Statistics Decomposition and Monitoring in Original Variable Space

Abstract

AbstractThe traditional process monitoring method first projects the measured process data into the principle component subspace (PCS) and the residual subspace (RS), then calculates $$\mathrm T^2$$ T 2 and $$\mathrm SPE$$ S P E statistics to detect the abnormality. However, the abnormality by these two statistics are detected from the principle components of the process. Principle components actually have no specific physical meaning, and do not contribute directly to identify the fault variable and its root cause. Researchers have proposed many methods to identify the fault variable accurately based on the projection space. The most popular is contribution plot which measures the contribution of each process variable to the principal element (Wang et al. 2017; Luo et al. 2017; Liu and Chen 2014). Moreover, in order to determine the control limits of the two statistics, their probability distributions should be estimated or assumed as specific one. The fault identification by statistics is not intuitive enough to directly reflect the role and trend of each variable when the process changes.