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Interval estimation of multicomponent stress–strength reliability based on inverse Weibull distribution

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  • Jana, Nabakumar
  • Bera, Samadrita

Abstract

This paper considers interval estimation of stress–strength reliability of k-out-of-n system when the stress and strength components follow inverse Weibull distributions. Besides the asymptotic and bootstrap confidence intervals, we derive HPD credible intervals when the shape parameter is known or unknown. We also propose the pivotal quantity and generalized confidence interval of reliability. We study the estimation of multicomponent stress–strength reliability using lower record values. Generalized, asymptotic, and bootstrap confidence intervals are derived using lower record values. We also derive confidence intervals of multicomponent stress–strength reliability assuming the shape parameters are different. We propose HPD credible intervals, generalized and bootstrap confidence intervals. Monte Carlo simulation is performed to compare the confidence intervals. Real data examples are presented to demonstrate the practicability of the confidence intervals.

Suggested Citation

  • Jana, Nabakumar & Bera, Samadrita, 2022. "Interval estimation of multicomponent stress–strength reliability based on inverse Weibull distribution," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 191(C), pages 95-119.
    • Handle: RePEc:eee:matcom:v:191:y:2022:i:c:p:95-119
    DOI: 10.1016/j.matcom.2021.07.026
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    References listed on IDEAS

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    1. Wang, Bing Xing & Yu, Keming & Coolen, Frank P.A., 2015. "Interval estimation for proportional reversed hazard family based on lower record values," Statistics & Probability Letters, Elsevier, vol. 98(C), pages 115-122.
    2. Wang, Bing Xing & Ye, Zhi-Sheng, 2015. "Inference on the Weibull distribution based on record values," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 26-36.
    3. 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.
    4. Baklizi, Ayman, 2008. "Likelihood and Bayesian estimation of using lower record values from the generalized exponential distribution," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3468-3473, March.
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