Vision based inspection systems for 3D measurements using single camera, are extensively used in several industries, today. Due to transportation and/or servicing of these systems, the camera in this system is prone to mis-alignment from its original position. In such situations, although a high quality calibration exists, the accuracy of 3D measurement is affected. In this paper, we propose a statistical tool or methodology which involves. a) Studying the significance of the effects of 3d measurements errors due to camera mis-alignment. b) Modelling the error data using regression models. c) Deducing expressions to determine tolerances of camera mis-alignment for an acceptable inaccuracy of the system. This tool can be used by any 3D measuring system using single camera. Resulting tolerances can be directly used for mechanical design of camera placement in the vision based inspection systems.