Optimal tolerance allocation with loss functions

The tolerance allocation problem is formulated as a nonlinear integer model under the constraints of process capability. The problem is to minimize the sum of machining cost and quality loss. When the statistical tolerance limits are used and Taguchi's quadratic loss function is defined, the total cost function becomes a convex function for a given feature and process. A complex search method is used to solve the model and ensure the optimal tolerance allocation. Numerical examples are presented demonstrating successful model implementation for both linear and nonlinear design functions.