A New Fuzzy Set Approach to the Tolerance Analysis and Parameter Design Problems

Abstract

Tolerance is believed to be unavoidable and necessary in engineering design and manufacturing due to universal randomness. The Tolerance Analysis and Parameter Design problems are therefore critical to quality control in the modern engineering context. Both the tolerance analysis and the parameter design problem have been studied and explored over the past decades with success. However, most of them use probability theory and statistical methods, and there are drawbacks or restrictions to these approaches.

We tackle down these problems from a new perspective using fuzzy set technology. We model the tolerance in the manufacturing process as fuzzy variables instead of using conventional random variables to represent the process uncertainty and imprecision. We develop and present a new approach to the tolerance analysis problem and also a new mathematical model to solve the parameter design problem in the fuzzy environment, respectively. Finally we present several case studies for both problems. Numerical results show that the new approach and model generate consistent and compatible results with conventional methods.