Bayesian Fault Isolation in Multivariate Statistical Process Monitoring

Consider a set of multivariable input/output process data. Given a new observation we ask the following questions: is the new observation normal or abnormal? is one of the inputs or outputs abnormal (faulty) and which? Assuming a linear regression model of the process, the problem is solved through Bayesian hypothesis testing. The proposed formulation differs from existing multivariable statistical process control methods by taking uncertainty (variance) of the empirical regression model into account. The derived solution matches the established methods for anomaly detection and fault isolation in case there is no model uncertainty. Taking the model uncertainty into account, the proposed solution yields significant accuracy improvement compared to existing approaches. This is because ill-conditioned multivariable regression models can have large uncertainty even for large training data sets. The paper also demonstrates that isolating faults to a small ambiguity group works significantly better than the exact isolation.