1.4. Uncertainty of the analytical assay from the in-house data of method validation (precision and trueness)

Intralaboratory assessment of method accuracy encompasses both precision and trueness study.

2. Fluorimetric determination of quinine in tonic water

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

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

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

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.

<sup>V</sup>0<sup>R</sup> <sup>f</sup> prec (15)

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

115

<sup>Z</sup> <sup>¼</sup> CcalV

corresponding calibration curve. All analytical operations were done at 20 � 4�C.

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

samples is given by

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 precision uncertainty, uIP.

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


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

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 indicated in the method scope.

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. The term sx=<sup>y</sup> <sup>b</sup>1<sup>m</sup> in Eq. 13 features the estimated precision of the analyte concentration in the calibration experiment. The estimated precision (from in-house validation) considers all the sources of variability, including calibration, therefore the contribution of sx=<sup>y</sup> <sup>b</sup>1<sup>m</sup> in the calibration 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 budget [13].

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.
