Electro-thermal-compliant mechanisms are mechanisms onto which electric voltage is applied as input. This mechanism is based on the thermal expansion properties of the materials. This study considered all of the convection effects according to layouts produced after each topology optimization process. A new material mixing method based on bi-directional evolutionary structural optimization (BESO) was suggested to obtain optimal topologies for compliant mechanisms composed of two materials. Reliability-based topology optimization (RBTO) based on BESO was also applied to the topology optimizations of the mechanisms. Performance measurement approach (PMA), which estimates has probabilistic constraints that are formulated in terms of the reliability index, was adopted to evaluate the probabilistic constraints. The procedure has been tested in numerical applications, and the results were compared with those obtained by the level set and solid isotropic material with penalization (SIMP) methods for validation of the proposed approaches.