Based on the reliability analysis of aviation equipment with maintenance-free operating period (MFOP), the fault-free operation ability and task completion rate of the equipment can be improved by rationally planning the maintenance intervals. At present, the calculation of MFOP reliability indicators only considers the random uncertain factors based on specific distributions. However, for complex aviation equipment systems, it is difficult to obtain sample data of some uncertain factors, making it impossible to accurately establish probability distributions. Moreover, the reliability results obtained based on the ideally assumed probability distributions entail substantial deviations. Therefore, the probability-interval hybrid uncertainty was introduced into the MFOP reliability analysis framework. For the uncertain factors with sufficient sample sizes, they were characterized in a probabilistic way; for the uncertain factors with scarce sample sizes, they were characterized in an interval way. At the same time, taking into account the correlations among uncertain factors, a reliability analysis method for aviation equipment systems considering multi-source uncertainty was proposed. Finally, through an analytical example with four uncertain parameters and an engineering example of the water-landing airbag buffer system for aviation equipment involving six uncertain parameters, the effectiveness of the proposed method was verified. The research results provide a theoretical basis for maintenance decisions of aviation equipment.