Statistical Monitoring of Complex Multivariate Processes: With Applications in Industrial Process Control

Chapter 8

Monitoring changes in covariance structure

Over the past decades, many successful MSPC application studies have been reported in the literature, for example Al-Ghazzawi and Lennox (2008); Aparisi (1998); Duchesne et al. (2002); Knutson (1988), Kourti and MacGregor (1995, 1996), Kruger et al. (2001), MacGregor et al. (1991), Marcon et al. (2005), Piovoso and Kosanovich (1992), Raich and Çinar (1996), Sohn et al. (2005), Tates et al. (1999), Veltkamp (1993), Wilson (2001). This chapter shows that the conventional MSPC framework, however, may be insensitive to certain fault conditions that affect the underlying geometric relationships of the LV sets. Section 8.1 demonstrates that even substantial alterations in the geometry of the sample projections may not yield acceptance of the alternative hypothesis that the process is out-of-statistical-control.

As the construction of the model and residuals subspaces as well as the control ellipses/ellipsoid for PCA/PLS models originate from data covariance and cross-covariance matrices, this problem is referred to as a change in covariance structure. Any change in these matrices consequently affects the orientation of these subspaces. Thus, in order to detect such alterations, it is imperative to monitor changes in the underlying data covariance structure, which Section 8.2 highlights. This section also presents preliminaries of the statistical local approach that allows constructing non-negative squared statistics that directly relate ...