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In complex systems, there are few critical failure modes. Prognostic models are focused at predicting the evolution of those critical faults, assuming that other subsystems in the same system are performing according to their design specifications. In practice, however, all the subsystems are undergoing deterioration that might accelerate the time evolution of the critical fault mode. This paper aims at analyzing this aspect, i.e. interaction between different fault modes in various subsystems, of the failure prognostic problem. The application domain focuses on an aero propulsion system of the turbofan type. Creep in the high-pressure turbine blade is one of the most critical failure modes of aircraft engines. The effects of health deterioration of low-pressure compressor and high-pressure compressor on creep damage of high-pressure turbine blades are investigated and modeled.