Quantifying Uncertainty in Analytical Measurements

Abstract

In providing chemical, biochemical and agricultural materials testing services for quality specification, the analytical chemists are increasingly required to address the fundamental issues related to the modern concepts of Chemical Metrology such as Method Validation, Traceability and Uncertainty of Measurements. Without this knowledge, the results cannot be recognized as a scientific fact with defined level of acceptability. According to ISO/IEC 17025:2005, this is an essential requirement of all testing laboratories to attain competence to test materials for the desired purpose. of these three concepts of chemical metrology, the most complex is the calculation of uncertainties from different sources associated with a single measurement and incorporate them into the final result(s) as the expanded uncertainty(U_E) with a defined level of reliability (e.g., at 95% CL). In this paper the concepts and practice of uncertainty calculation in analytical measurements are introduced by using the principles of statistics. The calculation procedure indentifies the primary sources of uncertainties and quantifies their respective contributions to the total uncertainty of the final results. The calculations are performed by using experimental data of Lead (Pb) analysis in soil by GF-AAS and pesticides analysis in wastewater by GC-MS method. The final result of the analytical measurement is expressed as: Result (mg/kg) = Measured Value of Analyte (mg/kg) ± Uncertainty (mg/kg), where the uncertainty is the parametric value associated with individual steps in measurements such as sample weighing(U_m), extraction of analyte (U_e) (Pb from soil or pesticides from water), volumetry in measurement (U_v), concentration calibration(U_x), etc. The propagation of these individual uncertainties from different sources is expressed as combined relative uncertainty (U_c), which is calculated by using the formula:

Combined uncertainty U_c/c = {(U_x/x)²+(U_m/m)²+(U_v/v)²+(U_e/e)²+…}^1/2

The overall uncertainty associated with the final result of the analyte is expressed as Expanded Uncertainty (U_E) at certain level of confidence (e.g. 95%). The Expanded Uncertainty is calculated by multiplication of Combined Uncertainty (U_c) with a coverage factor (K) according to the proposition of level of confidence. In general, the level of confidence for enormous data is considered at 95%, CL where K is 2. Hence, the final result of the analyte is expressed as: X ± U_E (unit) at 95% CL, where U_E = 2U_c.

Journal of Bangladesh Academy of Sciences, Vol. 41, No. 2, 145-163, 2017