Chemometric evaluation of repeatability of internal standard methods in high-performance liquid chromatography with a Japanese pharmacopoeia assay for indomethacin as an example

•Uncertainty structures of internal standard (IS) method were elucidated.•In IS methods, precision profiles were obtained by applying the FUMI theory.•Statistical advantages of IS methods were experimentally and theoretically demonstrated.•An acceptable lower limit of IS amounts can be found from precision profiles.•Statistical efficacy of IS methods can be known from the precision profiles. The purpose of this study is to elucidate uncertainty structures of internal standard (IS) methods as compared with absolute calibration methods in liquid chromatography. A quantitative test of indomethacin with butyl 4-hydroxybenzoate as an IS in high-performance liquid chromatography with ultra-violet detection is taken here as an example. The repeatability is evaluated by both a usual statistical method of repetition and a theoretical approach, called the function of mutual information (FUMI) theory. The latter predicts the precision from noise and signals of instrumental output. Plots of relative standard deviations (RSDs) of measurements against analyte amounts, called precision profiles, are compared between the IS methods for indomethacin and their corresponding absolute calibration methods over a wide range of amount. Sample injection errors are observed to be effectively eliminated at high amounts by the IS methods, but at low amounts where background random noise dominates over the other error, the superiority of the IS methods is overshadowed and the precision of both the methods is almost comparable. The smallest possible amount of IS material without spoiling the integrity of analysis is estimated from the precision profiles.