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

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 (UHPLCUV) 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 (chi 2) 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 chi 2 of s(k) was well-fitted to the chi 2 distribution curve (freedom degree, upsilon = 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.