Modeling the dependency structure between quality characteristics in multi-stage manufacturing processes with copula functions

This study is about multi-stage manufacturing processes and their control by statistical process control modeling. There are two kinds of dependence structures in a multi-stage manufacturing process: one is the dependence between the stages of the process, and the other is the dependence between the concerned quality characteristics. This study employs state-space models to demonstrate the dependency structure between the process stages and uses the Kalman filter method to estimate the states of the processes. In this setup, copula modeling is proposed to determine the dependence structure between the quality characteristics of interest. A simulation study is conducted to assess the model's accuracy. As a result, it was found that the model gives highly accurate predictions according to the mean absolute percentage error (MAPE) criteria (<10%).