Least cost-tolerance allocation based on Lagrange multiplier

Industry-related competitiveness and reduction in manufacturing cost can be achieved by selection of ideal tolerance. Implementing non-traditional techniques for tolerance allocation to various parts in a mechanical assembly is an enervating procedure. Analytical methods are implemented to obtain creditable design. The main objective of this article is to minimize the manufacturing cost, quality loss, and TRSS (root sum square tolerance) for complex mechanical assemblies. The proposed methodology deals with the reciprocal exponential function. Hence, it is used to solve the problem for obtaining the closed-form solution by Lagrange multiplier method which integrates Lambert W function. The illustrations used in the research article demonstrate the feasibility and effectiveness of the traditional approaches. The results obtained also show that tolerance can be allocated economically and precisely. Here, non-traditional optimization methods are correlated and finally their performances are analyzed.