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Analysis of Block Adaptive Type-II Progressive Hybrid Censoring with Weibull Distribution

Author

Listed:
  • Kundan Singh

    (Department of Mathematics, Indian Institute of Technology Patna, Bihta 801106, India)

  • Yogesh Mani Tripathi

    (Department of Mathematics, Indian Institute of Technology Patna, Bihta 801106, India)

  • Liang Wang

    (School of Mathematics, Yunnan Normal University, Kunming 650500, China)

  • Shuo-Jye Wu

    (Department of Statistics, Tamkang University, New Taipei City 251301, Taiwan)

Abstract

The estimation of unknown model parameters and reliability characteristics is considered under a block adaptive progressive hybrid censoring scheme, where data are observed from a Weibull model. This censoring scheme enhances experimental efficiency by conducting experiments across different testing facilities. Point and interval estimates for parameters and reliability assessments are derived using both classical and Bayesian approaches. The existence and uniqueness of maximum likelihood estimates are established. Consequently, reliability performance and differences across different testing facilities are analyzed. In addition, a Metropolis–Hastings sampling algorithm is developed to approximate complex posterior computations. Approximate confidence intervals and highest posterior density credible intervals are obtained for the parametric functions. The performance of all estimators is evaluated through an extensive simulation study, and observations are discussed. A cancer dataset is analyzed to illustrate the findings under the block adaptive censoring scheme.

Suggested Citation

  • Kundan Singh & Yogesh Mani Tripathi & Liang Wang & Shuo-Jye Wu, 2024. "Analysis of Block Adaptive Type-II Progressive Hybrid Censoring with Weibull Distribution," Mathematics, MDPI, vol. 12(24), pages 1-21, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:24:p:4026-:d:1549866
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    References listed on IDEAS

    as
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    2. El-Sayed A. El-Sherpieny & Ehab M. Almetwally & Hiba Z. Muhammed, 2023. "Bayesian and Non-Bayesian Estimation for the Parameter of Bivariate Generalized Rayleigh Distribution Based on Clayton Copula under Progressive Type-II Censoring with Random Removal," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1205-1242, August.
    3. Kumari, Rani & Tripathi, Yogesh Mani & Sinha, Rajesh Kumar & Wang, Liang, 2023. "Reliability estimation for bathtub-shaped distribution under block progressive censoring," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 213(C), pages 237-260.
    4. Hon Keung Tony Ng & Debasis Kundu & Ping Shing Chan, 2009. "Statistical analysis of exponential lifetimes under an adaptive Type‐II progressive censoring scheme," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(8), pages 687-698, December.
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