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Advancements in reliability estimation for the exponentiated Pareto distribution: a comparison of classical and Bayesian methods with lower record values

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  • Shubham Saini

    (Graphic Era Hill University)

Abstract

Estimating the reliability of multicomponent systems is crucial in various engineering and reliability analysis applications. This paper investigates the multicomponent stress strength reliability estimation using lower record values, specifically for the exponentiated Pareto distribution. We compare classical estimation techniques, such as maximum likelihood estimation, with Bayesian estimation methods. Under Bayesian estimation, we employ Markov Chain Monte Carlo techniques and Tierney–Kadane’s approximation to obtain the posterior distribution of the reliability parameter. To evaluate the performance of the proposed estimation approaches, we conduct a comprehensive simulation study, considering various system configurations and sample sizes. Additionally, we analyze real data to illustrate the practical applicability of our methods. The proposed methodologies provide valuable insights for engineers and reliability analysts in accurately assessing the reliability of multicomponent systems using lower record values.

Suggested Citation

  • Shubham Saini, 2025. "Advancements in reliability estimation for the exponentiated Pareto distribution: a comparison of classical and Bayesian methods with lower record values," Computational Statistics, Springer, vol. 40(1), pages 353-382, January.
    • Handle: RePEc:spr:compst:v:40:y:2025:i:1:d:10.1007_s00180-024-01497-y
    DOI: 10.1007/s00180-024-01497-y
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    References listed on IDEAS

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    1. Shubham Saini & Renu Garg, 2022. "Reliability inference for multicomponent stress–strength model from Kumaraswamy-G family of distributions based on progressively first failure censored samples," Computational Statistics, Springer, vol. 37(4), pages 1795-1837, September.
    2. G. Srinivasa Rao & Muhammad Aslam & Debasis Kundu, 2015. "Burr-XII Distribution Parametric Estimation and Estimation of Reliability of Multicomponent Stress-Strength," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(23), pages 4953-4961, December.
    3. 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.
    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, 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.
    6. Mustafa Nadar & Alexander Papadopoulos & Fatih Kızılaslan, 2013. "Statistical analysis for Kumaraswamy’s distribution based on record data," Statistical Papers, Springer, vol. 54(2), pages 355-369, May.
    7. Lauren Sauer & Yuhlong Lio & Tzong-Ru Tsai, 2020. "Reliability Inference for the Multicomponent System Based on Progressively Type II Censored Samples from Generalized Pareto Distributions," Mathematics, MDPI, vol. 8(7), pages 1-14, July.
    8. Sang Gil Kang & Woo Dong Lee & Yongku Kim, 2021. "Objective Bayesian analysis for generalized exponential stress–strength model," Computational Statistics, Springer, vol. 36(3), pages 2079-2109, September.
    9. Mahdi Doostparast, 2009. "A note on estimation based on record data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 69(1), pages 69-80, January.
    10. 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.
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