ABSTRACT
The most popular multivariate control chart is based on the T2 statistic and is sometimes referred to as the multivariate Shewhart chart. It was developed by Hotelling, who was among the first statisticians to note the inefficiency of using multiple univariate control charts when the variables of interest are correlated. The Euclidean distance between two multivariate observations is related to the familiar geometric concept of straight-line length. It is a function only of the magnitude of the distance between the points. Control charts used to detect shifts in a process mean may be designed to monitor sample or subgroup means or to monitor individual observations. The power of a statistical hypothesis test is defined to be the probability of rejecting the null hypothesis when it is false. In an outlier test, power would be the probability of correctly identifying multivariate observations as outliers.
