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A detailed study of hardware related tolerances for the undulator system for the European x-ray free-electron laser (XFEL) has been performed. Various realistic error scenarios were taken into account. These included girder deformation under magnetic loads, the influence of temperature variation, errors caused by limited accuracy of the motion control system, and phase matching errors. Undulator errors are classified into periodic and random errors. For periodic errors, such as girder deformation, a close and universal correlation between rms phase shake and power degradation was established, while the results of random errors show more scatter in the results, which have to be evaluated statistically. For XFEL parameters the correlation is very good and can be used to evaluate the influence of different error sources without the need to do extended FEL simulations. The method was applied to reevaluate some critical tolerances on the XFEL undulator systems: girder deformation, accuracy for gap control, and the requirement on temperature stability. The results show that these tolerances could be relaxed as compared to earlier work.