IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v35y1997i1p91-100.html
   My bibliography  Save this article

Preservation of certain dependent structures under bivariate homogeneous Poisson shock models

Author

Listed:
  • Balu, Mini N.
  • Sabnis, S. V.

Abstract

A bivariate Poisson shock model resulting from two devices receiving shocks from two independent sources is shown to preserve certain bivariate dependent structures such as total positivity of order 2 (TP2), stochastic increasing (SI), right tail increasing (RTI) etc. However, when two devices are subjected to the same source of shocks it is observed through a counter example that some of these preservation results do not hold any more. In such cases sufficient conditions are given under which the bivariate random vector denoting the life lengths of two devices is shown to have the above-mentioned bivariate dependent structures.

Suggested Citation

  • Balu, Mini N. & Sabnis, S. V., 1997. "Preservation of certain dependent structures under bivariate homogeneous Poisson shock models," Statistics & Probability Letters, Elsevier, vol. 35(1), pages 91-100, August.
    • Handle: RePEc:eee:stapro:v:35:y:1997:i:1:p:91-100
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(97)81253-9
    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. Robert L. Launer, 1984. "Inequalities for NBUE and NWUE Life Distributions," Operations Research, INFORMS, vol. 32(3), pages 660-667, June.
    2. A-Hameed, M. S. & Proschan, F., 1973. "Nonstationary shock models," Stochastic Processes and their Applications, Elsevier, vol. 1(4), pages 383-404, October.
    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. Sheu, Shey-Huei, 1998. "A generalized age and block replacement of a system subject to shocks," European Journal of Operational Research, Elsevier, vol. 108(2), pages 345-362, July.
    2. Dheeraj Goyal & Nil Kamal Hazra & Maxim Finkelstein, 2022. "On Properties of the Phase-type Mixed Poisson Process and its Applications to Reliability Shock Modeling," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2933-2960, December.
    3. Ji Hwan Cha & Jie Mi, 2011. "On a Stochastic Survival Model for a System Under Randomly Variable Environment," Methodology and Computing in Applied Probability, Springer, vol. 13(3), pages 549-561, September.
    4. van Noortwijk, J.M., 2009. "A survey of the application of gamma processes in maintenance," Reliability Engineering and System Safety, Elsevier, vol. 94(1), pages 2-21.
    5. Dequan Yue & Jinhua Cao, 2001. "The NBUL class of life distribution and replacement policy comparisons," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(7), pages 578-591, October.
    6. Willmot, Gordon E., 1997. "Bounds for compound distributions based on mean residual lifetimes and equilibrium distributions," Insurance: Mathematics and Economics, Elsevier, vol. 21(1), pages 25-42, October.
    7. Hyunju Lee & Ji Hwan Cha, 2021. "A general multivariate new better than used (MNBU) distribution and its properties," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(1), pages 27-46, January.
    8. Henry W. Block & Thomas H. Savits & Harshinder Singh, 2002. "A Criterion for Burn-in that Balances Mean Residual Life and Residual Variance," Operations Research, INFORMS, vol. 50(2), pages 290-296, April.
    9. Abdolsaeed Toomaj & Antonio Di Crescenzo, 2020. "Connections between Weighted Generalized Cumulative Residual Entropy and Variance," Mathematics, MDPI, vol. 8(7), pages 1-27, July.
    10. Al-Zahrani, Bander & Stoyanov, Jordan, 2008. "Moment inequalities for DVRL distributions, characterization and testing for exponentiality," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1792-1799, September.
    11. Song, Sanling & Coit, David W. & Feng, Qianmei, 2014. "Reliability for systems of degrading components with distinct component shock sets," Reliability Engineering and System Safety, Elsevier, vol. 132(C), pages 115-124.
    12. Ji Hwan Cha & Massimiliano Giorgio, 2018. "Modelling of Marginally Regular Bivariate Counting Process and its Application to Shock Model," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1137-1154, December.
    13. Zhao, Xian & Guo, Xiaoxin & Wang, Xiaoyue, 2018. "Reliability and maintenance policies for a two-stage shock model with self-healing mechanism," Reliability Engineering and System Safety, Elsevier, vol. 172(C), pages 185-194.
    14. Chadjiconstantinidis, Stathis, 2023. "Some bounds for the renewal function and the variance of the renewal process," Applied Mathematics and Computation, Elsevier, vol. 436(C).
    15. Chen, Yunxia & Zhang, Wenbo & Xu, Dan, 2019. "Reliability assessment with varying safety threshold for shock resistant systems," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 49-60.
    16. Mini N. Balu & S.V. Sabnis, 1999. "Preservation of unimodality under shock models," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(8), pages 952-957, December.
    17. Cha, Ji Hwan & Finkelstein, Maxim, 2016. "New shock models based on the generalized Polya process," European Journal of Operational Research, Elsevier, vol. 251(1), pages 135-141.
    18. Ji Hwan Cha & Maxim Finkelstein, 2018. "On a New Shot Noise Process and the Induced Survival Model," Methodology and Computing in Applied Probability, Springer, vol. 20(3), pages 897-917, September.
    19. Sophie Mercier & Hai Ha Pham, 2016. "A Random Shock Model with Mixed Effect, Including Competing Soft and Sudden Failures, and Dependence," Methodology and Computing in Applied Probability, Springer, vol. 18(2), pages 377-400, June.
    20. Francisco Germán Badía & María Dolores Berrade, 2022. "On the Residual Lifetime and Inactivity Time in Mixtures," Mathematics, MDPI, vol. 10(15), pages 1-20, August.

    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:35:y:1997:i:1:p:91-100. 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.