Hotelling’s T2 control chart with two adaptive sample sizes

Some quality control schemes have been developed when several related quality characteristics are to be monitored. The familiar multivariate process monitoring and control procedure is the Hotelling's T² control chart for monitoring the mean vector of the process. It is a direct analog of the univariate shewhart x̄ chart. As in the case of univariate, the ARL improvements are very important particularly for small process shifts. In this paper, we study the T² control chart with two-state adaptive sample size, when the shift in the process mean does not occur at the beginning but at some random time in the future. Further, the occurrence time of the shift is assumed to be exponentially distributed random variable.