Directional MEWMA schemes for multistage process monitoring and diagnosis

Statistical process control, monitoring, and diagnosis of a multistage process remain challenging problems in both the manufacturing and service industries. This paper proposes a directional multivariate exponentially weighted moving average (directional MEWMA) scheme integrating the EWMA scheme with the generalized likelihood ratio test (GLRT) scheme that can incorporate directional information based on the multistage state-space model and effectively monitor the process mean shift. The proposed directional MEWMA scheme not only provides a statistical process control (SPC) solution that incorporates both interstage and intrastage correlations but also resolves the confounding issue in monitoring and diagnosis due to the cumulative effects from stage to stage. In addition, a systematic diagnostic approach is provided to isolate and identify an out-of-control stage and to locate its change point. Our simulation results show that the proposed monitoring and diagnostic scheme consistently outperforms almost all existing approaches to multistage processes. A sensitivity analysis and discussion on performance indicators for multistage process monitoring are also presented.