Retention time shift adjustments of two-way chromatograms using Besselʹs inequality

For two-way data (data stemming from so-called hyphenated methods), several methods have been developed for quantification of analytes. One of the better known methods is rank annihilation factor analysis (RAFA). However, an effect observed in chromatographic data seriously reduces the usability of this method. Like any other method based on the use of standards, RAFA fails to estimate the correct concentrations in the presence of retention time shifts. Hence, a retention time shift correction method is necessary. Besselʹs inequality can be used to adjust for the retention time shifting of the data relative to the standards. RAFA can then be used to estimate the concentrations with a high degree of precision. This procedure is demonstrated on four data sets of varying complexity, and is found to perform excellently for all sets.