Abstract
The T2 statistic associated with an observation from a multivariate process is a function of the residuals taken from a set of linear regressions existing among the various process variables. These residuals are contained in the conditional T2 terms of the orthogonal decomposition of the statistic. It is shown in this paper that a large residual in one of these fitted models can be due to incorrect model specification. By improving model specification at the time that the historical data set is constructed, it may be possible to increase the sensitivity of the T2 statistic to signal detection. The resulting regression residuals also can be used to improve the sensitivity of the T2 statistic to small but consistent process shifts. This is accomplished using plots that are similar to cause-selecting control charts.
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