Given the rapidly increasing turbine inlet temperature and aerodynamic loads, turbine endwalls are bearing exceptionally harsh flow and thermal conditions. Therefore, the turbine endwalls must be meticulously and efficiently designed, with special attention to the influences of geometric and operational uncertainties. This is of vital importance to the efficient and reliable operation of gas turbines. In this paper, a generic uncertainty analysis framework was established for different endwall schemes. Operational fluctuations of the mainstream and geometrical tolerances of the purge slot were taken as input uncertainties. The aero-thermal performance of a benchmark flat endwall and a non-axisymmetric endwall contouring (NEC) was statistically analyzed and compared under the propagation of the input uncertainties. Results showed that, despite the impact of the input uncertainties, the NEC endwall remained effective in enhancing the statistical performance of all three criteria. It was noteworthy that the NEC endwall also greatly reduced the sensitivity of the areas dominated by secondary vortices to the input uncertainties. However, its profiled regions were found to be highly sensitive to the input uncertainties. Furthermore, the influential uncertain parameters were also identified and compared for the flat and NEC endwalls. The inlet flow angle was the most significant parameter for the three performance criteria of the flat endwall. However, for the NEC endwall, the importance of the inlet flow angle was significantly reduced. Instead, the mainstream turbulence intensity became the most influential parameter for the aerodynamic and heat transfer performance, and the slot width became the most influential parameter for the film cooling performance. The underlying flow physics was well explained by CFD results.