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Statistical Analysis of a Lifetime Distribution with a Bathtub-Shaped Failure Rate Function under Adaptive Progressive Type-II Censoring

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  • Siyi Chen

    (Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China)

  • Wenhao Gui

    (Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China)

Abstract

In this paper, the estimation problem of two parameters of a lifetime distribution with a bathtub-shaped failure rate function based on adaptive progressive type-II censored data is discussed. This censoring scheme allows the experiment to be more efficient in the use of time and cost while ensuring the statistical inference efficiency based on the experimental results. Maximum likelihood estimators are proposed and the approximate confidence intervals for two parameters are computed using the asymptotic normality. Lindley approximation and Gibbs sampling are used to obtain Bayes point estimates and the latter is also used to generate Bayes two-sided credible intervals. Finally, the performance of various estimation methods is evaluated through simulation experiments, and the proposed estimation method is illustrated through the analysis of a real data set.

Suggested Citation

  • Siyi Chen & Wenhao Gui, 2020. "Statistical Analysis of a Lifetime Distribution with a Bathtub-Shaped Failure Rate Function under Adaptive Progressive Type-II Censoring," Mathematics, MDPI, vol. 8(5), pages 1-21, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:670-:d:351363
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    References listed on IDEAS

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    1. Vikas Kumar Sharma & Sanjay Kumar Singh & Umesh Singh & Faton Merovci, 2016. "The generalized inverse Lindley distribution: A new inverse statistical model for the study of upside-down bathtub data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(19), pages 5709-5729, October.
    2. 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.
    3. 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.
    4. Manoj Kumar Rastogi & Yogesh Mani Tripathi & Shuo-Jye Wu, 2012. "Estimating the parameters of a bathtub-shaped distribution under progressive type-II censoring," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(11), pages 2389-2411, July.
    5. Chen, Zhenmin, 2000. "A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function," Statistics & Probability Letters, Elsevier, vol. 49(2), pages 155-161, August.
    6. Mohammad Z. Raqab & Omar M. Bdair & Fahad M. Al-Aboud, 2018. "Inference for the two-parameter bathtub-shaped distribution based on record data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(3), pages 229-253, April.
    7. Essam A. Ahmed, 2014. "Bayesian estimation based on progressive Type-II censoring from two-parameter bathtub-shaped lifetime model: an Markov chain Monte Carlo approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(4), pages 752-768, April.
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    Cited by:

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