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CUSUM Control Schemes for Multivariate Time Series

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Frontiers in Statistical Quality Control 8

Summary

Up to now only a few papers (e.g., Theodossiou (1993), Kramer and Schmid (1997)) dealt with the problem of detecting shifts in the mean vector of a multivariate time series. Here we generalize several well-known CUSUM charts for independent multivariate normal variables (Crosier (1988), Pignatiello and Runger (1990), Ngai and Zhang (2001)) to stationary Gaussian processes. We consider both modified control charts and residual charts.

It is analyzed under which conditions the average run lengths of the charts do not depend on the covariance matrix of the white noise process. In an extensive Monte Carlo study these schemes are compared with the multivariate EWMA chart of Kramer and Schmid (1997). The underlying target process is a vector autoregressive moving average process of order (1,1). For measuring the performance of a control chart the average run length is used.

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Author information

Authors and Affiliations

  1. Department of Statistics, European University, PO Box 1786, 15207, Frankfurt (Oder), Germany

    Olha Bodnar & Wolfgang Schmid

Authors
  1. Olha Bodnar
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  2. Wolfgang Schmid
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Editor information

Editors and Affiliations

  1. Institut für Statistik und Ökonometrie, Freie Universität Berlin, Garystraße 21, 14195, Berlin, Germany

    Hans-Joachim Lenz  & Peter-Theodor Wilrich  & 

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© 2006 Physica-Verlag Heidelberg

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Bodnar, O., Schmid, W. (2006). CUSUM Control Schemes for Multivariate Time Series. In: Lenz, HJ., Wilrich, PT. (eds) Frontiers in Statistical Quality Control 8. Physica-Verlag HD. https://doi.org/10.1007/3-7908-1687-6_4

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