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Reliability analysis of bathtub-shaped distribution using empirical Bayesian and E-Bayesian estimations under progressive Type-II censoring

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  • Weihua Shi
  • Wenhao Gui

Abstract

This paper investigates the performance of empirical Bayesian and E-Bayesian estimation of the bathtub-shaped distribution based on the progressive Type-II censored samples. These two estimations overcome the selection of hyperparameters in the Bayesian method. The empirical Bayesian analysis employs the classical approach to determine the hyperparameters. The E-Bayesian estimation uses the prior distribution of hyperparameters to derive the expectation of Bayesian estimates. The estimates of parameters are derived under the squared error loss and LINEX loss functions. The extensive simulations show the results of the empirical Bayesian estimates and the E-Bayesain estimates. Further, the empirical Bayesian estimation is also presented to analyze the parameters of bathtub-shaped distribution based on the general progressive Type-II censored samples. The two datasets from the electromechanical field and medical survival analysis are analyzed using the empirical Bayesian and E-Bayesian methods.

Suggested Citation

  • Weihua Shi & Wenhao Gui, 2024. "Reliability analysis of bathtub-shaped distribution using empirical Bayesian and E-Bayesian estimations under progressive Type-II censoring," Journal of Risk and Reliability, , vol. 238(3), pages 604-621, June.
    • Handle: RePEc:sae:risrel:v:238:y:2024:i:3:p:604-621
    DOI: 10.1177/1748006X231157827
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    References listed on IDEAS

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    1. Abdalla Rabie & Eslam Hussam & Abdisalam Hassan Muse & Ramy Abdelhamid Aldallal & Amirah Saeed Alharthi & Hassan M. Aljohani & Melike Kaplan, 2022. "Estimations in a Constant-Stress Partially Accelerated Life Test for Generalized Rayleigh Distribution under Type-II Hybrid Censoring Scheme," Journal of Mathematics, Hindawi, vol. 2022, pages 1-9, April.
    2. Shuo-Jye Wu, 2008. "Estimation of the two-parameter bathtub-shaped lifetime distribution with progressive censoring," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(10), pages 1139-1150.
    3. Hassan Piriaei & Gholamhossein Yari & Rahman Farnoosh, 2020. "On E-Bayesian estimations for the cumulative hazard rate and mean residual life under generalized inverted exponential distribution and type-II censoring," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(5), pages 865-889, April.
    4. Anurag Pathak & Manoj Kumar & Sanjay Kumar Singh & Umesh Singh, 2022. "Assessing the effect of E-Bayesian inference for Poisson inverse exponential distribution parameters under different loss functions and its application," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(17), pages 5763-5805, September.
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