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Bayesian and classical estimation of reliability in a multicomponent stress-strength model under adaptive hybrid progressive censored data

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  • Akram Kohansal

    (Imam Khomeini International University)

  • Shirin Shoaee

    (Shahid Beheshti University)

Abstract

The statistical inference of multicomponent stress-strength reliability under the adaptive Type-II hybrid progressive censored samples for the Weibull distribution is considered. It is assumed that both stress and strength are two Weibull independent random variables. We study the problem in three cases. First assuming that the stress and strength have the same shape parameter and different scale parameters, the maximum likelihood estimation (MLE), approximate maximum likelihood estimation (AMLE) and two Bayes approximations, due to the lack of explicit forms, are derived. Also, the asymptotic confidence intervals, two bootstrap confidence intervals and highest posterior density (HPD) credible intervals are obtained. In the second case, when the shape parameter is known, MLE, exact Bayes estimation, uniformly minimum variance unbiased estimator (UMVUE) and different confidence intervals (asymptotic and HPD) are studied. Finally, assuming that the stress and strength have the different shape and scale parameters, ML, AML and Bayesian estimations on multicomponent reliability have been considered. The performances of different methods are compared using the Monte Carlo simulations and for illustrative aims, one data set is investigated.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:62:y:2021:i:1:d:10.1007_s00362-019-01094-y
    DOI: 10.1007/s00362-019-01094-y
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Kundu, Debasis & Joarder, Avijit, 2006. "Analysis of Type-II progressively hybrid censored data," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2509-2528, June.
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    Cited by:

    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. 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.
    3. Marco Capaldo & Antonio Di Crescenzo & Alessandra Meoli, 2024. "Cumulative information generating function and generalized Gini functions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 87(7), pages 775-803, October.
    4. Liang Wang & Sanku Dey & Yogesh Mani Tripathi, 2022. "Classical and Bayesian Inference of the Inverse Nakagami Distribution Based on Progressive Type-II Censored Samples," Mathematics, MDPI, vol. 10(12), pages 1-18, June.
    5. Tzong-Ru Tsai & Yuhlong Lio & Jyun-You Chiang & Ya-Wen Chang, 2023. "Stress–Strength Inference on the Multicomponent Model Based on Generalized Exponential Distributions under Type-I Hybrid Censoring," Mathematics, MDPI, vol. 11(5), pages 1-17, March.
    6. Akram Kohansal & Carlos J Pérez-González & Arturo J Fernández, 2024. "Inference on the stress-strength reliability of multi-component systems based on progressive first failure censored samples," Journal of Risk and Reliability, , vol. 238(5), pages 1053-1073, October.
    7. Syed Ejaz Ahmed & Reza Arabi Belaghi & Abdulkadir Hussein & Alireza Safariyan, 2024. "New and Efficient Estimators of Reliability Characteristics for a Family of Lifetime Distributions under Progressive Censoring," Mathematics, MDPI, vol. 12(10), pages 1-18, May.

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