Statistical reliability of a relative standard deviation of chromatographic peak area estimated by a chemometric tool based on the FUMI theory

Abstract

In pharmaceutical analysis using a high-performance liquid chromatography (HPLC) system, repeatability assessment is significant to obtain reliable and precise quantitative results. The purpose of the present study is to experimentally show the statistical reliability of a relative standard deviation (RSD) of peak area estimated by a chemometric tool based on probability theory, called the function of mutual information (FUMI) theory, which stochastically provided an RSD of peak area and SD of baseline areas with width k (s(k)) from noises and a signal on a single chromatogram. An ultra-high-performance liquid chromatography with ultraviolet detection (UHPLC-UV) for determining ergosterol was applied as an example of the repeatability assessment. In addition, the statistical reliability of an RSD of peak area in the UHPLC-UV system was certified according to a chi-square (χ2) distribution. The 712 values of s(k) were experimentally obtained from a data series of 1001 points in the noise regions of 712 chromatograms. The histogram of χ2 of s(k) was well-fitted to the χ2 distribution curve (freedom degree, ν = 50), indicating that the statistical reliability of an RSD of the peak area in the UHPLC-UV estimated by the FUMI theory (n = 1) was equivalent to that estimated by 50 runs of chromatographic measurements.