Model-based process monitoring using robust generalized linear models

Abstract

Model-based process-monitoring procedures are extremely useful in situations where an output variable of interest is impacted by one or more inputs to the process, and where there are multistage processes with multiple inputs and outputs. To build the model relating input and output variables, the procedure uses historical data, which often contain outliers. To accommodate the presence of these outliers, a robust fitting scheme is introduced for the Generalized Linear Model in process monitoring. Robust deviance residuals are defined and used as the basis of the monitoring procedure. An example and a simulation study for a gamma-distributed response are included. The average run length performance reveals that the procedure is effective for detecting small process shifts when outliers are present.

Keywords:

• Robust generalized linear models (GLMs)
• M-estimator
• Robust deviance
• Gamma-distributed data