Spatial quantization error and displacement error are inherent in automated visual inspection. This kind of error introduces significant distortion and dimensional uncertainty in the inspection of a part. For example, centroid, area, perimeter, length, and orientation of parts are inspected by the vision inspection system. This paper discusses the effect of the spatial quantization error and the displacement error on the precision dimensional measurement of an edge segment of a 3D model. Probabilistic analysis in terms of the resolution of the image is developed for one dimensional and two dimensional quantization error. The mean and variance of these errors are derived. The position and orientation errors (displacement error) of the active vision sensor are assumed to be normally distributed. The probabilistic analysis utilizes these errors and the angle of the line projected on the image. Using this analysis, one can determine whether a given set of sensor setting parameters in an active system is suitable to obtain a desired accuracy for specific line segment dimensional measurements. In addition, based on this approach, one can determine sensor positions and viewing direction which meet the necessary range for tolerance and accuracy of inspection. These mechanisms are helpful for achieving effective, economic, and accurate active inspection.