Two blind analyses for $^{241}$Pu(nth,f) isobaric fission yields have been conducted, one analysis using a mix of a Monte-Carlo and an analytical method, the other one relying only on analytical calculations. The calculations have been derived from the same analysis path and experimental data, obtained on the LOHENGRIN mass spectrometer at the Institut Laue-Langevin. The comparison between the two analyses put into lights several biases and limits of each analysis and gives a comprehensive vision on the construction of the correlation matrix. It gives confidence in the analysis scheme used for the determination of the fission yields and their correlation matrix.