CUSUM Control Schemes for Multivariate Time Series

Olha Bodnar · Wolfgang Schmid

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Advanced Statistical Process Monitoring Statistical Methods and Applications Fault Detection and Control Systems

Abstract

SummaryUp 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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References

1954CONTINUOUS INSPECTION SCHEMES 2000Control Chart Tests Based on Geometric Moving Averages 1992A Multivariate Exponentially Weighted Moving Average Control Chart 1986Optimal Stopping Times for Detecting Changes in Distributions 1988Time-Series Modeling for Statistical Process Control 1988Multivariate Generalizations of Cumulative Sum Quality-Control Schemes 1991Some Statistical Process Control Methods for Autocorrelated Data 1985Optimal Detection of a Change in Distribution

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