IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v128y2018icp367-379.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947318301798
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2018.07.013?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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.
    4. 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.
    5. 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.
    6. 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).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Shahid Hussain & Sun Mei & Muhammad Riaz & Saddam Akber Abbasi, 2020. "On Phase-I Monitoring of Process Location Parameter with Auxiliary Information-Based Median Control Charts," Mathematics, MDPI, vol. 8(5), pages 1-21, May.
    2. Wei-Heng Huang, 2022. "The Performance of S Control Charts for the Lognormal Distribution with Estimated Parameters," Sustainability, MDPI, vol. 14(24), pages 1-16, December.
    3. Kim, Dukpa & Oka, Tatsushi & Estrada, Francisco & Perron, Pierre, 2020. "Inference related to common breaks in a multivariate system with joined segmented trends with applications to global and hemispheric temperatures," Journal of Econometrics, Elsevier, vol. 214(1), pages 130-152.
    4. Hoderlein, Stefan & Su, Liangjun & White, Halbert & Yang, Thomas Tao, 2016. "Testing for monotonicity in unobservables under unconfoundedness," Journal of Econometrics, Elsevier, vol. 193(1), pages 183-202.
    5. Silvennoinen Annastiina & Teräsvirta Timo, 2016. "Testing constancy of unconditional variance in volatility models by misspecification and specification tests," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 20(4), pages 347-364, September.
    6. Marcus J. Chambers, 2015. "A Jackknife Correction to a Test for Cointegration Rank," Econometrics, MDPI, vol. 3(2), pages 1-21, May.
    7. Corradi, Valentina & Fosten, Jack & Gutknecht, Daniel, 2024. "Predictive ability tests with possibly overlapping models," Journal of Econometrics, Elsevier, vol. 241(1).
    8. Davidson, Russell & Trokić, Mirza, 2020. "The fast iterated bootstrap," Journal of Econometrics, Elsevier, vol. 218(2), pages 451-475.
    9. Hidalgo, Javier & Seo, Myung Hwan, 2015. "Specification Tests For Lattice Processes," Econometric Theory, Cambridge University Press, vol. 31(2), pages 294-336, April.
    10. González, Andrés & Teräsvirta, Timo & van Dijk, Dick & Yang, Yukai, 2005. "Panel Smooth Transition Regression Models," SSE/EFI Working Paper Series in Economics and Finance 604, Stockholm School of Economics, revised 11 Oct 2017.
    11. Norbert Henze & María Dolores Jiménez-Gamero, 2019. "A new class of tests for multinormality with i.i.d. and garch data based on the empirical moment generating function," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 499-521, June.
    12. Christian H. Weiß & Esmeralda Gonçalves & Nazaré Mendes Lopes, 2017. "Testing the compounding structure of the CP-INARCH model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(5), pages 571-603, July.
    13. Giuseppe Cavaliere & Indeewara Perera & Anders Rahbek, 2021. "Specification tests for GARCH processes," Papers 2105.14081, arXiv.org.
    14. Fiorentini, Gabriele & Sentana, Enrique, 2021. "New testing approaches for mean–variance predictability," Journal of Econometrics, Elsevier, vol. 222(1), pages 516-538.
    15. Elia Lapenta, 2022. "A Bootstrap Specification Test for Semiparametric Models with Generated Regressors," Papers 2212.11112, arXiv.org, revised Oct 2023.
    16. Francq, Christian & Jiménez Gamero, Maria Dolores & Meintanis, Simos, 2015. "Tests for sphericity in multivariate garch models," MPRA Paper 67411, University Library of Munich, Germany.
    17. Moneta, Alessio & Pallante, Gianluca, 2022. "Identification of Structural VAR Models via Independent Component Analysis: A Performance Evaluation Study," Journal of Economic Dynamics and Control, Elsevier, vol. 144(C).
    18. Elia Lapenta & Pascal Lavergne, 2022. "Encompassing Tests for Nonparametric Regressions," Papers 2203.06685, arXiv.org, revised Oct 2023.
    19. Fresoli, Diego E. & Ruiz, Esther, 2016. "The uncertainty of conditional returns, volatilities and correlations in DCC models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 170-185.
    20. Christian Francq & Baye Matar Kandji & Jean-Michel Zakoian, 2022. "Inference on Multiplicative Component GARCH without any Small-Order Moment," Working Papers 2022-09, Center for Research in Economics and Statistics.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:128:y:2018:i:c:p:367-379. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.