Properties of Multivariate Control Chart with Estimated Parameters

The Hotelling's T2, multivariate exponentially weighted moving average (MEWMA), and several multivariate cumulative sum (MCUSUM) charts are examined in this paper. Two descriptions are given of each chart with estimated parameters for monitoring the mean of a vector of quality measurements. For each chart, one description explains how the chart can be applied with estimated parameters in practice, and the other description is useful for analyzing the run length performance of the chart. It is shown that, if the covariance matrix is in control, the run length distribution of most of these charts depends only on the distributional parameters through the size of the process shift in terms of statistical distance. Simulation is used to provide performance analyses and comparisons of these charts. An example is given to illustrate the MCUSUM and MEWMA charts when parameters are estimated.