IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v94y2021i1d10.1007_s00186-021-00750-0.html
   My bibliography  Save this article

Stochastic comparisons and ageing properties of residual lifetime mixture models

Author

Listed:
  • Arijit Patra

    (Rajiv Gandhi Institute of Petroleum Technology)

  • Chanchal Kundu

    (Rajiv Gandhi Institute of Petroleum Technology)

Abstract

In this article, we enhance the study of stochastic comparisons and ageing properties of residual lifetime mixture models. To this aim, first we perform stochastic comparisons of two different mixture models under likelihood ratio, hazard rate, mean residual life and variance residual life orders having different baseline distributions as well as two different mixing distributions. Then, we develop some sufficient conditions which lead to the stochastic comparisons of these mixture models based on reversed hazard rate, mean inactivity time and variance inactivity time orders. Furthermore, we show that increasing likelihood ratio, increasing failure rate, decreasing mean residual life, increasing variance residual life and decreasing variance residual life classes are preserved under the formation of the model. Few applications in reliability engineering are also investigated.

Suggested Citation

  • Arijit Patra & Chanchal Kundu, 2021. "Stochastic comparisons and ageing properties of residual lifetime mixture models," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(1), pages 123-143, August.
    • Handle: RePEc:spr:mathme:v:94:y:2021:i:1:d:10.1007_s00186-021-00750-0
    DOI: 10.1007/s00186-021-00750-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00186-021-00750-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00186-021-00750-0?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. Ramesh C. Gupta, 2006. "Variance residual life function in reliability studies," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 343-355.
    2. Dewan, Isha & Khaledi, Baha-Eldin, 2014. "On stochastic comparisons of residual life time at random time," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 73-79.
    3. Khaledi, Baha-Eldin & Shaked, Moshe, 2010. "Stochastic comparisons of multivariate mixtures," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2486-2498, November.
    4. Ji Hwan Cha & Maxim Finkelstein, 2018. "On stochastic comparisons for population age and remaining lifetime," Statistical Papers, Springer, vol. 59(1), pages 199-213, March.
    5. Maxim Finkelstein & James Vaupel, 2015. "On random age and remaining lifetime for populations of items," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 31(5), pages 681-689, September.
    6. Chanchal Kundu & Arijit Patra, 2018. "Some results on residual life and inactivity time at random time," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(2), pages 372-384, January.
    7. Xiaohu Li & Rui Fang, 2018. "Stochastic properties of two general versions of the residual lifetime at random times," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 34(4), pages 528-543, July.
    8. Arijit Patra & Chanchal Kundu, 2019. "On generalized orderings and ageing classes for residual life and inactivity time at random time," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(6), pages 691-704, August.
    9. Joag-dev, Kumar & Kochar, Subhash & Proschan, Frank, 1995. "A general composition theorem and its applications to certain partial orderings of distributions," Statistics & Probability Letters, Elsevier, vol. 22(2), pages 111-119, February.
    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. 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.
    2. Mansour Shrahili & Mohamed Kayid, 2022. "Characterizations of the Exponential Distribution by Some Random Hazard Rate Sequences," Mathematics, MDPI, vol. 10(17), pages 1-11, August.
    3. Elham Khaleghpanah Noughabi & Majid Chahkandi & Majid Rezaei, 2022. "On the Mean and Variance Residual Life Comparisons of Coherent Systems with Identically Distributed Components," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2801-2822, 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. Arijit Patra & Chanchal Kundu, 2019. "On generalized orderings and ageing classes for residual life and inactivity time at random time," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(6), pages 691-704, August.
    2. Mansour Shrahili & Mohamed Kayid, 2022. "Characterizations of the Exponential Distribution by Some Random Hazard Rate Sequences," Mathematics, MDPI, vol. 10(17), pages 1-11, August.
    3. Nil Kamal Hazra & Maxim Finkelstein & Ji Hwan Cha, 2018. "Stochastic ordering for populations of manufactured items," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 173-196, March.
    4. Dewan, Isha & Khaledi, Baha-Eldin, 2014. "On stochastic comparisons of residual life time at random time," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 73-79.
    5. Ebrahim Amini-Seresht & Baha-Eldin Khaledi, 2015. "Multivariate stochastic comparisons of mixture models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(8), pages 1015-1034, November.
    6. Khaledi, Baha-Eldin & Shaked, Moshe, 2010. "Stochastic comparisons of multivariate mixtures," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2486-2498, November.
    7. Salehi, E.T. & Badía, F.G. & Asadi, M., 2012. "Preservation properties of a homogeneous Poisson process stopped at an independent random time," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 574-585.
    8. Omid Shojaee & Majid Asadi & Maxim Finkelstein, 2021. "On Some Properties of $$\alpha $$ α -Mixtures," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(8), pages 1213-1240, November.
    9. Zarezadeh, S. & Asadi, M. & Balakrishnan, N., 2014. "Dynamic network reliability modeling under nonhomogeneous Poisson processes," European Journal of Operational Research, Elsevier, vol. 232(3), pages 561-571.
    10. Bartoszewicz, Jaroslaw, 2000. "Stochastic orders based on the Laplace transform and infinitely divisible distributions," Statistics & Probability Letters, Elsevier, vol. 50(2), pages 121-129, November.
    11. Badía, F.G. & Sangüesa, C. & Cha, J.H., 2014. "Stochastic comparison of multivariate conditionally dependent mixtures," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 82-94.
    12. Francisco Villavicencio & Tim Riffe, 2016. "Symmetries between life lived and left in finite stationary populations," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 35(14), pages 381-398.
    13. Badía, Francisco German & Sangüesa, Carmen & Cha, Ji Hwan, 2018. "Stochastic comparisons and multivariate dependence for the epoch times of trend renewal processes," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 174-184.
    14. Bartoszewicz, Jaroslaw, 1998. "Characterizations of the dispersive order of distributions by the Laplace transform," Statistics & Probability Letters, Elsevier, vol. 40(1), pages 23-29, September.
    15. Finkelstein, Maxim & Cha, Ji Hwan & Bedford, Tim, 2023. "Optimal preventive maintenance strategy for populations of systems that generate outputs," Reliability Engineering and System Safety, Elsevier, vol. 237(C).
    16. Balakrishnan, Narayanaswamy & Barmalzan, Ghobad & Haidari, Abedin, 2016. "Multivariate stochastic comparisons of multivariate mixture models and their applications," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 37-43.
    17. Antonio Di Crescenzo & Franco Pellerey, 2019. "Some Results and Applications of Geometric Counting Processes," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 203-233, March.
    18. Jafar Ahmadi & H. N. Nagaraja, 2020. "Conditional properties of a random sample given an order statistic," Statistical Papers, Springer, vol. 61(5), pages 1971-1996, October.
    19. Bartoszewicz, Jaroslaw, 1998. "Applications of a general composition theorem to the star order of distributions," Statistics & Probability Letters, Elsevier, vol. 38(1), pages 1-9, May.
    20. Fatemeh Hooti & Jafar Ahmadi & N. Balakrishnan, 2022. "Stochastic Comparisons of General Proportional Mean Past Lifetime Frailty Model," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 844-866, 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:spr:mathme:v:94:y:2021:i:1:d:10.1007_s00186-021-00750-0. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.