Optimization for statistical tolerance allocation

Abstract

We present a scheme for tolerance allocation in any dimensions based on a statistical tolerance model. People commonly use tolerances to account for uncertainty and errors in the modeling and manufacturing process. Tolerance allocation refers to the process of arranging tolerance values across an object in order to meet some overall requirements. Statistical tolerance models treat variations as some form of statistical distribution. We treat allocation as an optimization problem where we need to define both constraints and an objective function. With the statistical tolerance model, the calculation of the tolerance stack-up through the cascading of tolerance zones is straightforward. Constraints can be defined on the cascaded result. We present a general approach to optimization that allows different objective functions to be used to achieve different goals. Specific objective functions are described as examples. Finally, we present an effective method for solving the allocation problems in our scheme with these different functions. We demonstrate how the scheme works and its advantages on a small set of examples.