Power systems are designed to meet power demands of the communities with high reliability. Distributed generators (DGs) could play an essential role in improving the power system reliability and resilience. To date, influence of the uncertainty of the DGs to power system reliability has not been well addressed. Consequently, placement of the DGs considering reliability constraints may not be optimally conducted. This paper proposes reliability analysis and design of power systems under time-dependent load uncertainty and wind power generation uncertainty using an efficient uncertainty quantification (UQ) method, i.e., the eigenvector dimension reduction (EDR) method. Furthermore, binary particle swarm optimization (B-PSO) is proposed to address the optimal placement of DGs considering the reliability constraint. Two case studies, including an IEEE 14-bus power system and an IEEE 57-bus power system, are used to demonstrate the effectiveness of the proposed methodology.