Optimal tolerance design of hierarchical products based on quality loss function

Taguchi’s loss function has been used for optimal tolerance design, but the traditional quadratic quality loss function is inappropriate in the tolerance design of hierarchical products, which are ubiquitous in industrial production. This study emphasizes hierarchical products and extends the traditional quality loss function on the basis of Taguchi’s quadratic loss function; the modified formulas are subsequently used to establish quality loss function models of the nominal-the-best, larger-the-better, and smaller-the-better characteristics of hierarchical products. An example is presented to demonstrate the application of the extended smaller-the-better characteristic loss function model to the optimal tolerance design of hierarchical products. Furthermore, the problem associated with selecting materials of various grades in the design process is discussed. The results show that the extended quality loss function model demonstrates good operability in the tolerance design of hierarchical products.