Capability of discrimination: application to soft calibration methods

Abstract

Given a nominal concentration, in order to know the behaviour of an analytical procedure in samples with similar concentrations, the minimum discriminable concentration is defined as the smallest concentration of the analyte in a sample which can be distinguished, with probability 1− β, from the nominal value. This definition generalises the concept of minimum detectable net concentration established by ISO norm 11843 which is restricted to the case in which the nominal concentration is zero. Given an analytical procedure with a well-established net detectable concentration (detection limit), it may not be possible to discriminate this same concentration when the procedure is used in samples with a much higher nominal concentration. For this reason, the discrimination capability is a criterion for the selection of an analytical procedure when it is going to be used to determine concentrations well above its detection limit. The discrimination capability is established as a hypothesis test based on the data of a calibration carried out in a range of concentrations which contains the nominal value. As an application, the discrimination capability has been estimated when the concentration of a sample test is obtained by means of a partial least squares (PLS) calibration. In this case, the proposed procedure is composed of three steps, the first of which consists of the soft multivariate calibration. The second step is the evaluation of the discrimination capability by a regression of the concentration found with the multivariate calibration versus the true concentration of a new set of reference samples. The standard deviation of the regression estimates the repeatability (analytical procedure and soft calibration jointly) at the concentration range analysed in the regression. In the third step, the capability of discrimination calculated is applied to a new test sample if the repeatability has not changed at the level of concentration considered. The procedure developed has been applied to the determination of benzaldehyde by means of differential pulse polarography (DPP), where univariate calibration cannot be applied and a PLS calibration is appropriate. The capability of discrimination has been evaluated at two different concentration ranges: from 0.10 to 1.05 μM, and from 0.0199 to 0.1740 mM, with an estimated repeatability of 3.1×10 −2 μM and 3.2×10 −3 mM, respectively. The “ DPP+ PLS” capability of discrimination performance is analysed by means of the “false noncompliance” and the “false compliance” probability in the case that the analysis method has to discriminate differences lower than 10% of the nominal concentration with sufficient warranty.