IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-7908-1687-7_13.html
   My bibliography  Save this book chapter

Generalization of the Run Rules for the Shewhart Control Charts

In: Frontiers in Statistical Quality Control 8

Author

Listed:
  • Seiichi Yasui

    (Tokyo University of Science, Department of Industrial Administration)

  • Yoshikazu Ojima

    (Tokyo University of Science, Department of Industrial Administration)

  • Tomomichi Suzuki

    (Tokyo University of Science, Department of Industrial Administration)

Abstract

Summary It is well-known that the Shewhart control charts are useful to detect large shifts of a process mean, but it is insensitive for small shifts and/or other types of variation. We extend the Shewhart’s three sigma rule and propose two new rules based on successive observations. One is that a signal occurs when m successive observations exceed k 1 sigma control limit. The other is that a signal occurs when m − 1 of m successive observations exceed k 2 sigma control limit. The original Shewhart control chart is included in the first generalized rule as m = 1. The performance of the proposed rules is evaluated under several out-of-control situations by both the average run length and the standard deviation of the run length. These rules are more powerful than Shewhart’s three sigma rule at detecting moderate step shifts.

Suggested Citation

  • Seiichi Yasui & Yoshikazu Ojima & Tomomichi Suzuki, 2006. "Generalization of the Run Rules for the Shewhart Control Charts," Springer Books, in: Hans-Joachim Lenz & Peter-Theodor Wilrich (ed.), Frontiers in Statistical Quality Control 8, pages 207-219, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7908-1687-7_13
    DOI: 10.1007/3-7908-1687-6_13
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Statistics

    Access and download 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:spr:sprchp:978-3-7908-1687-7_13. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.