Overview: MVPMODEL Procedure

The MVPMODEL procedure is used in conjunction with the MVPMONITOR procedure to monitor multivariate process variation over time in order to determine whether the process is stable or to detect changes in a stable process.

The MVPMODEL procedure provides computational and graphical tools for building a principal components model from multivariate process data in which the measured variables are continuous and correlated. This model then serves as input to the MVPMONITOR procedure, described in Chapter 11, The MVPMONITOR Procedure. The MVPMONITOR procedure creates various multivariate control charts, including charts and SPE (squared prediction error) charts, which are used to detect and diagnose changes in the process. Multivariate control charts can detect unusual variation which would not be uncovered by individually monitoring the variables with univariate control charts, such as Shewhart charts.

The MVPMODEL procedure implements principal components analysis (PCA) techniques which evolved in the field of chemometrics for monitoring hundreds or even thousands of correlated process variables; refer to Kourti and MacGregor (1995, 1996) for an introduction. These techniques differ from the classical multivariate chart in which Hotelling’s statistic is computed as a distance from the multivariate mean scaled by the covariance matrix of the variables; refer to Alt (1985). Instead, principal component methods compute based on a small number of principal components that model most of the variation in the data.

One advantage of PCA methods over the classical chart is that they avoid computational issues that arise when the process measurement variables are collinear and their covariance matrix is nearly singular. A second advantage is that they offer diagnostic tools for interpreting unusual values of . A third advantage is that by projecting the data to a low-dimensional subspace, a PCA model more adequately describes the variation in a multivariate process, which is often driven by a small number of underlying factors that are not directly observable.