The traditional Taguchi product optimization design should be tested many times and has high manufacturing cost. Therefore

we introduce the asymmetric quality loss and the parameter and tolerance concurrent design method with the process capability index considered. The concurrent design can effectively save the high manufacturing cost while ensuring the product quality. Firstly

the central composite experimental design is carried out

and then the response surface model of mean and variance is established with the experimental data. Then the asymmetric quality loss function is proposed and the tolerance cost model is established according to the empirical data. The improved process capability index is constructed. Finally

the asymmetric quality loss function and tolerance cost model are substituted into the process capability index function

which is optimized with the improved genetic algorithm (NSGA - Ⅱ). At the same time

the parameters and their tolerance combinations are obtained. The numerical analysis of bridge amplification mechanism tests shows that this method improves the quality and performance of products and reduces the production and operation costs.