Battery energy storage systems (BESS) feature rapid response and strong regulation capabilities, making them effective in handling the intermittency of renewable energy. However, as the penetration of BESS increases, their failure characteristics pose a growing influence on power system reliability. To address this issue, this paper proposes a reliability assessment method for power system operation that explicitly accounts for BESS failures. First, a multi-dimensional performance degradation probability model of BESS is established using the generalized generating function. By integrating this model with the probability of thermal runaway failure, an available output power model that comprehensively considers BESS failure is established. Then, a load curtailment optimization model considering BESS is constructed. Furthermore, a Monte Carlo simulation-based reliability assessment method is proposed to capture both thermal runaway failures and multi-dimensional performance degradation of BESS. Finally, the effectiveness of the proposed method is verified through case studies in the IEEE RTS-79 bus system.