Safety-critical systems must be shown to be acceptably safe to deploy and use in their operational environment. One of the key concerns of developing safety-critical systems is to understand how the system behaves in the presence of failures, regardless of whether that failure is triggered by the external environment or caused by internal errors. Safety assessment at the early stages of system development involves analysis of potential failures and their consequences. Increasingly, for complex systems, model-based safety assessment is becoming more widely used. In this paper we propose an approach for safety analysis based on system interface models. By extending interaction models on the system interface level with failure modes as well as relevant portions of the physical system to be controlled, automated support could be provided for much of the failure analysis. We focus on fault modeling and on how to compute minimal cut sets. Particularly, we explore state space reconstruction strategy and bounded searching technique to reduce the number of states that need to be analyzed, which remarkably improves the efficiency of cut sets searching algorithm.