Multivariate detection limits with fixed probabilities of error

In this paper, a new approach to calculate multivariate detection limits (MDL) for the commonly used inverse calibration model is discussed. The derived estimator follows the latest recommendations of the International Union of Pure and Applied Chemistry (IUPAC) concerning the detection capabilities of analytical methods. Consequently, the new approach: (a) is based on the theory of hypothesis testing and takes into account the probabilities of false positive and false negative decisions, and (b) takes into account all the different sources of error, both in calibration and prediction steps, which affect the final result. The MDL is affected by the presence of other analytes in the sample to be analysed; therefore, it has a different value for each sample to be tested and so the proposed approach attempts to find whether the concentration derived from a given response can be detected or not at the fixed probabilities of error. The estimator has been validated with and applied to real samples analysed by NIR spectroscopy.