In complex mechanical systems involving multiple parts and contact interfaces, failure modes are not only statistically correlated but may also interact through underlying physical mechanisms. These interactions, often neglected in current reliability analysis, can lead to significant deviations in failure predictions, especially in rotor systems and actuators. Taking aeroengine turbine rotor assemblies as an example, multiple failure modes, such as wear, fatigue and slip at contact interfaces, affect key mechanical property parameters including assembly preload, cylindrical interference fit and cooling performance. These variations lead to evolving stress/strain and temperature fields with increasing load cycles, thereby inducing physical interactions among different failure modes. This study systematically analyzes the interaction mechanisms among multiple failure modes within a turbine rotor assembly. A mechanics model is established to quantify these interactions and their effects on failure evolution. Furthermore, a time-dependent reliability evaluation method is proposed based on Monte Carlo simulation and the Probability Network Evaluation Technique. A case study illustrates that both continuous-type and trigger-type interactions significantly affect the failure probabilities of wear and low-cycle fatigue. The results emphasize the necessity of accounting for interaction of multi-failure modes to improve the accuracy of failure prediction and enhance the design reliability of turbine rotor assemblies.