A closed-form method for statistical tolerance allocation considering quality loss and different kinds of manufacturing cost functions

  • Shaogang Liu
  • Qiu Jin
  • Yinghuai Dong
  • Yan Wang


In order to specify proper tolerances in the product design process, the tolerance optimization model should be established properly and solved accurately. In this paper, several kinds of widely used manufacturing cost functions, including exponential function, reciprocal power function, and polynomial function, are considered simultaneously to calculate the manufacturing cost of different components. Then, the most suitable manufacturing cost function for each component is chosen so that the fitting error is minimized. After the manufacturing cost functions are determined, the tolerance optimization model is established to minimize the total cost including manufacturing cost and quality loss. In the tolerance optimization model, both assembly tolerance constraint and process accuracy constraints are considered. In order to solve the tolerance optimization model accurately, the Lagrange multiplier method is applied and closed-form solutions of optimal tolerances are established. The calculating results demonstrate that the proposed method has high accuracy.


Manufacturing cost Quality loss Lagrange multiplier method Closed-form solution 


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Copyright information

© Springer-Verlag London Ltd. 2017

Authors and Affiliations

  • Shaogang Liu
    • 1
  • Qiu Jin
    • 1
  • Yinghuai Dong
    • 1
  • Yan Wang
    • 1
  1. 1.Tianjin Key Laboratory of Integrated Design and On-line Monitoring for Light Industry & Food Machinery and Equipment, College of Mechanical EngineeringTianjin University of Science & TechnologyTianjinChina

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