Surveillance of the mean behavior of multivariate time series
In this paper several cumulative sum (CUSUM) charts for the mean of a multivariate time series are introduced. We extend the control schemes for independent multivariate observations ofcrosier[Technometrics (1988) Vol. 30, pp. 187–194],pignatielloandrunger[Journal of Quality Technology (1990) Vol. 22, pp. 173–186], andngaiandzhang[Statistica Sinica (2001) Vol. 11, pp. 747–766] to multivariate time series by taking into account the probability structure of the underlying stochastic process. We consider modified charts and residual schemes as well. It is analyzed under which conditions these charts are directionally invariant. In an extensive Monte Carlo study these charts are compared with the CUSUM scheme oftheodossiu[Journal of the American Statistical Association (1993) Vol. 88, pp. 441–448], the multivariate exponentially weighted moving-average (EWMA) chart ofkramerandschmid[Sequential Analysis (1997) Vol. 16, pp. 131–154], and the control procedures ofbodnarandschmid[Frontiers of Statistical Process Control (2006) Physica, Heidelberg]. As a measure of the performance, the maximum expected delay is used.
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