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Inference on a Multicomponent Stress-Strength Model Based on Unit-Burr III Distributions

Author

Listed:
  • Devendra Pratap Singh

    (Indian Institute of Technology Patna)

  • Mayank Kumar Jha

    (Indian Institute of Technology Patna
    Data Scientist, GEP Worldwide)

  • Yogesh Mani Tripathi

    (Indian Institute of Technology Patna)

  • Liang Wang

    (Yunnan Normal University)

Abstract

We make inference for a multicomponent stress-strength (MS) model under type-II censoring. It is assumed that lifetimes of strength and stress components follow unit Burr III distributions. Maximum likelihood estimator of MS parameter is obtained under a common shape parameter and in sequel approximate confidence intervals are constructed. Pivotal quantities based inference is also discussed. The case of unequal common parameters is considered as well and various inferences are derived. In addition, likelihood ratio tests are constructed to test the equivalence of parameters of interest. We conduct a simulation study to examine the behavior of proposed estimation procedures. A real data set is also analyzed from application viewpoint.

Suggested Citation

  • Devendra Pratap Singh & Mayank Kumar Jha & Yogesh Mani Tripathi & Liang Wang, 2023. "Inference on a Multicomponent Stress-Strength Model Based on Unit-Burr III Distributions," Annals of Data Science, Springer, vol. 10(5), pages 1329-1359, October.
    • Handle: RePEc:spr:aodasc:v:10:y:2023:i:5:d:10.1007_s40745-022-00429-1
    DOI: 10.1007/s40745-022-00429-1
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    References listed on IDEAS

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    1. G. Srinivasa Rao & Muhammad Aslam & Osama H. Arif, 2017. "Estimation of reliability in multicomponent stress–strength based on two parameter exponentiated Weibull Distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(15), pages 7495-7502, August.
    2. Rao G. Srinivasa & Kantam R. R. L., 2010. "Acceptance Sampling Plans from Truncated Life Tests Based on the Log-Logistic Distributions for Percentiles," Stochastics and Quality Control, De Gruyter, vol. 25(2), pages 153-167, January.
    3. Kızılaslan, Fatih, 2017. "Classical and Bayesian estimation of reliability in a multicomponent stress–strength model based on the proportional reversed hazard rate mode," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 136(C), pages 36-62.
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    5. Subrata Chakraborty & Laba Handique & Rana Muhammad Usman, 2020. "A Simple Extension of Burr-III Distribution and Its Advantages over Existing Ones in Modelling Failure Time Data," Annals of Data Science, Springer, vol. 7(1), pages 17-31, March.
    6. Sanku Dey & Josmar Mazucheli & M. Z. Anis, 2017. "Estimation of reliability of multicomponent stress–strength for a Kumaraswamy distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(4), pages 1560-1572, February.
    7. Tanmay Kayal & Yogesh Mani Tripathi & Sanku Dey & Shuo-Jye Wu, 2020. "On estimating the reliability in a multicomponent stress-strength model based on Chen distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(10), pages 2429-2447, May.
    8. Abhimanyu Singh Yadav & Emrah Altun & Haitham M. Yousof, 2021. "Burr–Hatke Exponential Distribution: A Decreasing Failure Rate Model, Statistical Inference and Applications," Annals of Data Science, Springer, vol. 8(2), pages 241-260, June.
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