Methanol (HPLC grade) was obtained from Merck, (Darmstadt, Germany). Pure caffeine (100%) was purchased from Sigma-Aldresh (St. Louis, Missouri, USA). The caffeine CRM, NMIA M724c (99.8% ± 0.6%) was obtained from the national metrology institute of Australia, NMIA. Ultrapure water was obtained from Millipore Milli-Q RG, USA.

The HPLC-UV system used was of the model Ulti Mate 3000 equipped with an auto-sampler, quaternary pump and a UV detector of the same model produced by Thermoscientic (Wathham, Massachusetts, USA). The chromatographic separation was performed on a hypersll gold column (50 mm × 2.1 mm × 1.9 μm) and the HPLC-UV was run by the software Chromeleon 6. The mobile phase was assembled from 75% water and 25% methanol (v:v). The flow rate was 0.25 mL/min, the injection volume was 10 μL and the column temperature was kept at 21˚C.

Analytical selectivity relates to the extent to which the method can be used to determine particular analytes in mixtures or matrices without interferences from other components of similar behavior [5] [12] [13] [14] [15] . The selectivity of the HPLC-UV method was evaluated by observing no peaks or distortions of the base line at the same retention time of caffeine when a blank sample was injected as it can be seen from Figure 1(a). The selectivity of the method was then demonstrated by spiking a blank sample and observing the peak of caffeine at 1.875 min with no other peaks interfered with it as it can be seen from Figure 1(b).

Linearity of an analytical method can be defined as the ability to produce measurement results proportional to a defined number of calibration points of a calibrant [5] [16] . A linear multipoint calibration curve was obtained by five concentrations of caffeine CRM as shown in Figure 2.

The concentration levels were evenly distributed and the calibration mode was achieved by external standard (ESTD) methodology. This methodology was selected because the sample preparation and the HPLC-UV response were very good. The linear model was expressed by Equation (1) which shows a relationship between the concentration and the response of HPLC-UV and has a slope (a) and intercept (b). The symbol ε is the standard error of the residuals [17] .

y = a x + b + ε (1)

By visual inspection of the calibration data, it can be noticed that this data does not suffer outliers or nonlinear trends. The quality of the regression line was also evaluated by the coefficient R², which ideally equals one, but values higher than 0.990 are considered adequate [8] . In our method, R² approached 1 indicating a very good fitting of the linear model [5] [17] . Furthermore, linearity was evaluated by plotting the residuals produced by linear regression, which allow inspection of errors in the variance as it can be seen in Figure 3. From this figure, it was noticed that the residuals are randomly distributed around zero giving rise to a good linearity of the calibration line [18] .

The limit of quantitation (LOQ) is defined as the lowest amount of an analyte in a sample that can be quantitatively measured with suitable accuracy and precision under experimental conditions established for the analytical method [3] . When the LOQ corresponds to the first level of the analytical curve, it can be referred to as the lower limit of quantification (LLoQ). The LOQ is expressed as concentration and should be reported associated with its precision and accuracy [19] [20] . In our method, the blank sample did not give a response area when injected into the HPLC-UV, therefore, the study of LOQ was conducted by spiking the blank with different concentrations of caffeine (15, 20, 25 and 30 ppb) and measuring the area of each concentration 10 times. The obtained area results were recorded in Table 1 and the average, SD and %RSD were calculated and recorded also in the same table. The LOQ is taken as the concentration value corresponding to an RSD value of approximately 5% at which quantification is considered to be with acceptable precision and accuracy. Looking to the %RSD values reported in Table 1, it can be noticed that the RSD value 4.069% resulting from the concentration 20 ppb can be taken as the LOQ of the method.

The limit of detection (LOD) is the lowest concentration of analyte in a sample that can be reliably detected and identified but not necessarily quantified. Since the concentration of the target caffeine sample which, is to be measured as a reference material was 25 mg/kg, it has been measured in the range 10 - 50 mg/kg. This 25 mg/kg concentration was large enough and can be detected by HPLC-UV with very good precision and accuracy. Therefore, estimation of the limit of detection (LOD) parameter is not necessary. However, it has been calculated as an information value by dividing the LOQ by 3.3 and was found 6 ppb.

Accuracy is defined as the closeness of agreement between a measured quantity

value and a true quantity value of a measurand [3] [5] . It can be assessed after confirmation of the method selectivity and determination of the linear range. Accuracy should be verified using three levels (low, medium, high) along the linear range. For this purpose, three samples of a caffeine reference material were prepared as 10, 30 and 50 mg/kg and each one was measured 10 times by HPLC-UV calibrated by the CRM. The value of (x_i) was calculated from the linear equation of the calibration curve and the percentage accuracy was calculated by dividing each value (x_i) by the value (x_CRM) and multiplying this ratio by 100 as in Equation (2).

%   A c u r a c y = x i x ( C R M ) × 100 (2)

The results obtained are shown in Tables 2-4 for 10 mg/kg, 30 mg/kg and 50 mg/kg respectively. Looking to the accuracy values, it can be realized that in case of the three studied concentrations, the lowest value was 99.20% and the largest value was 100.24%.

The precision of the method is defined as the closeness of agreement between indications or measured quantity values obtained by replicate [3] [5] . It accounts for systematic and random errors. Systematic errors can result from instrumental, personal or procedural mistakes and they are repeatable in a set of measurements deviating the measured results from the reference value. Meanwhile, random errors occur by unknown variables that lead to dispersion of the measured values and they are unrepeatable. According to the EURACHEM guide, precision of the method can be estimated by repeatability and intermediate precision [21] [22] . Three analysts have prepared three samples of concentrations, 25.14, 25.01 and 25.00 mg/kg. Every analyst has measured a sample 10 times by a calibrated HPLC-UV. The results obtained were recorded in Table 5 that shows the average and standard deviation by each analyst in addition to the grand mean.

In order to estimate the intermediate precision, the sets of results produced by the three analysts were analyzed by ANOVA one way and the results were shown in Table 6.

The standard deviation between groups, S_b was calculated by Equation (3) in which MS_b and MS_w are the mean square between and within groups respectively and n is the number of measurements [3] . The S_b was found 0.066 and was recorded in Table 7.

S between = M S b   − M S w n (3)

The standard deviation of the repeatability, S_r was calculated by Equation (4) as 0.044 and recorded in Table 7 [3] .

S r = M S w (4)

From the values of S_r and S_b, the intermediate precision S_I was calculated by Equation (5) as 0.082 and recorded in Table 7 [3] .

S I = S r 2 + S between 2 (5)

The precision expressed as %RSD was calculated by Equation (6) as 0.33 and recorded in Table 7.

% RSD = S I x ¯ ¯ × 100 (6)

The %RSD value, 0.33 was small giving rise to a very good precision of the method.

Recovery is defined as the proportion of the amount of analyte present in or added to the analytical portion of the test material, which is extracted and presented for measurement. Since the caffeine sample has been measured directly in water without extraction, the recovery of the method was studied by measuring a sample of concentration 25.14 mg/kg 10 times using a calibrated HPLC-UV and the results obtained were measured in Table 8. The average x ¯ was calculated and divided by the value x_CRM to obtain the % recovery as 99.78 % according to Equation (7).

%   Recovery = x ¯ x CRM × 100 (7)

The bias of the method was calculated using Equation (8) and was found 0.06 ppm and the %bias was calculated using Equation (9) and was found 0.22% [3] .

bias = x ¯ − x Ref (8)

bias ( % ) = x ¯ − x Ref x Ref × 100 (9)

The acceptance criteria of the bias was expressed in Equation (10) in which ơ is an uncertainty term, which was calculated by Equation (11) in which u_CRM is the uncertainty of the CRM used in the calibration of HPLC-UV and n is the number of measurements [23] [24] [25] . The u_CRM was calculated by dividing the expanded uncertainty 0.6% by 2.

− 2 σ ≤ b ≤ + 2 σ (10)

σ = ( S b ) 2 + ( S w n ) 2 + ( u CRM ) 2 (11)

Since the uncertainty of the CRM purity is in % and that of the S_b and S_w are in mg/kg, the uncertainty ratios (u_x/x) of the three contributions in Equation (11) were combined under the square root and multiplied by the grand mean (24.97 mg/kg) to express σ in mg/kg. The values of σ, +2σ and −2σ were recorded in Table 9. From these values, it can be noticed that no bias of the method was found since the observed bias (0.06 ppm) falls within ±2σ at confidence level 95%.