Simultaneous multi-response optimisation for parameter and tolerance design using Bayesian modelling method

In the study of simultaneous optimisation of parameter and tolerance design with multiple quality characteristics, the existing modelling methods rarely consider the influence of the response variability related to the model parameter uncertainty and other random errors on the optimisation results. In this paper, an integrated total cost model, including the tolerance cost, quality loss, and rejection cost is proposed to deal with the above issue in a unified framework of Bayesian modelling and optimisation. The proposed method not only considers the model parameter uncertainty but also considers the change of design factors within the limited tolerances through using the Bayesian modelling method. Moreover, the quality loss function and the rejection cost (i.e. scrap cost and rework cost) function are established by using the posterior samples of simulated responses, respectively. Finally, the total cost function is minimised by using a hybrid genetic algorithm to find the optimal parameter settings and tolerance values. Two examples illustrate the advantages of the proposed method in this paper. The results show that the proposed approach may give more reasonable solutions than the existing approaches when considering the variability of predictive responses and the change of design factors.