This paper describes a procedure for the statistical analysis of geometric tolerances. The proposed procedure assumes that a manufactured surface lies between two ideal offset surfaces positioned at equal distance from the nominal surface. These surfaces do not represent a tolerance zone, but rather the volume which has the highest probability of containing a point on the generated surface. The generated surface is represented by a set of points, which are assumed to be random variables having a multinormal distribution. Using the generated points, the minimum deviation zone of each geometric deviation in each set is compared with the tolerances specified for the feature. Genetic algorithms are used to conduct these checks to ensure reaching the global optimum value of the minimum deviation zone. If the set of points is acceptable the Monte Carlo simulation is updated. To ensure that the probability of rejection of the feature due to the violation of the specified tolerances is calculated with a low variance of error, two methods of variance reduction techniques were used during the simulation. These are, Latin Hypercube Sampling and Antithetic Variates. An example for simulating a cylindrical feature is given at the end of the paper and the results of the algorithms using the proposed variance reduction techniques is compared with those using simple Monte Carlo simulation.
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