Maximum Value of Hotelling's T~2 Statistics Based on the Successive Differences Covariance Matrix Estimator

摘要

In statistical process control applications, the multivariate T~2 control chart based on Hotelling 's T~2 statistic is useful for detecting the presence of special causes of variation. In particular, use of the T~2 statistic based on the successive differences covariance matrix estimator has been shown to be very effective in detecting the presence of a sustained step or ramp shift in the mean vector. However, the exact distribution of this statistic is unknown. In this article, we derive the maximum value of the T~2 statistic based on the successive differences covariance matrix estimator. This distributional property is crucial for calculating an approximate upper control limit of a T2 control chart based on successive differences, as described in Williams et al. (2006).