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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
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    References listed on IDEAS

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    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.
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    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.
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    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.

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