IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v43y1999i4p421-426.html
   My bibliography  Save this article

Convolution of geometrics and a reliability problem

Author

Listed:
  • Sen, Ananda
  • Balakrishnan, N.

Abstract

In single-shot expensive tests of a destructive nature, an inverse sampling scheme is often pursued in order to use the available resources efficiently. This is particularly relevant for evaluating reliabilities for systems that are subjected to test-analyze-and-fix programs at successive stages, which cause a change in the failure probabilities across different stages. This note presents an elementary derivation of the distribution of the number of failures under this construct. A numerical illustration is presented by means of a discrete reliability growth model used in the literature. A correspondence with the well-studied pure birth process is pointed out.

Suggested Citation

  • Sen, Ananda & Balakrishnan, N., 1999. "Convolution of geometrics and a reliability problem," Statistics & Probability Letters, Elsevier, vol. 43(4), pages 421-426, July.
    • Handle: RePEc:eee:stapro:v:43:y:1999:i:4:p:421-426
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(98)00284-3
    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. Ananda Sen & Arthur Fries, 1997. "Estimation in a Discrete Reliability Growth Model Under an Inverse Sampling Scheme," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(2), pages 211-229, June.
    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. Zhao, Peng, 2011. "Some new results on convolutions of heterogeneous gamma random variables," Journal of Multivariate Analysis, Elsevier, vol. 102(5), pages 958-976, May.
    2. Anindya S. Chakrabarti, 2011. "Firm dynamics in a closed, conserved economy: A model of size distribution of employment and related statistics," Papers 1112.2168, arXiv.org.
    3. Stepanov, A. V. & Balakrishnan, N. & Hofmann, Glenn, 2003. "Exact distribution and Fisher information of weak record values," Statistics & Probability Letters, Elsevier, vol. 64(1), pages 69-81, August.
    4. Zhao, Xuejing & Fouladirad, Mitra & Bérenguer, Christophe & Bordes, Laurent, 2010. "Condition-based inspection/replacement policies for non-monotone deteriorating systems with environmental covariates," Reliability Engineering and System Safety, Elsevier, vol. 95(8), pages 921-934.
    5. Thierry E. Huillet, 2019. "Partitioning Problems Arising From Independent Shifted-Geometric and Exponential Samples With Unequal Intensities," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 8(6), pages 1-31, November.
    6. Zhao, Peng & Balakrishnan, N., 2009. "Likelihood ratio ordering of convolutions of heterogeneous exponential and geometric random variables," Statistics & Probability Letters, Elsevier, vol. 79(15), pages 1717-1723, August.
    7. Zhao, Peng & Balakrishnan, N., 2010. "Ordering properties of convolutions of heterogeneous Erlang and Pascal random variables," Statistics & Probability Letters, Elsevier, vol. 80(11-12), pages 969-974, June.
    8. Chaoran Hu & Vladimir Pozdnyakov & Jun Yan, 2020. "Density and distribution evaluation for convolution of independent gamma variables," Computational Statistics, Springer, vol. 35(1), pages 327-342, March.
    9. Zhao, Peng & Balakrishnan, N., 2009. "Mean residual life order of convolutions of heterogeneous exponential random variables," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1792-1801, September.
    10. Zhao, Peng & Hu, Taizhong, 2010. "On hazard rate ordering of the sums of heterogeneous geometric random variables," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 44-51, January.
    11. George P. Yanev, 2020. "Exponential and Hypoexponential Distributions: Some Characterizations," Mathematics, MDPI, vol. 8(12), pages 1-10, December.
    12. Ben O’Neill, 2022. "An Examination of the Negative Occupancy Distribution and the Coupon-Collector Distribution," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 3229-3260, December.

    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. Nibedita Bandyopadhyay & Ananda Sen, 2005. "Non-standard asymptotics in an inhomogeneous gamma process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(4), pages 703-732, December.

    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:43:y:1999:i:4:p:421-426. 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.