## 1 Introduction  
High-power transmission system technology is a core technology field for improving the performance of the heavy lift helicopter, reducing its noise and vibration levels, and controlling its life cycle cost [1]. Among the largest number of heavy lift helicopters currently in service, the large aviation planetary mechanism, as the basis and core of the transmission systems, determines the scientific and technological level of the transmission systems to a great extent, and is one of the bottlenecks restricting the development of transmission system technologies in the heavy lift helicopter [2]. As a deceleration terminal directly connected with the main rotor, the large aviation planetary mechanism is a power transmission link with the worst load environment and highest strength requirements in the heavy lift helicopter transmission system [3]. With the speed and bearing limits of the large aviation planetary mechanism continuing to break through, the structure and power sharing forms become more complex. These increase the complexity and uncertainty in structural strength design and analysis for the planetary system, and lead to a higher risk of structural failure when the new generation of heavy aviation planetary equipment pursues lightweight design [4]. Additionally, the transmission system is one of the three key dynamic systems in a helicopter. The reliability of its core link will directly determine the service safety and life cycle cost of the helicopter [5]. In terms of reliability analysis and modeling of gear transmission systems, [PERSON] [6] improved the ISO gear design specification, and proposed a tooth root bending fatigue damage analysis and modeling method for long-life large gears. [PERSON] [7] established a dynamic reliability model for gear systems under part life correlation conditions to give the variation law of system fatigue reliability with time and part-life correlation degree. [PERSON] [8] proposed a generic modeling and simulation framework for the reliability assessment of gear systems. There are also some related works [9; 10] that have carried out specific studies in terms of the relationship between systems and components, the way they achieve their functions, and temporal properties. The scholars have analyzed in detail the specificity of gearing in terms of system configuration, load transfer, and failure correlation from the perspective of reliability analysis and modeling. However, these current studies have heavily simplified the structural form of the gear system in reliability analysis processes, and it is difficult to reflect the way and degree of influence of the structural characteristics within the system on system reliability indexes. The stress-strength interference theory is a basic tool for reliability analysis of mechanical structures [11; 12; 13; 14]. [PERSON] [15] introduced an application of the stress-strength interference theory in fatigue reliability calculation for gear systems, and used the genetic algorithm to optimize the volume and reliability indexes for large-scale gear systems globally. During fatigue failure, the residual strength of a mechanical structure decreases continuously with the number of load actions, and the rate of strength decrease is directly related to the level of cyclic stresses [16]. In other words, for fatigue failure problems, the fatigue strength distribution at a specified life is a function of time and load, which is difficult to determine directly and efficiently by tests, whereas what is easily obtained directly by tests is the fatigue life distribution at a specified cyclic stress level [17; 18]. It can be seen that it is also necessary to propose a mathematical tool capable of calculating fatigue reliability directly based on the life probability distribution in the framework of the stress-strength interference theory.