During the manufacturing process of a product, variability in its parts is unavoidable. Tolerance analysis allows estimating the consequences of the component's deviation of a mechanism on its functionality. Nowadays, it is possible to determine the contribution of each surface and/or contact on the final result in isostatic mechanisms by using the tools already presented in the literature; however, it is still a challenge to do so in over-constrained mechanisms. In previous works, we introduced a method based on prismatic polyhedra to model over-constrained mechanisms. In this paper, several simulations based on the previous approach are performed, varying the tolerances of the surfaces and contacts of the mechanism. The use of statistical methods to analyze the previous simulations’ data is proposed to quantify the contribution of local deviations with respect to the total variation of the mechanism. This analysis determines the most relevant contacts, hence the most critical parts of the mechanism. The process is applied to a pump as an over-constrained case study and uses the prismatic polyhedra method for tolerance analysis.