Assessment of T2- and Q-statistics for detecting additive and multiplicative faults in multivariate statistical process monitoring

The pioneering multivariate statistical process monitoring (MSPM) methods use the Q-statistic as an alternative for the T2-statistic to detect faults occurring in the residual subspace spanned by the process variables, since directly using T2 for this subspace can lead to numerical problems. Such use has also spread to current work in MSPM field. However, substantial improvement of computational resource has sufficiently mitigated the numerical problem, which, thus, leads to a need to assess their detectability when using in the same position. This paper seeks to solve this historical issue by examining the two statistics in light of the fault detection rate (FDR) index to assess their performance when detecting both additive and multiplicative faults. Theoretical and simulation results show that the two statistics have different impacts on computing the FDR. Furthermore, it is shown that, the T2-statistic performs, in terms of the FDR, better at detecting most additive and multiplicative faults. Finally, based on the achieved results, a remedy to the interpretation of traditional MSPM methods are given.