Machine vision inspection systems are on the threshold of becoming commercial. Their great advantage is that they can be used to check the geometric quality of parts that are too complex for human inspectors. Their great disadvantage is that they are too slow, partly because they process vast amounts of data and computation times, therefore, are too long. This work will result in ways to get around this problem, using statistical sampling to reduce, rationally, the amount of data required to assure part quality. The scope of the work is restricted to the basic measurements of straightness and roundness. The approach is to develop a mathematical relationship between sample size and inspection accuracy. Next, a relationship will be established between sample size and processing time for selected machine vision systems. Then criteria will be established for selection of a proper sampling method. These will be put into forms easily referenced by quality assurance practitioners. Sample size will be stated in terms of number of scans across the test part, and number of points within each scan. Inspection accuracy will be expressed in terms of the size of the confidence interval (error) of the measured quality characteristics.