Practical method of cost-based tolerancing

The tolerances are given to keep the performance criteria within the acceptable values in the manufactured lenses. If the tolerances and the performance criteria are given, the yield of the manufacturing can be estimated with the Monte Carlo simulation. The tolerance determines the manufacturing cost. The manufacturing cost should be as low as possible. The cost-based tolerancing is to determine the tolerances accounting for the manufacturing cost. This optimization problem looks complicated and time-consuming when the yield is viewed as a function of the tolerances. The author found the problem is dramatically simplified if the variances or averages of the critical performance criteria are used as the independent variables of the optimization. The optimal tolerance set can be found with a few trials of the Monte Carlo simulation.