IDEAS home Printed from https://ideas.repec.org/a/wly/apsmbi/v32y2016i5p565-573.html
   My bibliography  Save this article

A note on efficient performance evaluation of the Cumulative Sum chart and the Sequential Probability Ratio Test

Author

Listed:
  • Aleksey S. Polunchenko

Abstract

We establish a simple connection between certain in‐control characteristics of the Cumulative Sum (CUSUM) Run Length and their out‐of‐control counterparts. The connection is in the form of paired integral (renewal) equations. The derivation exploits Wald's likelihood ratio identity and the well‐known fact that the CUSUM chart is equivalent to repetitive application of Wald's Sequential Probability Ratio Test (SPRT). The characteristics considered include the entire Run Length distribution and all of the corresponding moments, starting from the zero‐state average run length. A particular practical benefit of our result is that it enables the in‐control and out‐of‐control characteristics of the CUSUM Run Length to be computed concurrently. Moreover, owing to the equivalence of the CUSUM chart to a sequence of SPRTs, the Average Sample Number and Operating Characteristic functions of an SPRT under the null and under the alternative can all be computed simultaneously as well. This would double up the efficiency of any numerical method that one may choose to devise to carry out the actual computations. Copyright © 2016 John Wiley & Sons, Ltd.

Suggested Citation

  • Aleksey S. Polunchenko, 2016. "A note on efficient performance evaluation of the Cumulative Sum chart and the Sequential Probability Ratio Test," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 32(5), pages 565-573, September.
    • Handle: RePEc:wly:apsmbi:v:32:y:2016:i:5:p:565-573
    DOI: 10.1002/asmb.2181
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/asmb.2181
    Download Restriction: no
    File URL: https://libkey.io/10.1002/asmb.2181?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
    ---><---

    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:wly:apsmbi:v:32:y:2016:i:5:p:565-573. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1526-4025 .

    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.