Recognition of the circuit-breaker's (CB) vital role in reliable operation and protection of power systems (i.e., during energization, disconnecting loads, and clearing faults), helps to understand the requirement and importance of its maintenance management as well as maintenance scheduling. Condition-based maintenance (CBM), employing online monitoring (OLM) of CBs, has been long reported as the most practical maintenance policy on the power system CBs. There are a large number of CBs in a power system to be monitored; however, to address the financial limitations for OLM implementation (in utilities), a method will be proposed to find the most critical breakers for enforcing effectively the CBs CBM planning in this power system. This paper employs some qualitative and quantitative criteria to develop this method. While, the former criterion is deals with through assessing the condition of CBs through fuzzy sets theory. And the latter criterion is dealt with through the evaluation of CBs' influence on the overall system reliability (through introduced indices). This method is applied on a sample transmission substation with a breaker-and-a-half configuration. Numerical analysis of this simulation results demonstrates how this method can be employed to prioritize the CBs for OLM.