IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v33y2006i1p17-34.html
   My bibliography  Save this article

Properties of the Weibull cumulative exposure model

Author

Listed:
  • Yoshio Komori

Abstract

This article is aimed at the investigation of some properties of the Weibull cumulative exposure model on multiple-step step-stress accelerated life test data. Although the model includes a probabilistic idea of Miner's rule in order to express the effect of cumulative damage in fatigue, our result shows that the application of only this is not sufficient to express degradation of specimens and the shape parameter must be larger than 1. For a random variable obeying the model, its average and standard deviation are investigated on a various sets of parameter values. In addition, a way of checking the validity of the model is illustrated through an example of the maximum likelihood estimation on an actual data set, which is about time to breakdown of cross-linked polyethylene-insulated cables.

Suggested Citation

  • Yoshio Komori, 2006. "Properties of the Weibull cumulative exposure model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 33(1), pages 17-34.
  • Handle: RePEc:taf:japsta:v:33:y:2006:i:1:p:17-34
    DOI: 10.1080/02664760500389475
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/02664760500389475
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1080/02664760500389475?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. Sang-Jun Park & Bong-Jin Yum, 1998. "Optimal design of accelerated life tests under modified stress loading methods," Journal of Applied Statistics, Taylor & Francis Journals, vol. 25(1), pages 41-62.
    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. Preeti W Srivastava & Neha Mittal, 2013. "Optimum multi-objective modified constant-stress accelerated life test plan for the Burr type-XII distribution with type-I censoring," Journal of Risk and Reliability, , vol. 227(2), pages 132-143, April.
    2. Refah Alotaibi & Faten S. Alamri & Ehab M. Almetwally & Min Wang & Hoda Rezk, 2022. "Classical and Bayesian Inference of a Progressive-Stress Model for the Nadarajah–Haghighi Distribution with Type II Progressive Censoring and Different Loss Functions," Mathematics, MDPI, vol. 10(9), pages 1-19, May.
    3. Haitao Liao & Elsayed A. Elsayed, 2010. "Equivalent accelerated life testing plans for log‐location‐scale distributions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(5), pages 472-488, August.
    4. Cheng‐Hung Hu & Robert D. Plante & Jen Tang, 2013. "Statistical equivalency and optimality of simple step‐stress accelerated test plans for the exponential distribution," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(1), pages 19-30, February.
    5. Haitao Liao, 2009. "Optimal design of accelerated life testing plans for periodical replacement with penalty," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(1), pages 19-32, February.

    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:taf:japsta:v:33:y:2006:i:1:p:17-34. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/CJAS20 .

    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.