Aiming at the multi-source uncertainties in the assembly and service process of spatial drive components, a non?probabilistic analysis method based on interval theory is introduced. A finite element model of the spatial drive component is established, and transmission error prediction data are obtained through assembly/service process simulation. Interval variables and a multidimensional ellipsoidal model are employed to characterize the correlation and uncertainty domain among multi?source uncertain assembly errors. A surrogate model is constructed to formulate the limit state function of the transmission error, based on which reliability and sensitivity analyses of the system are performed using non?probabilistic reliability theory. An interval process model is introduced, and the Karhunen–Loève (K?L) expansion is utilized to sample the vibration uncertainty during the service process. The sampled data are then used to inversely determine the interval process of the transmission error, enabling time?varying reliability and sensitivity analyses. The results indicate that the non?probabilistic reliability index (η=0.97) during the assembly process of the spatial drive component reveals a potential risk of failure, with the highest sensitivity observed to the cam eccentricity error along the x?axis. During the service process, the correlation time length significantly affects the fluctuation range of the transmission error. The bounds of the transmission error of the spatial drive component are 118–123″. The time?varying reliability index suggests that the transmission error may exceed the allowable limit at the 1?second mark.