Regression-based process monitoring with consideration of measurement errors

Multivariate process monitoring and fault detection is an important problem in quality improvement. Most existing methods are based on a common assumption that the measured values of variables are the true values, with limited consideration of the various types of measurement errors embedded in the data. On the other hand, research on measurement errors has been conducted from a pure theoretical statistics point of view, without any linking of the modeling and analysis of measurement errors with monitoring and fault detection objectives. This paper proposes a method for multivariate process monitoring and fault detection considering four types of major measurement errors, including sensor bias, sensitivity, noise and dependency of the relationship between a variable and its measured value on some other variables. This method includes the design of new control charts based on data with measurement errors, and identification of the maximum allowable measurement errors to fulfill certain fault detectability requirements. This method is applicable to processes where the natural ordering of the variables is known, such as for cascade or multistage processes, and processes where the causal relationships among variables are known and can be described by a Bayesian network. The method is demonstrated in two industrial processes.