Monitoring multivariate time-varying processes
As outlined in the first three chapters, MSPC relies on linear parametric PCA or PLS models that are time invariant. Such models, however, may become unrepresentative in describing the variable interrelationships some time after they were identified. Gallagher et al. (1997) pointed out that most industrial processes are time-varying and that the monitoring of such processes, therefore, requires the adaptation of PCA and PLS models to accommodate this behavior. In addition to the parametric models, the monitoring statistics, including their control limits, may also have to vary with time, as discussed in Wang et al. (2003). Another and very important requirement is that the adapted MSPC monitoring model must still be able to detect abnormal process behavior.
Focussing on PCA, this chapter discusses three techniques that allow an adaptation of the PCA model, Recursive PCA (RPCA), Moving Window PCA (MWPCA), and a combination of both. Embedding an adaptive PLS model for constructing the associated monitoring statistics, however, is a straightforward extension and is discussed in Section 7.7. The research literature discussed adaptive PLS algorithms, for example in Dayal and MacGregor (1997c); Helland et al. (1991); Qin (1998); Wang et al. (2003). For the non-causal data representation in (2.2) and the causal ones in (2.24) and (2.51), two properties are of particular interest: