Multi-response robust parameter design based on Bayesian mixed effects model

Abstract

In robust parameter design for blocked experiments, the correlation of response observations within each block and model parameter uncertainty often impact acquiring ideal operating conditions. In this paper, a Bayesian mixed regression-based multi-response surface modeling and optimization method is suggested to address the above issues. Firstly, the mixed effects model is incorporated into the Bayesian framework, and posterior distributions of the model parameters are derived using Bayes' theorem. Secondly, the hybrid Monte Carlo algorithm is employed to calculate the model parameters. Thirdly, the expected quality loss function satisfying the specification is constructed to lessen the impact of outliers on the results of optimization, and the optimal factor settings are obtained by the hybrid genetic algorithm. In addition, the posterior probability is used to assess the conformance of the optimization results. Finally, a simulated study and real-world example of the additive manufacturing process are used to illustrate the viability of the proposed method. Compared with the current techniques, the proposed method can reduce the impact of model uncertainty on the modeling and optimization results, leading to more conformant and robust optimization results.