2. Fluorimetric determination of quinine in tonic water

1.4. Uncertainty of the analytical assay from the in-house data of method validation

Again, according to EURACHEM [2], the trueness (bias) study can be performed

• by comparing the results of analyzed samples against a reference method; and

or spiked samples instead, and evaluating the recovery.

Thus, an estimation of the uncertainty of bias or recovery is calculated.

Intralaboratory assessment of method accuracy encompasses both precision and trueness

As EURACHEM guide advices [2], "the precision should be estimated as far as possible over an extended period of time." This may be accomplished by performing a between-day laboratory precision study. This precision study is carried out either by analyzing a typical sample, a quality control check sample or a validation standard [14] in "intermediate precision" conditions. Intermediate precision is the intralaboratory global precision under varied conditions as expected within a laboratory in a future assay. Accordingly, if a between-day precision study is carried out by spacing out the measurement days in such a way that the analysts, the apparatuses, glassware, stock solutions…really change, the precision estimation (from ANOVA) is a suitable "intermediate precision" estimation [14], leading to an evaluation of intermediate

• by repeated analysis of a certified reference materials (CRM), using the complete mea-

• by applying recovery assays, using spiked placebos (validation standards) when available

Both precision and trueness studies have to be carried out at least at three analyte concentration levels (low, medium and high) in order to cover the full range of analyte concentration

In his excellent paper, Kadis [13] discussed the double counting risk in the uncertainty budget when calibration uncertainty is considered together with the precision uncertainty.

calibration experiment. The estimated precision (from in-house validation) considers all the

tion uncertainty is redundant. Accordingly, the first term under the radical in Eq. (13) must be omitted to avoid double counting, or alternatively, the precision uncertainty can be omitted in the budget. Moreover, the recovery uncertainty includes the precision of the analyte mean value, which is used in the computation of recovery. Thus, some authors do not include the precision uncertainty together with the recovery uncertainty in the

The use of cause and effect diagrams for designing the uncertainty budget including the inhouse validation data is illustrated in the following worked example selected as case study.

sources of variability, including calibration, therefore the contribution of sx=<sup>y</sup>

<sup>b</sup>1<sup>m</sup> in Eq. 13 features the estimated precision of the analyte concentration in the

<sup>b</sup>1<sup>m</sup> in the calibra-

(precision and trueness)

114 Quality Control in Laboratory

precision uncertainty, uIP.

surement procedure;

indicated in the method scope.

The term sx=<sup>y</sup>

budget [13].

study.

This working example has been prepared from the papers of O'Reilly [15] and González and Herrador [14], and deals with the determination of quinine in tonic water samples from fluorescence measurements. Solutions that contain quinine in acid medium (0.05 M sulfuric acid) show fluorescence with a maximum excitation wavelength at 350 nm and a maximum emission wavelength at 450 nm. The determination of quinine in tonic water samples is carried out according to the following procedure [16]: 1 mL of tonic water (previously degassed by 15 min sonication in an ultrasonic bath) was pipetted into a 100 mL volumetric flask and dilute to the mark with 0.05 M sulfuric acid. The fluorescence intensity of this solution is measured in a fluorescence spectrometer in 10 mm pathway quartz cells at 350 nm excitation wavelength and at 450 nm emission wavelength. The quinine concentration is interpolated in the corresponding calibration curve. All analytical operations were done at 20 � 4�C.

The specification equation for estimating the quinine concentration (mg/L) in tonic water samples is given by

$$Z = \frac{\mathbb{C}\_{\text{cal}} V}{V\_0 \mathbb{R}} f\_{\text{prec}} \tag{15}$$

where Ccal is the value (mg/L of quinine) interpolated in the calibration curve from the measured fluorescence intensity of the assay, V is the volume of the assay (100 mL), V<sup>0</sup> is the sample volume (1 mL), R is the recovery of the assay and f prec is the factor corresponding to the assay precision which has a value of 1, but an uncertainty equals to the precision standard deviation of the Z measurement. Recovery and precision data are taken from the in-house validation study of the method. The corresponding cause and effect Ishikawa diagram is depicted in Figure 1.

Figure 1. Cause and effect diagram for the fluorimetric determination of quinine in tonic water.

According to the fishbone plot, the uncertainty budget is as follows:

$$\mu\_{\rm rel}^2(Z) = \mu\_{\rm rel}^2(\mathbb{C}\_{\rm cat}) + \sum\_{i=1}^5 \mu\_{\rm rel}^2(\mathbb{C}\_i) + \mu\_{\rm rel}^2(V) + \mu\_{\rm rel}^2(V\_0) + \mu\_{\rm rel}^2(R) + RSD\_{\rm proc}^2 \tag{16}$$

u Cð Þ¼ cal <sup>4</sup> � <sup>10</sup>�<sup>3</sup>

2 3

s

¼

(for delivering volumes from 0.1 to 0.6 mL) which is �0.006.

ð Þ <sup>0</sup>:<sup>006</sup> <sup>2</sup> 6 þ

ð Þ <sup>0</sup>:<sup>006</sup> <sup>2</sup> 6 þ

ð Þ <sup>0</sup>:<sup>006</sup> <sup>2</sup> 6 þ

ð Þ <sup>0</sup>:<sup>006</sup> <sup>2</sup> 6 þ

ð Þ <sup>0</sup>:<sup>006</sup> <sup>2</sup> 6 þ

ð Þ <sup>0</sup>:<sup>006</sup> <sup>2</sup> 6 þ

ð Þ <sup>0</sup>:<sup>3</sup> <sup>2</sup> 6 þ

ð Þ <sup>0</sup>:<sup>05</sup> <sup>2</sup> 6 þ

tion, Vs ¼ 1000mL and Vf ¼ 50mL. Accordingly, we get

s

s

s

s

s

s

s

s

ð Þ <sup>0</sup>:<sup>2</sup> <sup>2</sup> <sup>þ</sup>

3

u mð Þ¼ std

rectangular distribution. Thus, u Pð Þ¼ <sup>0</sup>:<sup>005</sup>ffiffi

u Vð Þ¼ <sup>1</sup>

u Vð Þ¼ <sup>2</sup>

u Vð Þ¼ <sup>3</sup>

u Vð Þ¼ <sup>4</sup>

u Vð Þ¼ <sup>5</sup>

u Vð Þ¼ <sup>6</sup>

u Vð Þ¼ <sup>s</sup>

u Vf � � <sup>¼</sup>

2.5 � <sup>10</sup>�<sup>6</sup> <sup>K</sup>�<sup>1</sup>

ΔT=4�. Thus, we have:

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

. The calibration certificate indicates an expanded uncertainty of 8 � <sup>10</sup>�<sup>4</sup> g with

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

std <sup>2</sup>:<sup>5</sup> � <sup>10</sup>�<sup>6</sup> � �<sup>2</sup>

<sup>18</sup> <sup>þ</sup> ð Þ Ccal � <sup>0</sup>:<sup>7</sup> <sup>2</sup> 2:1

> ð Þ<sup>4</sup> <sup>2</sup> <sup>9</sup> <sup>þ</sup> ð Þ <sup>0</sup>:<sup>4</sup> <sup>2</sup>

> > ; 0:432mg

. Uncertainty in volumes (from pipettes

http://dx.doi.org/10.5772/intechopen.72048

<sup>¼</sup> <sup>2</sup>:<sup>45</sup> � <sup>10</sup>�<sup>3</sup>

<sup>¼</sup> <sup>2</sup>:<sup>45</sup> � <sup>10</sup>�<sup>3</sup>

<sup>¼</sup> <sup>2</sup>:<sup>46</sup> � <sup>10</sup>�<sup>3</sup>

<sup>¼</sup> <sup>2</sup>:<sup>46</sup> � <sup>10</sup>�<sup>3</sup>

<sup>¼</sup> <sup>2</sup>:<sup>46</sup> � <sup>10</sup>�<sup>3</sup>

<sup>¼</sup> <sup>2</sup>:<sup>47</sup> � <sup>10</sup>�<sup>3</sup>

¼ 0:5

¼ 0:0317

(17)

117

1 3 þ 1

A Practical Way to ISO/GUM Measurement Uncertainty for Analytical Assays Including In-House Validation Data

Uncertainty due to preparation of working calibration standards is computed from Eq. (12). The uncertainty of the standard mass can be evaluated according to Eq. (7). In our case, the balance specifications were: Linearity ð Þ aL : 0.2 mg. Sensitivity temperature coefficient ð Þ aT :

a coverage factor, k = 2. Because the analytical operations are performed at 20� � 4�C and

m2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>0</sup>:<sup>187</sup> <sup>þ</sup> <sup>1</sup>:<sup>11</sup> � <sup>10</sup>�<sup>11</sup>m<sup>2</sup> std <sup>q</sup>

The uncertainty of purity is evaluated from the specification: 0.995 � 0.005 and assuming a

<sup>p</sup> <sup>¼</sup> <sup>2</sup>:<sup>9</sup> � <sup>10</sup>�<sup>3</sup>

or volumetric flasks) are calculated from Eq. (8). The corresponding tolerances for glassware laboratory (Class A) are gathered in Table 2, except for the class A graduated pipette of 1 mL

In the case of working standards, Vi ¼ 0:1, 0:2, 0:3, 0:4, 0:5 and 0.6 mL for each working solu-

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

<sup>2</sup>:<sup>1</sup> � <sup>10</sup>�<sup>4</sup> � �<sup>2</sup>

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

<sup>2</sup>:<sup>1</sup> � <sup>10</sup>�<sup>4</sup> � �<sup>2</sup>

<sup>2</sup>:<sup>1</sup> � <sup>10</sup>�<sup>4</sup> � �<sup>2</sup>

<sup>2</sup>:<sup>1</sup> � <sup>10</sup>�<sup>4</sup> � �<sup>2</sup>

<sup>2</sup>:<sup>1</sup> � <sup>10</sup>�<sup>4</sup> � �<sup>2</sup>

<sup>2</sup>:<sup>1</sup> � <sup>10</sup>�<sup>4</sup> � �<sup>2</sup>

<sup>2</sup>:<sup>1</sup> � <sup>10</sup>�<sup>4</sup> � �<sup>2</sup>

<sup>2</sup>:<sup>1</sup> � <sup>10</sup>�<sup>4</sup> � �<sup>2</sup>

3

3

3

3

3

3

3

3

0:12 ð Þ<sup>4</sup> <sup>2</sup>

0:22 ð Þ<sup>4</sup> <sup>2</sup>

0:32 ð Þ<sup>4</sup> <sup>2</sup>

0:42 ð Þ<sup>4</sup> <sup>2</sup>

0:52 ð Þ<sup>4</sup> <sup>2</sup>

0:62 ð Þ<sup>4</sup> <sup>2</sup>

1000<sup>2</sup> ð Þ<sup>4</sup> <sup>2</sup>

> 502 ð Þ<sup>4</sup> <sup>2</sup>

s

Now, each uncertainty contribution is studied and evaluated.

#### 2.1. Uncertainty coming from calibration and standards

In order to establish the corresponding calibration curve, a stock solution of quinine was prepared by weighing 121.6 mg of quinine sulfate dihydrate with a minimum purity of 99% (or 99.5 � 0.5%) and dissolving and diluting 0.05 M sulfuric acid to 1000 ml in a volumetric flask. The concentration of this stock solution corresponds to 100 mg/L of quinine base.

Six working standards solution covering from 0.2 to 1.2 mg/L quinine were prepared by pipetting 0.1, 0.2, 0.3, 0.4, 0.5 and 0.6 mL of the stock solution and diluting with 0.05 M sulfuric acid in a 50 mL volumetric flask, leading to concentrations of 0.2, 0.4, 0.6, 0.8, 1.0 and 1.2 mg/L quinine, respectively. The fluorescence intensity of each working standard at 350 nm excitation wavelength and at 450 nm emission wavelength was measured in triplicate. The results are shown in Table 1.

Fluorescence intensities show a linear behavior against the quinine concentration according to a calibration straight line with a correlation coefficient of about 0.999, and the following features:

$$b\_1 = 784.76, \ b\_0 = 13.67, \ s\_{\mathbf{x}/y} = 3.15, \ N = 18, \ \overline{C} = 0.7, \ \sum\_{i=1}^{18} \left( \mathbb{C}\_i - \overline{\mathbb{C}} \right)^2 = 2.1$$

The corresponding calibration uncertainty assuming that the analytical signal is measured in triplicate (m = 3) from Eq. (11) is given by:


Table 1. Fluorescence intensities (UA) for the five working standard solutions, measured in triplicate.

A Practical Way to ISO/GUM Measurement Uncertainty for Analytical Assays Including In-House Validation Data http://dx.doi.org/10.5772/intechopen.72048 117

$$
\mu(\mathbb{C}\_{\rm cal}) = 4 \times 10^{-3} \sqrt{\frac{1}{3} + \frac{1}{18} + \frac{\left(\mathbb{C}\_{\rm cal} - 0.7\right)^2}{2.1}} \tag{17}
$$

Uncertainty due to preparation of working calibration standards is computed from Eq. (12). The uncertainty of the standard mass can be evaluated according to Eq. (7). In our case, the balance specifications were: Linearity ð Þ aL : 0.2 mg. Sensitivity temperature coefficient ð Þ aT : 2.5 � <sup>10</sup>�<sup>6</sup> <sup>K</sup>�<sup>1</sup> . The calibration certificate indicates an expanded uncertainty of 8 � <sup>10</sup>�<sup>4</sup> g with a coverage factor, k = 2. Because the analytical operations are performed at 20� � 4�C and ΔT=4�. Thus, we have:

According to the fishbone plot, the uncertainty budget is as follows:

X 5

relð Þþ Ci <sup>u</sup><sup>2</sup>

In order to establish the corresponding calibration curve, a stock solution of quinine was prepared by weighing 121.6 mg of quinine sulfate dihydrate with a minimum purity of 99% (or 99.5 � 0.5%) and dissolving and diluting 0.05 M sulfuric acid to 1000 ml in a volumetric flask. The concentration of this stock solution corresponds to 100 mg/L of quinine base.

Six working standards solution covering from 0.2 to 1.2 mg/L quinine were prepared by pipetting 0.1, 0.2, 0.3, 0.4, 0.5 and 0.6 mL of the stock solution and diluting with 0.05 M sulfuric acid in a 50 mL volumetric flask, leading to concentrations of 0.2, 0.4, 0.6, 0.8, 1.0 and 1.2 mg/L quinine, respectively. The fluorescence intensity of each working standard at 350 nm excitation wavelength and at 450 nm emission wavelength was measured in triplicate. The results are

Fluorescence intensities show a linear behavior against the quinine concentration according to a calibration straight line with a correlation coefficient of about 0.999, and the following

The corresponding calibration uncertainty assuming that the analytical signal is measured in

<sup>b</sup><sup>1</sup> <sup>¼</sup> <sup>784</sup>:76, b<sup>0</sup> <sup>¼</sup> <sup>13</sup>:67, sx=<sup>y</sup> <sup>¼</sup> <sup>3</sup>:15, N <sup>¼</sup> <sup>18</sup>, <sup>C</sup> <sup>¼</sup> <sup>0</sup>:7, <sup>X</sup>

0.2 171 172 171 0.4 327 328 330 0.6 484 481 481 0.8 642 640 643 1.0 800 798 799 1.2 954 958 955

Table 1. Fluorescence intensities (UA) for the five working standard solutions, measured in triplicate.

relð Þþ <sup>V</sup> <sup>u</sup><sup>2</sup>

relð Þþ <sup>V</sup><sup>0</sup> <sup>u</sup><sup>2</sup>

relð Þþ <sup>R</sup> RSD<sup>2</sup>

18

Ci � <sup>C</sup> � �<sup>2</sup> <sup>¼</sup> <sup>2</sup>:<sup>1</sup>

i¼1

Trial 1 Trial 2 Trial 3

prec (16)

i¼1 u2

Now, each uncertainty contribution is studied and evaluated.

2.1. Uncertainty coming from calibration and standards

relð Þþ Ccal

u2

116 Quality Control in Laboratory

shown in Table 1.

triplicate (m = 3) from Eq. (11) is given by:

Working standard solution, mg/L Fluorescence, AU

features:

relð Þ¼ <sup>Z</sup> <sup>u</sup><sup>2</sup>

$$u(m\_{std}) = \sqrt{\frac{2}{3}(0.2)^2 + \frac{m\_{std}^2\left(2.5 \times 10^{-6}\right)^2 (4)^2}{9} + (0.4)^2}$$

$$= \sqrt{0.187 + 1.11 \times 10^{-11} m\_{std}^2} \, 0.432mg$$

The uncertainty of purity is evaluated from the specification: 0.995 � 0.005 and assuming a rectangular distribution. Thus, u Pð Þ¼ <sup>0</sup>:<sup>005</sup>ffiffi 3 <sup>p</sup> <sup>¼</sup> <sup>2</sup>:<sup>9</sup> � <sup>10</sup>�<sup>3</sup> . Uncertainty in volumes (from pipettes or volumetric flasks) are calculated from Eq. (8). The corresponding tolerances for glassware laboratory (Class A) are gathered in Table 2, except for the class A graduated pipette of 1 mL (for delivering volumes from 0.1 to 0.6 mL) which is �0.006.

In the case of working standards, Vi ¼ 0:1, 0:2, 0:3, 0:4, 0:5 and 0.6 mL for each working solution, Vs ¼ 1000mL and Vf ¼ 50mL. Accordingly, we get

$$\begin{aligned} u(V\_1) &= \sqrt{\frac{(0.006)^2}{6} + \frac{(2.1 \times 10^{-4})^2 0.1^2 (4)^2}{3}} = 2.45 \times 10^{-3} \\ u(V\_2) &= \sqrt{\frac{(0.006)^2}{6} + \frac{(2.1 \times 10^{-4})^2 0.2^2 (4)^2}{3}} = 2.45 \times 10^{-3} \\ u(V\_3) &= \sqrt{\frac{(0.006)^2}{6} + \frac{(2.1 \times 10^{-4})^2 0.3^2 (4)^2}{3}} = 2.46 \times 10^{-3} \\ u(V\_4) &= \sqrt{\frac{(0.006)^2}{6} + \frac{(2.1 \times 10^{-4})^2 0.4^2 (4)^2}{3}} = 2.46 \times 10^{-3} \\ u(V\_5) &= \sqrt{\frac{(0.006)^2}{6} + \frac{(2.1 \times 10^{-4})^2 0.5^2 (4)^2}{3}} = 2.46 \times 10^{-3} \\ u(V\_6) &= \sqrt{\frac{(0.006)^2}{6} + \frac{(2.1 \times 10^{-4})^2 0.6^2 (4)^2}{3}} = 2.47 \times 10^{-3} \\ u(V\_5) &= \sqrt{\frac{(0.3)^2}{6} + \frac{(2.1 \times 10^{-4})^2 1000^2 (4)^2}{3}} = 0.5 \\ u(V\_7) &= \sqrt{\frac{(0.05)^2}{6} + \frac{(2.1 \times 10^{-4})^2 50^2 (4)^2}{3}} = 0.0317 \end{aligned}$$


2.3. Uncertainty of precision and trueness from in-house validation

replications of the assay. The results obtained are presented in Table 3.

the values of variance due to the condition (here, days), S<sup>2</sup>

<sup>B</sup> � <sup>S</sup><sup>2</sup> W n

ð Þ¼ R

; S<sup>2</sup> <sup>r</sup> <sup>¼</sup> <sup>S</sup><sup>2</sup>

IP � <sup>n</sup> � <sup>1</sup> n S2 r pT<sup>2</sup> ; u<sup>2</sup>

S2

results (within conditions variance, S<sup>2</sup>

S2

<sup>R</sup> <sup>¼</sup> <sup>x</sup> <sup>T</sup> ; u<sup>2</sup>

Table 3. Tolerances for class A laboratory glassware.

<sup>r</sup> , the variance of intermediate precision, S<sup>2</sup>

condition <sup>¼</sup> <sup>S</sup><sup>2</sup>

their uncertainties can be easily computed [14, 18]:

S2

The study of precision (intermediate precision) and trueness (recovery of assay) for the fluorimetric determination of quinine in tonic water was performed by using validation standards (spiked placebos) as indicated by González and Herrador [16]. Validation standards of quinine in tonic water matrix were prepared at low (66 mg/L), medium (83 mg/L) and high level (100 mg/L), covering the whole range of analyte concentrations (from 80 to 120% of 83 mg/L of quinine that is the recommended value of quinine in tonic waters by the FAD [17]). Both precision and trueness study was performed by predicting the actual concentrations of the three spiked placebos according to the recommended fluorimetric procedure for quinine determination. Measurements were made on 5 days for each validation standard with three

A Practical Way to ISO/GUM Measurement Uncertainty for Analytical Assays Including In-House Validation Data

The best way to estimate both the uncertainty contribution of intermediate precision and the recovery (or bias) of the analytical assay when validation standards are available, is using ANOVA at a given concentration of the validation standard, namely T, considering p different conditions (5 days in this case) and n replications (3 days in this case). From the ANOVA

<sup>W</sup> ; S<sup>2</sup>

Class A glassware. Capacity, mL Tolerance, mL

Burette 50 � 0.05

Pipette 40–50 �0.05

Volumetric flask 1000 �0.3

IP <sup>¼</sup> <sup>S</sup><sup>2</sup>

relð Þ¼ R

<sup>W</sup> , between conditions variance, S<sup>2</sup>

<sup>r</sup> <sup>þ</sup> <sup>S</sup><sup>2</sup>

S2

<sup>B</sup>, and total mean, x),

(20)

119

condition, the variance of repeatability,

http://dx.doi.org/10.5772/intechopen.72048

IP <sup>¼</sup> <sup>S</sup><sup>2</sup> IP x 2

IP as well as the bias and recovery together with

condition; RSD<sup>2</sup>

IP � <sup>n</sup> � <sup>1</sup> n S2 r

> px 2

25 � 0.03 10 � 0.02

15–30 �0.03 8–10 �0.02 3–7 � 0.01 1–2 �0.006

500 �0.15 100 �0.08 50 �0.05 25 �0.03

Table 2. Predicted concentration of the spiked placebos expressed in mg/L quinine.

The total relative uncertainty of the working standards can be evaluated by avoiding multiple counting as follows:

$$\begin{split} u\_{rel}^2(\mathbf{C}\_i) &= \frac{u^2(m\_{std})}{m\_{std}^2} + \frac{u^2(P)}{P^2} + \sum\_{i=1}^6 \frac{u^2(V\_i)}{V\_i^2} + \frac{u^2(V\_s)}{V\_s^2} + \frac{u^2(V\_f)}{V\_f^2} \\ &= \frac{0.432^2}{121.6^2} + \frac{\left(2.9 \times 10^{-3}\right)^2}{0.995^2} + \frac{\left(2.45 \times 10^{-3}\right)^2}{0.1^2} + \frac{\left(2.45 \times 10^{-3}\right)^2}{0.2^2} \\ &+ \frac{\left(2.46 \times 10^{-3}\right)^2}{0.3^2} + \frac{\left(2.46 \times 10^{-3}\right)^2}{0.4^2} + \frac{\left(2.47 \times 10^{-3}\right)^2}{0.5^2} \frac{\left(2.47 \times 10^{-3}\right)^2}{0.6^2} \\ &+ \frac{0.5^2}{1000^2} + \frac{0.0317^2}{50^2} \\ &= 9.18 \times 10^{-4} \end{split} \tag{18}$$

#### 2.2. Uncertainty of assay and sample volumes

The uncertainties of the assay and sample volume are also estimated from Eq. (8) and tolerances of Table 2:

$$\begin{aligned} u(V) &= \sqrt{\frac{(0.08)^2}{6} + \frac{\left(2.1 \times 10^{-4}\right)^2 (100)^2 (4)^2}{3}} = 0.058\\ u\_{\text{rel}}^2(V) &= \frac{0.058^2}{100^2} = 3.36 \times 10^{-7} \\ u(V\_0) &= \sqrt{\frac{(0.006)^2}{6} + \frac{\left(2.1 \times 10^{-4}\right)^2 (1)^2 (4)^2}{3}} = 2.5 \times 10^{-3} \\ u\_{\text{rel}}^2(V\_0) &= \frac{\left(2.5 \times 10^{-3}\right)^2}{1^2} = 6.25 \times 10^{-6} \end{aligned} \tag{19}$$

#### 2.3. Uncertainty of precision and trueness from in-house validation

The study of precision (intermediate precision) and trueness (recovery of assay) for the fluorimetric determination of quinine in tonic water was performed by using validation standards (spiked placebos) as indicated by González and Herrador [16]. Validation standards of quinine in tonic water matrix were prepared at low (66 mg/L), medium (83 mg/L) and high level (100 mg/L), covering the whole range of analyte concentrations (from 80 to 120% of 83 mg/L of quinine that is the recommended value of quinine in tonic waters by the FAD [17]). Both precision and trueness study was performed by predicting the actual concentrations of the three spiked placebos according to the recommended fluorimetric procedure for quinine determination. Measurements were made on 5 days for each validation standard with three replications of the assay. The results obtained are presented in Table 3.

The best way to estimate both the uncertainty contribution of intermediate precision and the recovery (or bias) of the analytical assay when validation standards are available, is using ANOVA at a given concentration of the validation standard, namely T, considering p different conditions (5 days in this case) and n replications (3 days in this case). From the ANOVA results (within conditions variance, S<sup>2</sup> <sup>W</sup> , between conditions variance, S<sup>2</sup> <sup>B</sup>, and total mean, x), the values of variance due to the condition (here, days), S<sup>2</sup> condition, the variance of repeatability, S2 <sup>r</sup> , the variance of intermediate precision, S<sup>2</sup> IP as well as the bias and recovery together with their uncertainties can be easily computed [14, 18]:

$$\begin{aligned} S\_{\text{condition}}^2 &= \frac{S\_B^2 - S\_W^2}{n}; \ S\_r^2 = S\_W^2; \ S\_{lp}^2 = S\_r^2 + S\_{\text{condition}}^2; \text{RSD}\_{lp}^2 = \frac{S\_{lp}^2}{\overline{\overline{\mathbf{x}}^2}}\\ R &= \frac{\overline{\overline{\mathbf{x}}}}{T}; \ u^2(R) = \frac{S\_{lp}^2 - \frac{n-1}{n}S\_r^2}{pT^2}; \ u\_{nl}^2(R) = \frac{S\_{lp}^2 - \frac{n-1}{n}S\_r^2}{p\overline{\overline{\mathbf{x}}^2}} \end{aligned} \tag{20}$$


Table 3. Tolerances for class A laboratory glassware.

The total relative uncertainty of the working standards can be evaluated by avoiding multiple

 66 65.33 66.81 67.44 65.72 66.61 66 65.38 66.79 67.48 65.70 66.36 66 65.22 66.72 67.48 65.88 66.70 83 84.49 82.83 82.65 82.30 83.74 83 84.53 82.77 82.70 82.51 83.82 83 84.60 82.92 82.56 82.48 83.65 100 100.25 101.36 99.98 98.84 99.60 100 100.20 101.44 100.02 98.93 99.77 100 100.32 101.50 99.87 98.75 99.82

> <sup>u</sup><sup>2</sup>ð Þ Vs V2 s þ u<sup>2</sup> Vf � � V2 f

<sup>0</sup>:12 <sup>þ</sup>

<sup>2</sup>:<sup>45</sup> � <sup>10</sup>�<sup>3</sup> � �<sup>2</sup> 0:22

Day 1 Day 2 Day 3 Day 4 Day 5

<sup>2</sup>:<sup>47</sup> � <sup>10</sup>�<sup>3</sup> � �<sup>2</sup> 0:62

(18)

(19)

<sup>2</sup>:<sup>47</sup> � <sup>10</sup>�<sup>3</sup> � �<sup>2</sup> 0:52

<sup>2</sup>:<sup>45</sup> � <sup>10</sup>�<sup>3</sup> � �<sup>2</sup>

<sup>0</sup>:42 <sup>þ</sup>

The uncertainties of the assay and sample volume are also estimated from Eq. (8) and toler-

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

<sup>2</sup>:<sup>1</sup> � <sup>10</sup>�<sup>4</sup> � �<sup>2</sup>

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

<sup>12</sup> <sup>¼</sup> <sup>6</sup>:<sup>25</sup> � <sup>10</sup>�<sup>6</sup>

<sup>2</sup>:<sup>1</sup> � <sup>10</sup>�<sup>4</sup> � �<sup>2</sup>

<sup>1002</sup> <sup>¼</sup> <sup>3</sup>:<sup>36</sup> � <sup>10</sup>�<sup>7</sup>

ð Þ <sup>100</sup> <sup>2</sup>

ð Þ<sup>1</sup> <sup>2</sup> ð Þ<sup>4</sup> <sup>2</sup>

3

3

ð Þ<sup>4</sup> <sup>2</sup>

¼ 0:058

<sup>¼</sup> <sup>2</sup>:<sup>5</sup> � <sup>10</sup>�<sup>3</sup>

i¼1

<sup>2</sup>:<sup>9</sup> � <sup>10</sup>�<sup>3</sup> � �<sup>2</sup> <sup>0</sup>:995<sup>2</sup> <sup>þ</sup>

Table 2. Predicted concentration of the spiked placebos expressed in mg/L quinine.

<sup>2</sup>:<sup>46</sup> � <sup>10</sup>�<sup>3</sup> � �<sup>2</sup>

<sup>0</sup>:32 <sup>þ</sup>

Level Theoretical concentration Predicted concentration

0:0317<sup>2</sup> 502

> ð Þ <sup>0</sup>:<sup>08</sup> <sup>2</sup> 6 þ

> > ð Þ <sup>0</sup>:<sup>006</sup> <sup>2</sup> 6 þ

<sup>2</sup>:<sup>5</sup> � <sup>10</sup>�<sup>3</sup> � �<sup>2</sup>

s

relð Þ¼ <sup>V</sup> <sup>0</sup>:058<sup>2</sup>

s

<sup>u</sup><sup>2</sup>ð Þ Vi V2 i þ

<sup>2</sup>:<sup>46</sup> � <sup>10</sup>�<sup>3</sup> � �<sup>2</sup>

counting as follows:

118 Quality Control in Laboratory

<sup>u</sup><sup>2</sup>ð Þ mstd m<sup>2</sup> std þ <sup>u</sup><sup>2</sup>ð Þ <sup>P</sup> <sup>P</sup><sup>2</sup> <sup>þ</sup><sup>X</sup> 6

<sup>¼</sup> <sup>0</sup>:432<sup>2</sup> <sup>121</sup>:6<sup>2</sup> <sup>þ</sup>

þ

þ 0:52 10002 <sup>þ</sup>

<sup>¼</sup> <sup>9</sup>:<sup>18</sup> � <sup>10</sup>�<sup>4</sup>

2.2. Uncertainty of assay and sample volumes

u Vð Þ¼

u Vð Þ¼ <sup>0</sup>

u2

u2 relð Þ¼ V<sup>0</sup>

u2 relð Þ¼ Ci

ances of Table 2:


3. Selected applications in tabular form

examples drawn from multiple areas of science and technology.

for Guides in Metrology 'Evaluation of Measurement Data' documents.

with a fixed coverage probability.

chemistry to toxicology.

development of the GUM

derived constants.

Eurachem Guide on uncertainty evaluation.

traceability chain is also discussed.

measurement uncertainty.

uncertainty.

misguided.

A more detailed picture of most recent selected papers about the "Guide to the Expression of Uncertainty in Measurement" is depicted in Table 5, giving an idea of the importance and

A Practical Way to ISO/GUM Measurement Uncertainty for Analytical Assays Including In-House Validation Data

Content Authors Ref.

The GUM revision: the Bayesian view toward the expression of measurement uncertainty. Lira, 2016 [22]

Validating the applicability of the GUM procedure. Cox and Harris, 2014 [28]

Overview about statistical models and computation to evaluate measurement uncertainty. Possolo, 2014 [33]

Possolo and Iyer, 2017 [19]

121

http://dx.doi.org/10.5772/intechopen.72048

Synek, 2017 [20]

Bailey, 2016 [21]

Stant et al., 2016 [23]

White, 2016 [24]

Willink, 2016 [25]

Bich, 2014 [27]

Ehrlich, 2014 [29]

Ellison, 2014 [30]

Nielsen, 2014 [32]

Imai,2013 [34]

Saffaj et al., 2013 [35]

Farrance and Frenkel,

[26]

[31]

Ramsey and Ellison,

2015

2014

General overview about concepts, models, methods, and computations that are commonly used for the evaluation of measurement uncertainty, and their application in realistic

A complete procedure to encompass an uncorrected bias into the expanded uncertainty

Reported scientific uncertainties by analyzing 41,000 measurements of 3200 quantities from medicine, nuclear and particle physics, and interlaboratory comparisons ranging from

Comparing methods for evaluating measurement uncertainty given in the Joint Committee

Three controversies faced in the development of GUM document: (i) the acceptance of the existence of 'true values', (ii) the association of variances with systematic influences and (iii)

A new way to express uncertainty of measurement is proposed that allows for the fact that the distribution of values attributed to the measurand is sometimes approximately

Revision of the GUM: reasons why the Guide needed a revision, and why that revision

The developments in uncertainty concepts and practices that led to the third edition of the

In pursuit of a fit-for-purpose uncertainty guide: the move away from a frequentist treatment of measurement error to a Bayesian treatment of states of knowledge is

the representation of fixed but unknown quantities by probability distributions.

lognormal and therefore asymmetric around the measurement value.

could not go in a direction different from the one that it has been taken.

Evolution in thinking and its impact on the terminology that accompanied the

A review of monte carlo simulation using microsoft excel for the calculation of uncertainties through functional relationships, including uncertainties in empirically

Evaluation of mass measurements in accordance with the GUM. The importance of reporting calibration results in a compact way that is easily propagated down the

Discussion about recent situation in measurement science, and how to obtain a reliable measurement result using the expression of metrological traceability together with

A new strategy for the analytical validation based on the uncertainty profile as a graphical decision-making tool, and to exemplify a novel method to estimate the measurement

Table 4. Relative precision and uncertainty of recovery for the three validation standards in the fluorimetric determination of quinine in tonic water.

Thus, values of RSD<sup>2</sup> IP and u<sup>2</sup> relð Þ R are obtained for each spiked placebo. These data are presented in Table 4. A significance test has been used to evaluate if the recovery is significantly different from unity for each spiked placebo:

$$t = \frac{|1 - \mathcal{R}|}{\mu(\mathcal{R})}$$

This value is then compared with the two-tailed critical value of tabulated Student-t statistic for np-1 degrees of freedom (14 in our case) at a 95% confidence level ð Þ tcritð Þ¼ 14; 95% 2:145 . For the three studied validation standards, recoveries were significantly equal to unity, and we can set R ¼ 1 in all cases.

As can be seen in Eq. (20), the value of RSD<sup>2</sup> IP contains u<sup>2</sup> relð Þ R and accordingly, as it was indicated above, we can neglect the contribution u<sup>2</sup> relð Þ R in the uncertainty budget. The value of relative precision for the determined quinine concentration is taken as RSD<sup>2</sup> prec <sup>¼</sup> RSD<sup>2</sup> IP <sup>m</sup> (here, m = 3).

Now, all contributions of specification factors have been included in the budget. Consider now that a sample of tonic water (Schweppes) has been analyzed by following the recommended procedure. The response is measured in triplicate (m = 3), leading to a fluorescence intensity (AU) of 617.5, 618.1 and 616.7. The mean value is Y<sup>0</sup> ¼ 617:43 that corresponds to a quinine concentration of the assay of Ccal <sup>¼</sup> <sup>617</sup>:43�13:<sup>67</sup> <sup>784</sup>:<sup>76</sup> ¼ 0:76936. Accordingly, the value of calibration uncertainty from Eq. (17), but neglecting the radical term 1/3 in order to avoid double counting, gives u Cð Þ¼ cal <sup>10</sup>�<sup>3</sup> and <sup>u</sup><sup>2</sup> relð Þ¼ Ccal <sup>1</sup>:<sup>7</sup> � <sup>10</sup>�<sup>6</sup> . The concentration of quinine in the sample according Eq. (15) with R ¼ 1 and f prec ¼ 1 is Z = 76.936 ppm. We can interpolate this value in Table 4 in order to estimate the corresponding RSD<sup>2</sup> IP <sup>¼</sup> <sup>1</sup>:<sup>31</sup> � <sup>10</sup>�<sup>4</sup> that leads to RSD<sup>2</sup> prec <sup>¼</sup> <sup>1</sup>:31�10�<sup>4</sup> <sup>3</sup> <sup>¼</sup> <sup>4</sup>:<sup>38</sup> � <sup>10</sup>�<sup>5</sup> . Then, by applying Eq. (16), disregarding the recovery contribution, we get

$$\begin{split} \mu\_{\rm rel}^2(Z) &= \mu\_{\rm rel}^2(\mathcal{C}\_{\rm call}) + \mu\_{\rm rel}^2(\mathcal{C}\_i) + \mu\_{\rm rel}^2(V) + \mu\_{\rm rel}^2(V\_0) + RSD\_{\rm proc}^2 \\ &= 1.7 \times 10^{-6} + 9.18 \times 10^{-4} + 3.37 \times 10^{-7} + 6.25 \times 10^{-6} + 4.38 \times 10^{-5} \\ &= 0.00097 \end{split}$$

Thus, urelð Þ¼ Z 0:03115 and u Zð Þ¼ 76:936 � 0:03115 ¼ 2:396. By assuming a Gaussian coverage factor of 95% confidence k = 2, the expanded uncertainty is U Zð Þ¼ 4:792 and the quinine concentration of Schweppes tonic water sample is Z ¼ 77 � 5ppm.
