This paper explores the integration of the Lambert W function to a tolerance optimization problem with the assessment of costs incurred by both the customer and a manufacturer. By trading off manufacturing and rejection costs, and a quality loss, this paper shows how the Lambert W function, widely used in physics, can be efficiently applied to the tolerance optimization problem, which may be the first attempt in the literature related to tolerance optimization and synthesis. Using the concept of the Lambert W function, a closed-form solution is derived, which may serve as a means for quality practitioners to make a quick decision on their optimal tolerance without resorting to rigorous optimization procedures using numerical methods. A numerical example is illustrated and a sensitivity analysis is performed.
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