Correlated multi‐response robust parameter design for different batches of products

Abstract

In the manufacturing process of products, it is common to produce in batches, and such complex products often have many interrelated processes and interdependent components. These lead to mutual correlations among multiple responses, correlations among response observations, and a complex relationship between inputs and responses. If aforementioned relationships cannot be addressed in the robust parameter design of batch products, it will influence the predictive precision of the model, subsequently impacting the reliability of the optimization results. To tackle the above three types of associations in products with batch effects, we propose a new approach, namely, the semiparametric mixed‐effects modeling approach for multi‐response correlation. Specifically, we begin by developing a multi‐response Bayesian semiparametric mixed‐effects model using spline, and then construct a multivariate loss function to obtain the optimal operating conditions, subsequently calculating the value of the entropy‐based weighted satisfaction function. The validity of the suggested method in modeling and optimization is verified through a simulation study and 3D printing example analysis.