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Estimation of reliability in a multicomponent stress-strength model for inverted exponentiated Rayleigh distribution under progressive censoring

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  • Amulya Kumar Mahto

    (Indian Institute of Technology Patna)

  • Yogesh Mani Tripathi

    (Indian Institute of Technology Patna)

Abstract

We consider estimation of the multicomponent stress-strength reliability for inverted exponentiated Rayleigh distributions under progressive Type II censoring. It is assumed that stress and strength variables follow inverted exponentiated Rayleigh distributions with a common scale parameter. Point and interval estimates of the reliability are obtained using maximum likelihood and Bayesian approaches when common parameter is unknown. Bayes estimates are derived using Lindley approximation and Markov chain Monte Carlo methods. The case of known common parameter is also considered. Then uniformly minimum variance unbiased estimator of the reliability is derived. We have also computed the exact Bayes estimates under the squared error loss function. The asymptotic and HPD intervals of the reliability are constructed under this case also. Proposed methods are compared numerically using simulations and comments are obtained. Finally, a real data set is analyzed for illustration purposes.

Suggested Citation

  • Amulya Kumar Mahto & Yogesh Mani Tripathi, 2020. "Estimation of reliability in a multicomponent stress-strength model for inverted exponentiated Rayleigh distribution under progressive censoring," OPSEARCH, Springer;Operational Research Society of India, vol. 57(4), pages 1043-1069, December.
    • Handle: RePEc:spr:opsear:v:57:y:2020:i:4:d:10.1007_s12597-020-00448-7
    DOI: 10.1007/s12597-020-00448-7
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    References listed on IDEAS

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    1. Mustafa Nadar & Fatih Kızılaslan, 2014. "Classical and Bayesian estimation of $$P(X>Y)$$ P ( X > Y ) using upper record values from Kumaraswamy’s distribution," Statistical Papers, Springer, vol. 55(3), pages 751-783, August.
    2. Fatih Kızılaslan, 2018. "Classical and Bayesian estimation of reliability in a multicomponent stress–strength model based on a general class of inverse exponentiated distributions," Statistical Papers, Springer, vol. 59(3), pages 1161-1192, September.
    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. Debasis Kundu & Rameshwar D. Gupta, 2005. "Estimation of P[Y > X] for generalized exponential distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 61(3), pages 291-308, 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.

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