Understanding PCA fault detection results by using expectation analysis method

Substantial statistical process monitoring approaches based on principal component analysis (PCA) have been presented in recent years. However, the nature of the fault detection behaviour of PCA is still equivocal and sometime leads to incorrect understanding of PCA detection results. This issue is explored in this paper using expectation analysis method. The expectation formulas of T^Q and SPE statistics are developed and their relations with the statistical parameters of process variables are revealed, respectively. Then different PCA detection behaviours in the cases of process disturbances and faults are discussed. The acquired results are verified by monitoring a double-effective evaporator process.