Abstract: The ability to assess the reliability of safety-critical systems is one of the most crucial requirements in the design of modern safety-critical systems where even a minor failure can result in loss of life or irreparable damage to the environment. Model checking is an automatic technique that verifies or refutes system properties by exploring all reachable states (state space) of a model. In large and complex systems, it is probable that the state space explosion problem occurs. In exploring the state space of systems modeled by graph transformations, the rule applied on the current state specifies the rule that can perform on the next state. In other words, the allowed rule on the current state depends only on the applied rule on the previous state, not the ones on earlier states. This fact motivates us to use a Markov chain (MC) to capture this type of dependencies and applies the Estimation of Distribution Algorithm (EDA) to improve the quality of the MC. EDA is an evolutionary algorithm directing the search for the optimal solution by learning and sampling probabilistic models through the best individuals of a population at each generation. To show the effectiveness of the proposed approach, we implement it in GROOVE, an open source toolset for designing and model checking graph transformation systems. Experimental results confirm that the proposed approach has a high speed and accuracy in comparison with the existing meta-heuristic and evolutionary techniques in safety analysis of systems specified formally through graph transformations.