Comparisons of MultivariateCUSUMCharts

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Abstract
We consider several distinct approaches for controlling the mean of a multivariate normal process including two new and distinct multivariate CUSUM charts, several multiple univariate CUSUM charts, and a Shewhart χ2 control chart. The performances of these charts are compared by estimating the average run lengths. A Markov chain is used to evaluate the average run length performance of one of the charts while Monte Carlo simulation is used to evaluate the other multivariate schemes. The ARL performance of the multiple univariate scheme is shown to be dependent upon the manner in which the process mean shifts whereas one of the multivariate CUSUM charts provides stable ARL performance over a diverse set of off-target conditions. The average run length data are presented.