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Guaranteed conditional ARL performance in the presence of autocorrelation

Author

Listed:
  • Weiß, Christian H.
  • Steuer, Detlef
  • Jentsch, Carsten
  • Testik, Murat Caner

Abstract

The Average Run Length (ARL) performance of a control chart conditional on parameter estimates from a Phase I study may deviate significantly from its designed performance. To circumvent this problem, the guaranteed conditional performance measure is proposed in the literature. Hence, one does not intend to reach a specified in-control ARL exactly, but to reach an ARL value greater than or equal to a specified in-control ARL with a certain probability. In the literature, the control chart design for a guaranteed conditional performance has only been discussed for the case of independent and identically distributed data. Therefore, a novel guaranteed conditional performance approach for an autocorrelated data generating process is proposed, assuming that the process parameters are unknown. The approach is exemplified by considering an AutoRegressive dependence structure of order 1, i.e., AR(1), and by designing individuals control chart. Appropriate bootstrap schemes are provided for implementation. These bootstrap schemes extend easily from order one to general order p for an AR(p) process. Through simulations, performance analyses of the proposed approach and a study about the robustness with respect to distributional assumptions are provided.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:128:y:2018:i:c:p:367-379
    DOI: 10.1016/j.csda.2018.07.013
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    References listed on IDEAS

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    1. Giovanna Capizzi & Guido Masarotto, 2009. "Bootstrap-based design of residual control charts," IISE Transactions, Taylor & Francis Journals, vol. 41(4), pages 275-286.
    2. Giacomini, Raffaella & Politis, Dimitris N. & White, Halbert, 2013. "A Warp-Speed Method For Conducting Monte Carlo Experiments Involving Bootstrap Estimators," Econometric Theory, Cambridge University Press, vol. 29(3), pages 567-589, June.
    3. Alireza Faraz & William H. Woodall & C. Heuchenne, 2015. "Guaranteed conditional performance of the S2 control chart with estimated parameters," International Journal of Production Research, Taylor & Francis Journals, vol. 53(14), pages 4405-4413, July.
    4. Giovanna Capizzi & Guido Masarotto, 2016. "Efficient control chart calibration by simulated stochastic approximation," IISE Transactions, Taylor & Francis Journals, vol. 48(1), pages 57-65, January.
    5. Faraz, Alireza & Woodall, William & Heuchenne, Cedric, 2015. "Guaranteed conditional performance of the S^2 control chart with estimated parameters," LIDAM Discussion Papers ISBA 2015004, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. 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.
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