Optimization of engineering tolerance design using revised loss functions

Abstract

Engineering tolerance design plays an important role in modern manufacturing. Both symmetric and asymmetric tolerances are common in many manufacturing processes. Recently, various revised loss functions have been proposed for overcoming the drawbacks of Taguchi's loss function. In this article, Kapur's economic tolerance design model is modified and the economic specification limits for both symmetric and asymmetric losses are established. Three different loss functions are compared in the optimal symmetric and asymmetric tolerance design: a revised Taguchi quadratic loss function, an inverted normal loss function and a revised inverted normal loss function. The relationships among the three loss functions and process capability indices are established. A numerical example is given to compare the economic specification limits established by using the three loss functions. The results suggest that the revised inverted normal loss function be used in determining economic specification limits.

Keywords:

• symmetric and asymmetric tolerance design
• Taguchi's quadratic loss function
• inverted normal loss function
• revised inverted normal loss function

Acknowledgements

The first author would like to gratefully acknowledge financial support from the National Science Council of Taiwan.