Robust tolerance allocation using stochastic programming

Tolerance allocation in manufacturing is a prominent industrial task for enhancing productivity and reducing manufacturing costs. The classical tolerance allocation problem can be formulated as a stochastic program to determine the assignment of component tolerances such that the manufacturing cost is minimized. However, tolerance design is a prerequisite to the overall quality and cost of a product; robust tolerance design is particularly important and should be considered. In this paper, robustness is considered in formulating the tolerance allocation problem by minimizing the manufacturing cost's sensitivity. Moreover, from a practical perspective, the process capability index for each component and the upper bound of the manufacturing cost are also considered. To effectively and efficiently resolve the robust tolerance allocation problem, a sequential quadratic programming algorithm embedded with a Monte Carlo simulation is developed. To demonstrate this design method's robustness, two commonly used test problems are solved. The designs devised in this paper have lower manufacturing costs and smaller variations in manufacturing costs than those in previous studies, indicating that the proposed method is highly promising in the robust tolerance design.