The Thyristor-controlled phase-shifting transformer (TCPST), a member of the flexible AC transmission systems (FACTS) family, offers an effective solution for mitigating transmission congestion while enhancing power system security and reliability. This paper introduces an innovative framework for determining the optimal location of TCPST to improve power system reliability under uncertainty. The proposed method accounts for power system uncertainties, including the availability of generation units and network components, modeled using forced outage rates (FORs) through scenario generation based on Monte Carlo simulation (MCS). To address the non-convex nature of the resulting mixed-integer non-linear programming problem, a linear approximation of power flow equations is employed, transforming the problem into a mixed-integer linear programming (MILP) formulation. The objective is to minimize load curtailment by identifying the optimal TCPST locations across different scenarios. The results are then ranked based on their contribution to reliability improvement, using the Probability of Load Curtailment (PLC) index. Extensive numerical studies on a modified reliability test system (RTS) demonstrate the efficacy of the proposed approach. Results show a 17.14% reduction in the annual Expected Energy Not Supplied (EENS) (from 646,640 MWh/year to 535,805 MWh/year) and a 25.29% improvement in the PLC index (from 0.344 to 0.257). These findings validate the effectiveness of the proposed stochastic optimization framework in enhancing power system reliability under uncertain conditions.