Recent experiments focused on the hypersonic boundary-layer transition process have been conducted at Japan Aerospace Exploration Agency's free-piston High Enthalpy Shock Tunnel facility. Numerical simulations of the experiments were conducted to generate mean-flow solutions upon which boundary-layer stability analyses were performed. These computations included the effects of chemical reactions and internal energy relaxation. The disturbances in the boundary layer were calculated by solving the linear parabolized stability equations. Comparisons of transition location, disturbance amplification rates, and disturbance frequencies were made between those measured experimentally and those calculated from the stability analysis. The results suggest that an N factor of 8.0 is the value that indicates the onset of transition for this facility. A disturbance frequency comparison between the computations and experiment showed a reasonable agreement for the locations at which the flow remained laminar. Additional theoretical operational conditions were examined to investigate effects of finite-rate chemistry and vibrational excitation. For the conditions examined, the inclusion or exclusion of chemical kinetics modeling in the mean-flow solution influenced boundary-layer stability to a greater extent than the inclusion or exclusion of chemical kinetics in the stability analysis alone. In general, the inclusion of these effects increased disturbance frequencies, peak amplification rates, and the distance over which the disturbance frequencies were amplified.