IDEAS home Printed from https://ideas.repec.org/a/bpj/ecqcon/v38y2023i1p11-24n2.html
   My bibliography  Save this article

An ARL-Unbiased Modified np-Chart for Autoregressive Binomial Counts

Author

Listed:
  • Morais Manuel Cabral

    (Department of Mathematics, & CEMAT (Center for Computational and Stochastic Mathematics), Instituto Superior Técnico, — Universidade de Lisboa, Av. Rovisco Pais, 1049-001, Lisboa, Portugal)

  • Wittenberg Philipp

    (Department of Mathematics and Statistics, Helmut Schmidt University, Holstenhofweg 85, 22043, Hamburg, Germany)

  • Cruz Camila Jeppesen

    (Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001, Lisboa, Portugal)

Abstract

Independence between successive counts is not a sensible premise while dealing, for instance, with very high sampling rates. After assessing the impact of falsely assuming independent binomial counts in the performance of np-charts, such as the one with 3-σ control limits, we propose a modified np-chart for monitoring first-order autoregressive counts with binomial marginals. This simple chart has an in-control average run length (ARL) larger than any out-of-control ARL, i.e., it is ARL-unbiased. Moreover, the ARL-unbiased modified np-chart triggers a signal at sample t with probability one if the observed value of the control statistic is beyond the lower and upper control limits L and U. In addition to this, the chart emits a signal with probability γL{\gamma_{L}} (resp. γU{\gamma_{U}}) if that observed value coincides with L (resp. U). This randomization allows us to set the control limits in such a way that the in-control ARL takes the desired value ARL0{\operatorname{ARL}_{0}}, in contrast to traditional charts with discrete control statistics. Several illustrations of the ARL-unbiased modified np-chart are provided, using the statistical software R and resorting to real and simulated data.

Suggested Citation

  • Morais Manuel Cabral & Wittenberg Philipp & Cruz Camila Jeppesen, 2023. "An ARL-Unbiased Modified np-Chart for Autoregressive Binomial Counts," Stochastics and Quality Control, De Gruyter, vol. 38(1), pages 11-24, June.
    • Handle: RePEc:bpj:ecqcon:v:38:y:2023:i:1:p:11-24:n:2
    DOI: 10.1515/eqc-2022-0052
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/eqc-2022-0052
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/eqc-2022-0052?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.

    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:bpj:ecqcon:v:38:y:2023:i:1:p:11-24:n:2. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    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.