IDEAS home Printed from https://ideas.repec.org/a/ids/ijrsaf/v14y2020i1p14-38.html
   My bibliography  Save this article

A log-third order polynomial normal transformation approach for high-reliability estimation with scarce samples

Author

Listed:
  • Palaniappan Ramu
  • Harshal Kaushik

Abstract

Normal transformations are often used in reliability analysis. A Third order Polynomial Normal Transformation (TPNT) approach is used in this work. The underlying idea is to approximate the Cumulative Distribution Function (CDF) of the response in probit space using a third order polynomial while imposing monotonicity constraints. The current work proposes to apply log transformation to the ordinate of the transformed CDF and hence names the approach Log-TPNT. The log transformed data assists in improved fitting to the tails of the distribution resulting in better predictions of extreme values. Log-TPNT is demonstrated on a suite of statistical distributions covering all types of tails and analytical examples that cover aspects of high dimensions, non-linearity and system reliability. Results reveal that Log-TPNT can predict the response values corresponding to high reliability, with samples as scarce as 9. Finally, the variations associated with the response estimates are quantified using bootstrap.

Suggested Citation

  • Palaniappan Ramu & Harshal Kaushik, 2020. "A log-third order polynomial normal transformation approach for high-reliability estimation with scarce samples," International Journal of Reliability and Safety, Inderscience Enterprises Ltd, vol. 14(1), pages 14-38.
    • Handle: RePEc:ids:ijrsaf:v:14:y:2020:i:1:p:14-38
    as

    Download full text from publisher

    File URL: http://www.inderscience.com/link.php?id=105890
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    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:ids:ijrsaf:v:14:y:2020:i:1:p:14-38. 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: Sarah Parker (email available below). General contact details of provider: http://www.inderscience.com/browse/index.php?journalID=98 .

    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.