Ch. 15. Effective sample sizes for T2 control charts

When Hotelling's T2 is used as a control statistic for a multivariate normal population with unknown parameters, the statistic is commonly expressed as a function of the sample mean vector and the sample covariance matrix. In this setting, it is well known that as the sample size increases, these sample estimators approach their true population values, as they are consistent estimators. However, it is not well established as to what sample size is needed to assure that this result is approximately true. This is due, in part, to the large number of parameters that must be estimated in the multivariate case. To solve this problem, we present three helpful procedures for determining an effective sample size when using the T2 statistic to monitor the performance of a process.