Replicated mosaic is an important way to make large size plane diffraction grating in astronomy. Considering cost control and grating development cycle, the mosaic system should be applicable to different parameters of grating and different test wavelengths. At the same time, the accuracy of the mosaic system must match the requirement. The mosaic error theory model is established based on the principle of Fraunhofer far field diffraction and the trend is analyzed and simulated when the wavelength of incident light, diffraction order, grating constant, and incident angle are changed. The variable range of above parameters is designed according to the actual mosaic demand. The mosaic error precision which can satisfy the usage requirement is computed when the grating parameters and detection conditions are changed. The simulation results will make a significant guidance for the replicated mosaic system design.