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Classical and Bayesian estimation of reliability in a multicomponent stress–strength model based on the proportional reversed hazard rate mode

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  • Kızılaslan, Fatih

Abstract

In this study, we consider a multicomponent system which has k statistically independent and identically distributed strength components X1,…,Xk and each component is exposed to a common random stress Y when the underlying distributions belonging to the proportional reversed hazard rate model. The system is regarded as operating only if at least s out of k(1≤s≤k) strength variables exceeds the random stress. The reliability of the system is estimated by using both frequentist and Bayesian approach. The Bayes estimates for the reliability of the system have been developed by using Lindley’s approximation and the Markov Chain Monte Carlo method due to the lack of explicit forms. The uniformly minimum variance unbiased and exact Bayes estimates for the reliability of the system are also obtained analytically when the common scale parameter is known. The asymptotic confidence interval and coverage probabilities are derived based on both the Fisher and the observed information matrices. The highest probability density credible interval is constructed by using Markov Chain Monte Carlo method. Monte Carlo simulations are performed to compare the performances of the proposed reliability estimators. Real data set is also analyzed for an illustration of the findings.

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  • 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.
    • Handle: RePEc:eee:matcom:v:136:y:2017:i:c:p:36-62
    DOI: 10.1016/j.matcom.2016.10.011
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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. EryIlmaz, Serkan, 2010. "On system reliability in stress-strength setup," Statistics & Probability Letters, Elsevier, vol. 80(9-10), pages 834-839, May.
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    6. Gupta, Ramesh C. & Ghitany, M.E. & Al-Mutairi, D.K., 2012. "Estimation of reliability in a parallel system with random sample size," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 83(C), pages 44-55.
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    Cited by:

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    2. Yuhlong Lio & Tzong-Ru Tsai & Liang Wang & Ignacio Pascual Cecilio Tejada, 2022. "Inferences of the Multicomponent Stress–Strength Reliability for Burr XII Distributions," Mathematics, MDPI, vol. 10(14), pages 1-28, July.
    3. 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.
    4. Liang Wang & Huizhong Lin & Kambiz Ahmadi & Yuhlong Lio, 2021. "Estimation of Stress-Strength Reliability for Multicomponent System with Rayleigh Data," Energies, MDPI, vol. 14(23), pages 1-23, November.

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