IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v64y2003i3p225-234.html
   My bibliography  Save this article

Shape and crossing properties of mean residual life functions

Author

Listed:
  • Bekker, Leonid
  • Mi, Jie

Abstract

In addition to the CDF or density function, the failure rate and mean residual life functions are the other important functions that can be used to characterize a lifetime. In the literature, much work on the properties of these quantities has been done. This paper points out and corrects some errors in the literature by giving a counterexample and new proofs. Moreover, it gives a more complete discussion on the shape of the mean residual life function when the associated failure rate function has a roller-coaster shape. It also discusses the crossing properties of two mean residual life functions in detail, when the associated failure rate functions have several crossing points.

Suggested Citation

  • Bekker, Leonid & Mi, Jie, 2003. "Shape and crossing properties of mean residual life functions," Statistics & Probability Letters, Elsevier, vol. 64(3), pages 225-234, September.
    • Handle: RePEc:eee:stapro:v:64:y:2003:i:3:p:225-234
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(03)00147-0
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Gupta, Ramesh C. & Gupta, Pushpa L., 2000. "On the crossings of reliability measures," Statistics & Probability Letters, Elsevier, vol. 46(3), pages 301-305, February.
    2. Jie Mi, 1993. "Discrete bathtub failure rate and upside‐down bathtub mean residual life," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(3), pages 361-371, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Mark Bebbington & Chin-Diew Lai & Ričardas Zitikis, 2010. "Life expectancy of a bathtub shaped failure distribution," Statistical Papers, Springer, vol. 51(3), pages 599-612, September.
    2. Braglia, Marcello & Carmignani, Gionata & Frosolini, Marco & Zammori, Francesco, 2012. "Data classification and MTBF prediction with a multivariate analysis approach," Reliability Engineering and System Safety, Elsevier, vol. 97(1), pages 27-35.
    3. Jie Mi, 2004. "A general approach to the shape of failure rate and MRL functions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(4), pages 543-556, June.
    4. Jorge Navarro & Pedro Hernandez, 2008. "Mean residual life functions of finite mixtures, order statistics and coherent systems," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 67(3), pages 277-298, April.

    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. Jie Mi, 2004. "A general approach to the shape of failure rate and MRL functions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(4), pages 543-556, June.
    2. Unnikrishnan Nair, N. & Asha, G., 1997. "Some Classes of Multivariate Life Distributions in Discrete Time," Journal of Multivariate Analysis, Elsevier, vol. 62(2), pages 181-189, August.
    3. Ibrahim Elbatal & Emrah Altun & Ahmed Z. Afify & Gamze Ozel, 2019. "The Generalized Burr XII Power Series Distributions with Properties and Applications," Annals of Data Science, Springer, vol. 6(3), pages 571-597, September.
    4. Refik Soyer & Feng Xu, 2010. "Assessment of mortgage default risk via Bayesian reliability models," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 26(3), pages 308-330, May.

    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:eee:stapro:v:64:y:2003:i:3:p:225-234. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.