Statistical process control for multistage processes with binary outputs

Statistical Process Control (SPC) including monitoring and diagnosis is very important and challenging for multistage processes with categorical data. This article proposes a Binary State Space Model (BSSM) for modeling multistage processes with binomial (binary) data and develops corresponding monitoring and diagnosis schemes by utilizing a hierarchical likelihood approach and directional information based on the BSSM. The proposed schemes not only provide an SPC solution that incorporates both interstage and intrastage correlations, but they also resolve the confounding issue in monitoring and diagnosis due to the cumulative effects from stage to stage. Simulation results show that the proposed schemes consistently outperform the existing χ2 scheme in monitoring and diagnosing for binomial multistage processes. An aluminum electrolytic capacitor example from the manufacturing industry is used to illustrate the implementation of the proposed approach.