Robust Parameter Design of Non‐Normal Correlated Multiple Responses via Bayesian SUR Modeling With Applications to 3D Printing Manufacturing Process

ABSTRACT An effective strategy to improve product quality is to construct an empirical model between input variables and output responses to determine the optimal parameter settings. However, many related studies ignore the high correlations and non‐normality between responses when constructing models. In practical quality design, multiple responses usually exhibit high correlation and non‐normality. To simultaneously consider the above quality characteristics, this paper proposes a robust parameter design (RPD) method based on the Bayesian seemingly unrelated regression (SUR) model. The proposed method addresses the correlations among responses and incorporates the skew‐normal distribution into the SUR model to consider the non‐normality of the responses. Then, we use Bayes' theorem to obtain posterior inferences for the model parameters and the Gibbs sampling method to obtain many posterior samples to estimate the model parameters and obtain the simulated response values. Finally, the desirability function is used as the optimization objective to find the optimal parameter settings. The proposed method has been applied to the 3D printing manufacturing process of Jiangsu Province Engineering Research Center of Quality Improvement for High‐end Equipment, and its validation test results show that the proposed method can still obtain relatively robust and reliable parameter optimization values when there are high correlation and skewed distribution characteristics among multiple responses.