Multivariate data modeling methods
The last chapter has introduced the principles of SPC and motivated the required multivariate extension to prevent excessive Type II errors if the recorded process variables are highly correlated. The aim of this chapter is to present different methods that generate a set of t-variables that are defined as score variables. Under the assumption that the process variables follow a multivariate Gaussian distribution, these score variables are statistically independent to circumvent increased levels of Type II errors. According to Figures 1.7 and 1.8, the generation of these score variables relies on projecting the recorded samples onto predefined directions in order to extract as much information from the recorded process variables as possible.
The data reduction techniques, introduced in the literature, are firmly based on the principle of establishing sets of latent variables that capture significant and important variation that is encapsulated within the recorded data. The score variables form part of these latent variable sets. For process monitoring, the variation that the latent variable sets extract from the recorded process variables is of fundamental importance for assessing product quality, process safety and, more generally, whether the process is in-statistical-control. These aspects are of ever growing importance to avert risks to the environment and to minimize pollution.
Data analysis and reduction techniques can be divided ...