Precision nanopositioning is an important technology in industry and requires tight design specifications. Tolerances, although very small, are allocated in all dimensions of structures at devices and are understood as sources of performance variations. In this research, we aim to study detail influence of tolerances on various system response functions of a precision stage, especially parasitic motion and resonant frequencies. A function approximation moment method (FAMM) is developed and applied to study it. The variations are mathematically expressed as their statistical moments and the probabilities of satisfaction are obtained as a result of the FAMM. A finite element model of the target stage, which is nonmonolithic, is generated and verified with basic measurements. The possible initial deformation after assembly is found by the formulation of minimizing strain energy. With this model, the FAMM is used to estimate the statistical moments and probability density functions of the performance functions. The calculated results facilitate understanding of the characteristics of the stage in terms of probability. The inevitable mismatch, even under a small tolerance, is found to cause a large parasitic motion and should be considered in the design and manufacturing process. (c) 2006 American Institute of Physics.