Because of the service reliability problem of the cycloid-pin planetary transmission system of the precision reducer, the mechanical properties and elastic deformation of the key transmission components are considered, and the transmission components such as the sun gear, cycloid wheel and pin are flexibly processed to establish the rigid-flexible coupling dynamic model of the cycloid-pin planetary transmission system. Following this, the dynamic characteristics of the key transmission components are analyzed. The fuzzy functions and interval uncertainty methods are used to characterize the strength degradation process of key transmission components. The time-varying reliability models of the reducer's gear and bearing systems are established based on the stress-strength interference theory and the Weibull distribution. The influences of the strength degradation and the parameter uncertainty on the time-varying reliability and sensitivity of key transmission components for the cycloid-pin planetary transmission system are explored. Moreover, the cycloid-pin planetary transmission system's failure risk map is developed, laying the foundation for the design of a high-reliability and highly efficient cycloid-pin planetary reducer.