Given the current trend of reviving the power system, which is considered by competitive markets, the privatization of the power system is forcing them to develop the necessary decision-making policies from a technical and economic point of view to improve their asset management practices. Reliability-centered maintenance is an efficient process to consider these two important aspects, i.e. technical and economic ones when performing maintenance optimization. This paper proposes a new technique to solve the actual stochastic Multi-Criteria Decision-Making (MCDM) problems with uncertain weight information using a combination of Stochastic Multi-Criteria Acceptability Analysis (SMAA) and Elimination Et Choice Translating Reality (ELECTREIII) methods combined with gray system theory. In maintenance planning, gray system theory is used to determine the specific types of power system components that should receive the most attention. Then, the optimal maintenance strategy of every critical component is determined by recognizing the lowest costs associated with various strategies. The suggested framework demonstrates its relevance and efficacy for actual asset management optimizations in electric power systems, as demonstrated in the IEEE 14-bus test system.