Improvement of the sensitivity of T2 quality control charts by variable grouping and dimension reducing

With increasing number of variables the Hotelling's T
²
statistic can detect only larger failures in the variables. A new method is introduced for reducing the dimension of the Hotelling's statistic in order to detect smaller failures. The basic idea is to group some variables into a combined variable and to calculate the T
²
value from this variable and from the remaining variables. As the new calculated variable has not a Gaussian distribution a proper static transformation is applied. Both uncorrelated and correlated data are dealt with. In the latter case principal component analysis is used before calculating T
²
. Several simulations show that the sensitivity of the new T
²
control charts is improved. The theory is confirmed by an application of sensor fault monitoring of a gas analyzer.