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Bootstrap-based design of residual control charts

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  • Giovanna Capizzi
  • Guido Masarotto

Abstract

One approach to monitoring autocorrelated data consists in applying a control chart to the residuals of a time series model estimated from process observations. Recent research shows that the impact of estimation error on the run length properties of the resulting charts is not negligible. In this paper a general strategy for implementing residual-based control schemes is investigated. The designing procedure uses the AR-sieve approximation assuming that the process allows an autoregressive representation of order infinity. The run length distribution is estimated using bootstrap resampling in order to account for uncertainty in the estimated parameters. Control limits that satisfy a given constraint on the false alarm rate are computed via stochastic approximation. The proposed procedure is investigated for three residual-based control charts: generalized likelihood ratio, cumulative sum and exponentially weighted moving average. Results show that the bootstrap approach safeguards against an undesirably high rate of false alarms. In addition, the out-of-control bootstrap chart sensitivity seems to be comparable to that of charts designed under the assumption that the estimated model is equal to the true generating process.[Supplementary materials are available for this article. Go to the publisher's online edition of IIE Transactions for the following free supplemental resource: Appendix]

Suggested Citation

  • Giovanna Capizzi & Guido Masarotto, 2009. "Bootstrap-based design of residual control charts," IISE Transactions, Taylor & Francis Journals, vol. 41(4), pages 275-286.
  • Handle: RePEc:taf:uiiexx:v:41:y:2009:i:4:p:275-286
    DOI: 10.1080/07408170802120059
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    Cited by:

    1. Axel Gandy & Jan Terje Kvaløy, 2013. "Guaranteed Conditional Performance of Control Charts via Bootstrap Methods," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(4), pages 647-668, December.
    2. Chenglong Li & Amitava Mukherjee & Qin Su & Min Xie, 2016. "Optimal design of a distribution-free quality control scheme for cost-efficient monitoring of unknown location," International Journal of Production Research, Taylor & Francis Journals, vol. 54(24), pages 7259-7273, December.
    3. Weiß, Christian H. & Steuer, Detlef & Jentsch, Carsten & Testik, Murat Caner, 2018. "Guaranteed conditional ARL performance in the presence of autocorrelation," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 367-379.

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