Studies of equilibrium breakdown were done for two flow problems representative of typical conditions for vehicles reentering the Earth atmosphere. The first studied problem was a 81 km Crew Exploration Vehicle (CEV) re-entry flow, with additional considerations for local flow features along the stagnation line. The second problem was a classical Couette flow, a volume of gas confined between two fast moving parallel plates of indefinite length and width. Both of the problems were solved by the DSMC technique with the particle velocity data collected to compute the distribution function at the areas of interest. In the case of stagnation line flow, a strong shock wave, formed in front of the vehicle at an altitude of 81 km was studied, and in the case of Couette flow, a high velocity boundary layer was examined in details at different Knudsen numbers. For both of the cases the Kolmogorov-Smirnov (K-S) test was applied to determine the degree of local flow non-equilibrium with following considerations regarding the applicability of coupled statistical BGK and DSMC techniques in the semi-rarefied flow regimes where the use of the baseline DSMC is limited due to the computational cost.