  Charge-changing cross section ($\sigma_{\text{cc}}$) measurements via the
transmission method have made important progress recently aiming to determine
the charge radii of exotic nuclei. In this work, we report a new
$\sigma_{\text{cc}}$ measurement of 304(9) MeV/nucleon $^{28}$Si on carbon at
the second Radioactive Ion Beam Line in Lanzhou (RIBLL2) and describe the data
analysis procedure in detail. This procedure is essential to evaluate the
systematic uncertainty in the transmission method. The determined
$\sigma_{\mathrm{cc}}$ of 1125(11) mb is found to be consistent with the
existing data at similar energies. The present work will serve as a reference
in the $\sigma_{\text{cc}}$ determinations at RIBLL2.
