphos Myclobutanil Buprofezin Cyproconazole Ethion Carbofenothion a Slope, b ; standard deviation of slope, s b ; intercept, a and standard deviation of residues, s resid ; recovery factors (R); validation data (repeatability and intermediate precision). R (%)

5 L. Cuadros-Rodríguez et al. / Analytica Chimica Acta 454 (2002) Fig. 1. Schemes of the standards preparation (A) and extraction procedure (B). standard solution for ECD analysis and 50, 150 and 250 l for NPD analysis, and diluting them to 2 ml, in a volumetric flask with blank matrix extract (Fig. 1A) Extraction and analysis The extracting method used was similar to that used by Martínez Vidal and co-workers [14], which consists in mixing 50 g of a chopped sample with 105 ml of dichloromethane, the mixture is homogenised with Polytron at rpm for 2 min, then 100 g of anhydrous sodium sulphate are added resting for 2 min and the mixture is filtered through a filter paper into a 250 ml round-bottom flask and the cake was washed twice with 20 ml of dichloromethane each time. The solvent is removed under vacuum at 40 C in a rotary evaporator until almost dry and then just to the point of dryness with a slight N 2 stream, being dissolved with 5 ml of cyclohexane. For ECD analysis, 1 ml of the sample extract is diluted adding ml of n-hexane. In all these steps, appropriate glass pipettes, A class, are used for measuring the volumes. The 40 l of internal standard (IS) solution (10 mg/l of dieldrin in hexane) is added in a 2 ml volumetric flask, the volume made up to 2 ml with the above solution and injected into the GC ECD (1 l). For NPD analysis, 100 l of the IS (20 mg/l of caffeine in acetone) is added in a 2 ml volumetric flask and the volume made up to 2 ml with the sample extract and injected into the GC NPD (1 l). For the MS confirmation, 1 ml of the NPD solution is diluted to 2 ml with cyclohexane and injected into the GC MS (5 l) (Fig. 1B) Recovery study The recovery study was carried out spiking 50 g of cucumber sample, which had not been treated with the pesticides, with a mixture of working standard solutions containing all pesticides at the second concentration level defined for the calibration curves

6 02 L. Cuadros-Rodríguez et al. / Analytica Chimica Acta 454 (2002) (Table 2). After evaporation of the solvent using a nitrogen stream, the sample was mixed thoroughly and homogenised for 2 min. Then the sample was extracted and analysed. Ten replicates of each recovery assay and 10 blank samples of cucumber were performed. Intermediate precision of recovery factors was estimated performing the recovery experiment each week during months.. Uncertainty estimation: theoretical aspects Depending on the way of expressing uncertainty, we find standard uncertainty (u(x)), expressed as a standard deviation, and expanded uncertainty (U(x)) which is calculated from a combined standard uncertainty and a coverage factor k. In some cases, it is feasible to use relative uncertainties (in both uncertainties), which represent the value of the uncertainty normalised. It is obtained as the quotient between the standard uncertainty u(x) and the value of x: from a confidence interval; from a maximum interval of variability; from a range of limits(upper and lower limits); finally from a given error value. Calculate combined uncertainty. The different contributions to the overall uncertainty have to be combined according to the appropriate rules for giving a combined standard uncertainty: u(f ) = c 2 (x)u 2 (x) + c 2 (y)u 2 (y) +, f = f(x,y,...) where c is a sensibility coefficient associated to each one of variables, given by the partial derivative of the function: c(x) = f/ x. Applying the appropriate coverage factor, the expanded uncertainty will be obtained. 4. Results and discussion U rel (x) = U(x) x or u rel (x) = u(x) x 4.1. Analysis Uncertainty estimation is simple in principle, the steps involved are as follows. Specify the measurand. It should be clearly written the relationship between the measurand and the input quantities upon which it depends, such as measured quantities, constants and calibration standard values. Identify uncertainty sources. Listing the possible sources of uncertainty, usually specified in the above step. Quantify uncertainty components. Estimating the uncertainty component associated with each potential source of uncertainty identified. The different contributions to the overall uncertainty have to be expressed as standard deviation which can be calculated depending on the data available: from a standard deviation value: this value is directly used; from a variation coefficient; from the standard deviation of experimental data sets; from a declared uncertainty value, which is given in a certificate of calibration; Chromatographic conditions were optimised for achieving a good resolution of the target pesticides. Figs. 2 and show the ECD and NPD chromatograms of a cucumber extract containing all the analytes and the IS, using the final selected chromatographic conditions. Table summarises the retention time window (RTW) determined for all the compounds. The RTW is defined for each pesticide as the average of the retention times, obtained from 10 replicates, plus or minus three times the S.D. of retention times (RT). Confirmation was carried out by GC MS/MS analysis, using the quantification ions summarised in Table. Target analytes were searched at RTW and were identified by comparing their spectra with those EI MS/MS libraries, stating a minimum spectral fit of 700 as confirmation requirement Validation Calibration curves were obtained from matrixmatching calibration solutions using IS calibration. The lowest concentration level in the calibration curve is established as a practical determination limit (PDL),

7 L. Cuadros-Rodríguez et al. / Analytica Chimica Acta 454 (2002) Fig. 2. ECD chromatogram of n-hexane extract of cucumber spiked at second concentration level of calibration curve and containing the IS (17.97 min). which is defined as a percentage of the maximum residue level (MRL) stated for each pesticide by the European Union regulations in vegetables commodities. All compounds exhibited good linearity in the studied range. Determination coefficients (the square of the correlation coefficients) found were higher than 0.98 in all cases. Limits of detection (LOD) and limits of quantification (LOQ) were calculated as - and 10-fold, respectively, the standard deviation of 10 blank samples, containing the IS, divided by the slope of the calibration curve. Table summarises the LOD and LOQ obtained for each pesticide. The values obtained are lower than their respective MRLs Precision The repeatability of the method was tested by determining the R.S.D. of chromatographic signals obtained from a spiked sample analysed 10 times. The values found (Table 2) were lower using ECD,

8 04 L. Cuadros-Rodríguez et al. / Analytica Chimica Acta 454 (2002) Fig.. NPD chromatogram of an acetone extract of cucumber spiked at second concentration level of calibration curve and containing the IS (22.11 min). 1 5% (except achrinathrin with a 12.% R.S.D.) than NPD, which showed R.S.D. ranging between 2 and 12%. The intermediate precision was determined by measuring the standard deviation of a set of spiked samples, which were extracted and analysed (one replicate) each week during months (Table 2). This experiment included in the R.S.D., the likely variation produced by changes in solvent batches, analysts, material, and the usual chromatography maintenance. As in the above case, values found expressed as %R.S.D. are higher for the compounds analysed by GC NPD, being the maximum R.S.D. 25.7% for myclobutanyl. The compounds determined by GC ECD present values lower than 10% except for acrinathrin (19.2%). 4.. Extraction procedure and recovery study The extraction procedure described above was applied to spiked cucumber samples for obtaining the recovery rates of pesticides. The extraction method is efficient for extracting pesticide residues from cucumber samples, as the analytes were determined with recovery factors ranging between 75 and 101% (Table 2) at the second calibration level of spiked concentration, being the precision above explained (Table 2) Quality control procedure A quality control procedure was established for ensuring that results obtained are under statistical control. This procedure consisted in incorporating to each batch of samples a blank extract, a matrix-matching calibration solutions and three spiked samples. Results were considered when the analysis of blank extracts showed that neither contamination nor degradation of sample had occurred, the recovery factors of spiked samples were between 70 and 120% and the calibration plots fit to lines with determination coefficients higher than Uncertainty of results The different aspects explained above for estimating the standard uncertainties have been applied to the multiresidue analytical method. Tables 1 and 4 show the relevant information for calculating uncertainties associated to the preparation of primary standard solutions and to the volumetric material, analytical balance and balance. Furthermore, calibration data obtained daily during 1 month have been used for each pesticide Identification of uncertainty sources The analyte concentration in the sample, expressed in mg/kg, is obtained from the equation: CON = CA F dil CS where CA is the analyte concentration obtained from the calibration (in mg/l); F dil the dilution factor and CS the sample concentration in the extract (kg/l).

9 L. Cuadros-Rodríguez et al. / Analytica Chimica Acta 454 (2002) Table RTW, MS/MS data, LOD and LOQ Compound Quantification ion (m/z) RTW LOD (mg/kg) LOQ (mg/kg) ECD -HCH Chlorothalonil Vinclozolin Dichlofluanid Triadimefon Chlozolinate Procymidone Endosulfan Endosulfan Endosulfan-s Nuarimol Iprodione Bromopropylate Tetradifon Acrinathrin NPD Dichlorvos Methamidofos Acephate Heptenophos Ethoprophos Dimetoate Diazinon Parathion-methyl Chlorpyrifos-methyl Pirimiphos-methyl Malathion Parathion-ethyl Chlorpyrifos Chlorfenvinphos Triadimenol Fenamiphos Myclobutanil Buprofezin Cyproconazole Ethion Carbophenothion Quantification of standard uncertainties associated to each step The dispersion of results around the true value depends upon the following steps (Fig. 4). 1. Estimation of the analyte concentration from the calibration curve. 2. Dilution factor of the sample extract.. Calculation of the sample concentration. The combined uncertainty (in terms of relative uncertainty) can be calculated with the expression: u rel (CON) = u 2 rel (CA) + u2 rel (F dil) + u 2 rel (CS) where each term of the sum, the relative standard uncertainty associated to each source identified above.

10 06 L. Cuadros-Rodríguez et al. / Analytica Chimica Acta 454 (2002) Table 4 Volumetric material used for preparing standards Equipment Tolerance a (ml) Correction b ( l) Variation coefficient (%) Uncertainty (k = 2) Volumetric flask 50 ml ±0.05 Volumetric flask 10 ml ±0.025 Volumetric flask 2 ml ±0.025 Glass pipette 10 ml ±0.05 Glass pipette 5 ml ±0.015 Glass pipette 1 ml ±0.007 Micropipette 5 40 l 0.0 (5) ± (10) ± (40) ±0.50 Micropipette l 0.18 (40) ± (70) ± (200) ±0.0 Micropipette l 0.2 (200) ± (00) ± (1000) ±0.0 Analytical balance (g) 0 ±0.001 Balance (g) ±0.0 a The tolerance is the confidence interval which is given by manufacturers. b The values in parenthesis are the volumes in which the correction value is established by manufacturers. Fig. 4. Cause and effect diagram for the determination of pesticides in vegetable sample.

11 L. Cuadros-Rodríguez et al. / Analytica Chimica Acta 454 (2002) Estimation of the uncertainty derived from the estimation of the analyte concentration from the calibration curve, u(ca). This is a combination of the uncertainties associated to the preparation of the calibration standard solutions (u 2 (std)), to the transformation of the chromatographic signals in concentrations (u 2 (cal)) and to the repeatability of the measurements (u 2 (repet)). This combination is calculated as u(ca) = u 2 (std) + u 2 (cal) + u 2 (repet) Estimation of u 2 (std). It is estimated for each analyte, being a combination of the uncertainty derived from the preparation of the primary and secondary standard solutions, u 2 (prim secon), and from the preparation of the calibration curve at three concentration levels by diluting the secondary standard solution, u 2 (dil). u rel (std) = u 2 rel (prim secon) + u2 rel (dil) The concentration of the primary and secondary standard solutions is given by the mass (m) of the solid standard weighted in the analytical balance, the volume (VF 1 ) of the first dilution, in the case of the primary standard; and by the volume (VP 1 ) taken with a so that the standard uncertainty associated to these steps can be obtained as u rel (C prim second ) = u 2 rel (m) + u2 rel (VF 1) + u 2 rel (VP 1) + u 2 rel (VF 2) The uncertainty associated to the equipment which have been previously calibrated is calculated as: correction/ + u. For example, the volume (VP 1 ) taken with a pipette was 1940 l and since the pipette was used twice (1000 l l), the uncertainty associated is u(vp 1 ) 1000 = correction + CV nominal = = 2.15 u(vp 1 ) 940 = correction + CV nominal = = 2.44 where the volume taken is different to the tabulated value, the correction and the coefficient of variation are the mean value from the interval to which they belong. u rel (C prim second ) = u 2 rel (m) + u2 rel (VF 1) + u 2 rel (VP 1) + u 2 rel (VF 2) = ( ) ( 1/ / ) 2 ( ( ) ( ) ) ( / ) 2 = pipette from the primary standard solution and the volume (VF 2 ) filled up in the second dilution in the case of the secondary standard. Tables 1 and 4 show the data used for the calculation of this term of the uncertainty. As an example data corresponding to -HCH are included in the following steps: C prim secon = m VP 1 = 1.0mg 1.94 ml VF 1 VF 2 50 ml 50 ml = mg/ml In similar way, the uncertainty associated to the preparation of the calibration curve is calculated for each concentration level as u rel (dil) = u 2 rel (VP 2) + u 2 rel (VF ) = ( ) 2 + ( 0.025/ ) 2 = where VP 2 is the volume taken from the secondary standard solution for preparing each calibration point

12 08 L. Cuadros-Rodríguez et al. / Analytica Chimica Acta 454 (2002) and VF the final volume of such solutions. u(vp 2 ) = correction + CV nominal = = In this case the correction and coefficient variation are also the mean value of the interval to which they belong. Finally, the uncertainty associated to the preparation of the calibration standard solutions is u rel (std) = u 2 rel (prim secon) + u2 rel (dil) = (0.09) 2 + (0.007) 2 = 0.09 u(std) = mg/l = mg/l Estimation of u 2 (cal). The uncertainty due to the transformation of chromatographic signals in concentrations is estimated by applying the expression for the linear regression of least squares of residuals [15] (Table 2) u(cal) = 1 s 2 1 b resid n +(C i C) 2 sb 2 = 1 (0.146) ( )2 (0.121) 2 = mg/l aliquots of a sample spiked at 0.5 mg/l were analysed in repeatability conditions. This uncertainty is given by the expression u(repet) = s s = = mg/l r 1 where s s is the standard deviation from the chromatographic signals and r the number of replicates of each sample when analysed in routine analysis (Table 2). Thus the uncertainty derived from the estimation of the analyte concentration from the calibration curve, u(ca), is given by u(ca) = u 2 (std) + u 2 (cal) + u 2 (repet) = (0.020) 2 + (0.005) 2 + (0.019) 2 u(ca) = mg/l, mg/l u rel (CA) = = mg/l Estimation of the uncertainty derived from the dilution of the sample extract u(f dil ). This uncertainty component is present only in the case of ECD analysis because, NPD analyses are performed without dilution of the sample extract (Fig. 1B). The dilution factor is calculated as F dil = V final = VP + VP 4 = 1 + = 4 V inic VP 1 where VP is the sample extract volume taken for diluting and VP 4 the n-hexane volume added (Table 4). The associated uncertainty is u rel (F dil ) = u 2 rel (VP + VP 4 ) + u 2 rel (VP ) (0.007/ ) = 2 + (0.015/ ) ( 0.007/ ) 2 + = where b is the slope of the calibration curve, s b its standard deviation, s resid the standard deviation of residuals, C i the analyte concentration at each calibration level, and C the average concentration Estimation of u 2 (repet). In order to estimate the uncertainty associated to the precision, Estimation of the uncertainty derived from the sample concentration, u(cs). The sample concentration in the final extract is given by the quotient between the sample weight m S and the volume of extract V S CS = m S = 50 g = 10 g/ml = 10 kg/l V S 5ml

13 L. Cuadros-Rodríguez et al. / Analytica Chimica Acta 454 (2002) and its uncertainty is calculated as (Table 4) u rel (CS) = u 2 rel (m S) + u 2 rel (V S) ( = u rel (CS) = / ) 2 ( / ) Combined uncertainty Once calculated, the relative standard uncertainty of each uncertainty source, the overall combined uncertainty of the analytical method can be estimated from the general expression stated above. u rel (CON) = u 2 rel (CA) + u2 rel (F dil) + u 2 rel (CS) = (0.056) 2 + (0.005) 2 + (0.002) 2 = The correction of results Usually, multiresidue analytical methods yield recovery factors different than 100% for a wide range of analytes. This led to two alternatives: to perform a correction of the obtained concentration value on the basis of the recovery of the analyte or to incorporate the recovery as another contribution to the combined uncertainty. To discuss the appropriate decision it is necessary to test the signification of the bias in function of the obtained recovery factors Testing the trueness of the analytical method. Bias is the difference between the estimated concentration CA and the actual concentration while recovery (R) (Table 2) is the quotient between the estimated concentration and the actual concentration, thus bias can be expressed as ( Bias = 1 1 ) ( CA = 1 1 ) R = mg/l and the uncertainty associated to bias is obtained with the expression u(bias) CA 2 = R 4 u2 (R) + = ( 1 1 R) 2 u 2 (CA) (0.409) 2 ( (0.818) 4 (0.015) ) 2 (0.028) = mg/l where u(r) is the uncertainty associated to recovery, which depends on the tolerance of the reference material u(tol stand) and on the standard deviation of recovery factors divided by the square root of the number of replicates, u(prec inter): u(r) = u 2 (tol stand) + u 2 (prec inter) (0.001 ) 2 ( ) = + 10 u(r) = In order to test the trueness, a test is used for verifying if the ratio between the value of the bias and its uncertainty, is greater (significant) than the corresponding coverage factor k. Depending on the result of the test, two situations can be noted: 1. Bias not significant NS : the correction of results is not necessary, the term u(r) can be included in the equation of the combined uncertainty: CON NS = CON u rel (CON) NS = u 2 rel (CON) + u2 rel (R) 2. Bias significant: in this case, it is necessary to decide whether correcting or not, the analyte content in the samples due to the recovery: 2.1. In the case that correcting results is chosen C, the R.S.D. is included in the global equation: CON C = CON R u rel(con) C = u 2 rel (CON) + u2 rel (R)

14 10 L. Cuadros-Rodríguez et al. / Analytica Chimica Acta 454 (2002) CON C = = mg/kg u rel (CON) C = If the decision is not correcting NC, the relative value of the bias is considered as a contribution to the combined uncertainty. CON NC = CON u rel (CON) NC = u 2 rel (CON) + (Bias)2 rel CON NC = mg/kg u rel (CON) NC = Therefore in -HCH, the test results that the ratio is greater than the coverage factor (k = 2) and the estimated concentration is statistically different to the actual concentration. Bias u(bias) = = 8.1 > Bias significant Estimation of the combined expanded uncertainty The expanded uncertainty U, is calculated as the product between the combined uncertainty u rel (CON) (bias not significant NS, bias significant and corrected C and bias significant and not corrected NC ) and the coverage factor k, U rel (CON) = ku rel (CON) k = 2 considering that the uncertainty estimation is obtained from at least 10 replicates of the measurand (ν ef 10), which provides a coverage probability of 95%. If the number of replicates is less than 10, it should be used as an estimated degrees of freedom obtained from the equation of Welch Satterwhaite: ν ef = u 4 i u4 i (x)/ν i where u is the combined uncertainty, u i (x) each one of the significant components of the uncertainty and ν i the degrees of freedom. In the case of -HCH, where the decision is correct, the result is calculated as (k = 2): CON C ± U(CON) C = ± 0.22 mg/kg U rel (CON) C = 11.6% Fig. 5 shows that the most significant component of the uncertainty is due to the estimation of the -HCH concentration from the calibration curve (u(ca)). It is also observed that this component increases as the concentration of standards decreases, due to the volume taken from the secondary standard solution for preparing the calibration solutions also decreases. On the other hand, since the bias is significant, it can be noted that when the pesticide content is corrected, the associate uncertainty (u(con) C ) is minor than the associate uncertainty (u(con) NC ) when the pesticide content is not corrected Factors influencing the uncertainty Figs. 6 and 7 show the uncertainty calculated for each identified source, u(ca), u(f dil ) and u(cs). It can be observed that the most influencing factor in the combined uncertainty is this associated to the preparation of standard solutions u(ca). Considering u(ca), the contribution of the uncertainty associated to the calibration curve is not significant compared with the contribution of the uncertainties associated to the preparation of the primary standard solutions and to the precision. As an example the combined uncertainty for achrinathrin is about 40 times greater than the obtained for most of pesticides (Table 5), mainly due to the small quantity of solid standard measured for preparing the primary calibration solution (.0 mg, Table 1) and the high standard deviation of recovery factors (Table 2). The u(prec) is affected by the spiking level in which the precision has been obtained, which is usually established on the basis of the MRL regulated for each pesticide in each commodity (Table 2). It can be seen in the case of chlozolinate, nuarimol and triadimefon that this contribution is the most important to the combined uncertainty. For rest of the analytes the contribution of the standard preparation and of the precision to the combined uncertainty is similar as can be seen in Figs. 6 and 7. In general NPD analysis shows a greater uncertainty level than ECD analysis, mainly due to the MRLs

15 L. Cuadros-Rodríguez et al. / Analytica Chimica Acta 454 (2002) Fig. 5. Diagram of the different uncertainty components for each standard concentration for -HCH. Fig. 6. Diagram of relative uncertainty of the pesticide analysed by GC ECD.

16 12 L. Cuadros-Rodríguez et al. / Analytica Chimica Acta 454 (2002) Fig. 7. Diagram of relative uncertainty of the pesticide analysed by GC NPD. established for OP pesticides are usually minor than the established for OC pesticides and also due to the precision of NPD is usually minor than the precision of ECD measurements. Other contributions such as u(f dil ) and u(cs) are less significant compared with the above factors The correction from recovery factors Table 5 shows the combined uncertainty for each analyte at the three concentration levels used for the calibration curves, including the obtained when the correction from recovery factors is carried out and when the correction from recovery factors is not performed. Previously, it has been stated whether the bias is significant or not with a t-test, which compares the recovery factors obtained with 100%. When recoveries have not a significant bias, the uncertainty considered is the same than when correction is carried out. It can be seen that the uncertainty is strongly depending upon the concentration level, being the greater these calculated at the first concentration level, which is usually established on the basis of MRLs requirements. This is the case of acrinathrin, triadimefon, ciproconazole, buprofezin, methamidofos and myclobutanil among others, which show uncertainties higher than 100%. Considering the correction of the bias when it is significant, it can be observed an increasing of the uncertainty, due to the inclusion of the relative value of the bias as a contribution to the combined uncertainty. In GC ECD analysis, the uncertainty with correction, at the lowest concentration level, range between 12.7 and 25.9% (excluding uncertainties higher than 100%, Table 5); these levels increase to % if the correction is not performed. It can also be observed that this effect is greater when the systematic error is greater, low recovery factors with low R.S.D., as an example dichlofluanid shows a combined uncertainty minor than 12.7% with correction, and increase to around 64% when the correction is not considered (recovery factors of dichlofluanid was 76.1% with 1.7% R.S.D., Table 2).

17 L. Cuadros-Rodríguez et al. / Analytica Chimica Acta 454 (2002) Table 5 Combined uncertainty at the different concentration levels a Pesticide Bias not significant u rel (CON) NS (%) Bias significant Level 1 Level 2 Level Corrected u rel (CON) C (%) Not corrected u rel (CON) NC (%) Level 1 Level 2 Level Level 1 Level 2 Level ECD -HCH Chlorothalonil Vinclozolin Dichlofluanid Triadimefon Chlozolinate Procymidone Endosulfan Endosulfan Endosulfan-s Nuarimol Iprodione Bromopropylate Tetradifon Acrinathrin NPD Dichlorvos Methamidofos Acephate Heptenophos Ethoprophos Dimetoate Diazinon Parathion-methyl Chlorpyrifos-methyl Pirimiphos-methyl Malathion Parathion-ethyl Chlorpyrifos Chlorfenvinphos Triadimenol Fenamiphos Myclobutanil Buprofezin Cyproconazole Ethion Carbophenothion a Levels 1 are the concentration levels of the calibration curve given in Table Strategies for decrease the uncertainty Figs. 6 and 7 show that pesticides as chlozolinate, nuarimol, triadimefon, diazinon, cyproconazole, carbofenothion, buprofezin, dimetoate, ethoprophos, methamidofos and myclobutanil present a component of the uncertainty due to the precision, u(prec), very important, this fact makes that the global uncertainty has a high value with regard to the rest of the pesticides. In addition most of these pesticides require concentration levels for the calibration curves very low, and therefore when the relative uncertainties are compared, the value of these increases, although the component of the uncertainty due to the calibration curves is not significant.

18 14 L. Cuadros-Rodríguez et al. / Analytica Chimica Acta 454 (2002) On the other hand, the uncertainty associated to the preparation of the standards, u(std), is quite similar in all pesticides and higher than other components of the global uncertainty because the amount of solid standard weighted for primary standard solution solutions was very little. Therefore in order to decrease the uncertainty of the analytical method it would be convenient to acts on the two components previously mentioned, on one hand trying to diminish the precision of the method or to increase the concentration levels and on the other hand increasing the amount of solid standard weighted for the preparation of primary standard solutions. would be difficult to establish whether a sample is positive or negative when such pesticides are detected unless an uncertainty level be established by regulatory norms. Acknowledgements The authors are grateful to Institute National of Investigation and Agrarian and Alimentary Technology (INIA), Ministerio de Agricultura, Pesca y Alimentación (Project CAL C2-2) for financial support. 5. Conclusions A methodology for calculating the uncertainty of results on the basis of in-house validation data has been applied to a pesticide multiresidue method. Uncertainty sources have been identified and standard uncertainty established. The most significant uncertainty sources are the preparation of the standard solutions, mainly the weigh-out step for preparing the primary standard solution, and the precision of the method. In this sense, when less than 10 mg of solid standard is measured for preparing the primary standard solution, the uncertainty increases dramatically to values higher than 100%. ECD determinations show in general less uncertainty than NPD analysis due to the MRL for organochlorine pesticides are usually greater than for organophosphate pesticides, so that the concentration level is another factor which influences very much the uncertainty level. This fact is because the uncertainty associated to the precision increase at low concentration levels. When a systematic error is present, the bias is significant, a correction of recovery factors would decrease the uncertainty of results dramatically. MRLs established at very low levels, close to 0.05 mg/kg, are usually determined with uncertainties around 00%, which means that the analytical method is semi-quantitative at this concentration level. So it References [1] M. Valcárcel, M.D. Luque de Castro, A hierarchical approach to analytical chemistry, Trends Anal. Chem. 14 (1995) 242. [2] A.M. García-Campaña, J.M. Bosque Sendra, L. Cuadros- Rodriguez, E. Almansa López, Biomed. Chromatogr. 14 (2000) 27. [] ISO, International Vocabulary of Basic and General Standard Terms in Metrology, International Standards Organisation, Geneva, 199. [4] ISO, Guide to the Expression of Uncertainty in Measurement, International Standards Organisation, Geneva, 199. [5] EURACHEM Guide, Quantifying Uncertainty in Analytical Measurement, 2nd Edition, quam2000-p1.pdf. [6] Analytical Methods Committee, Analyst 120 (1995) 20. [7] Protocol for In-house Method Validation, International Union of Pure and Applied Chemistry (IUPAC), [8] A.R. Hill, S.L. Reynolds, Analyst 124 (1999) 95. [9] A. Maroto, R. Boqué, J. Riu, F.X. Rius, Trends Anal. Chem. 18 (1999) 577. [10] A. Maroto, R. Boqué, J. Riu, F.X. Rius, Quím. Anal. 19 (2000) 85. [11] R.J.N. Bettencourt da Silva, M. Joäo Lino, J.R. Santos, M.F.G.F.C. Camöes, Analyst 125 (2000) [12] Harmonised Guidelines for the use of recovery Information in Analytical Measurements, IUPAC Technical Report, Pure Appl. Chem. 71 (1999) 7. [1] Quality Control procedures for pesticide residue analysis, Guidelines for residues monitoring in the European Union, Document 7826/VI/97, European Commission, Brussels, [14] F.J. Egea González, J.L. Martínez Vidal, M.L. Castro Cano, M. Martínez Galera, J. Chromatogr. A 829 (1998) 251. [15] L. Cuadros Rodríguez, A.M. García Campaña, J.M. Bosque Sendra, Anal. Lett. 29 (1996) 121.