Abstract: As for model parameter uncertainty of the dual response surface model, the hierarchical structure among different parameters and the model heteroscedasticity problem, a new mean-variance dual response surface model is proposed by using the hierarchical Bayesian modeling method. The robust parameter design of product or process can be achieved based on the proposed method. Firstly, a hierarchical Bayesian model is established, and the posterior inference of the parameters is obtained based on the prior information. Secondly, uses Gibbs sampling to obtain an estimate of the parameters. Thirdly, the quality loss function is constructed based on the posterior samples and then the genetic algorithm is used to optimize the quality loss function to find the optimal parameter settings. Finally, starting from the two cases of the model with the same variance structure and heteroscedastic structure, the ordinary least squares, weighted least squares and hierarchical Bayesian model are used respectively to establish the double response surface models and further carry out the comparative analysis, which are used to verify the effectiveness of the proposed method.

Key words: hierarchical Bayesian model, dual response surface, lost function, Gibbs sampling, robust parameter design