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Surveillance of non-stationary processes

Author

Listed:
  • Taras Lazariv

    (Technical University Dresden)

  • Wolfgang Schmid

    (European University Viadrina)

Abstract

In nearly all papers on process control for time-dependent data, it is assumed that the underlying target process is stationary. In the present paper, the target process is modeled by a multivariate state-space model which may be non-stationary. Our aim is to monitor its mean behavior. The likelihood ratio method, the sequential probability ratio test and the Shiryaev–Roberts procedure are applied to derive control charts signaling a change from the supposed mean structure. These procedures depend on certain reference values which have to be chosen by the practitioners. The corresponding generalized approaches are considered as well, and generalized control charts are determined for state-space processes. These schemes do not have further design parameters. In an extensive simulation study, the behavior of the introduced schemes is compared with each other using various performance criteria like the average run length, the average delay, the probability of a successful detection, and the probability of a false detection.

Suggested Citation

  • Taras Lazariv & Wolfgang Schmid, 2019. "Surveillance of non-stationary processes," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(3), pages 305-331, September.
    • Handle: RePEc:spr:alstar:v:103:y:2019:i:3:d:10.1007_s10182-018-00330-4
    DOI: 10.1007/s10182-018-00330-4
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    References listed on IDEAS

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    4. Margavio, Thomas M. & Conerly, Michael D. & Woodall, William H. & Drake, Laurel G., 1995. "Alarm rates for quality control charts," Statistics & Probability Letters, Elsevier, vol. 24(3), pages 219-224, August.
    5. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    6. Alwan, Layth C & Roberts, Harry V, 1988. "Time-Series Modeling for Statistical Process Control," Journal of Business & Economic Statistics, American Statistical Association, vol. 6(1), pages 87-95, January.
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