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Estimation of multicomponent stress-strength reliability based on a bivariate Topp-Leone distribution

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  • Hossein Pasha-Zanoosi

    (Khorramshahr University of Marine Science and Technology)

Abstract

In this endeavour, we study the statistical inference of multicomponent stress-strength reliability when components of the system have two paired elements experiencing common random stress. The k strength variables $$(X_1,Y_1),\ldots ,(X_k,Y_k)$$ ( X 1 , Y 1 ) , … , ( X k , Y k ) follow a bivariate Topp-Leone distribution and the stress variable which follows a Topp-Leone distribution. This system is unfailing when at least $$s(1\le s\le k)$$ s ( 1 ≤ s ≤ k ) out of k components simultaneously activate. The maximum likelihood estimate along with its asymptotic confidence interval, the uniformly minimum variance unbiased estimate, and the exact Bayes estimate of stress-strength reliability are derived. Further, we determined the Bayes estimates of the stress-strength reliability via different methods such as the Tierney and Kadane approximation, Lindley’s approximation, and the Markov Chain Monte Carlo (MCMC) method, to compare their performances with the exact Bayes estimate. Also, the highest probability density credible interval is obtained using the MCMC method. Monte Carlo simulations are implemented to compare the different suggested methods. Ultimately, the analysis of one real data is investigated for illustrative purposes.

Suggested Citation

  • Hossein Pasha-Zanoosi, 2024. "Estimation of multicomponent stress-strength reliability based on a bivariate Topp-Leone distribution," OPSEARCH, Springer;Operational Research Society of India, vol. 61(2), pages 570-602, June.
    • Handle: RePEc:spr:opsear:v:61:y:2024:i:2:d:10.1007_s12597-023-00713-5
    DOI: 10.1007/s12597-023-00713-5
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    References listed on IDEAS

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    1. 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.
    2. Akram Kohansal, 2019. "On estimation of reliability in a multicomponent stress-strength model for a Kumaraswamy distribution based on progressively censored sample," Statistical Papers, Springer, vol. 60(6), pages 2185-2224, December.
    3. Fatih Kızılaslan & Mustafa Nadar, 2018. "Estimation of reliability in a multicomponent stress–strength model based on a bivariate Kumaraswamy distribution," Statistical Papers, Springer, vol. 59(1), pages 307-340, March.
    4. 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.
    5. Akram Kohansal & Shirin Shoaee, 2021. "Bayesian and classical estimation of reliability in a multicomponent stress-strength model under adaptive hybrid progressive censored data," Statistical Papers, Springer, vol. 62(1), pages 309-359, February.
    6. Vikas Kumar Sharma & Sudhanshu V. Singh & Komal Shekhawat, 2022. "Exponentiated Teissier distribution with increasing, decreasing and bathtub hazard functions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 49(2), pages 371-393, January.
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