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Inference of improved adaptive progressively censored competing risks data for Weibull lifetime models

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  • Ahmed Elshahhat

    (Zagazig University)

  • Mazen Nassar

    (King Abdulaziz University
    Zagazig University)

Abstract

Recently, an improved adaptive Type-II progressive censoring scheme is proposed to ensure that the experimental time will not pass a pre-fixed time and ends the test after recording a pre-fixed number of failures. This paper studies the inference of the competing risks model from Weibull distribution under the improved adaptive progressive Type-II censoring. For this goal, we used the latent failure time model with Weibull lifetime distributions with common shape parameters. The point and interval estimation problems of parameters, reliability and hazard rate functions using the maximum likelihood and Bayesian estimation methods are considered. Moreover, making use of the asymptotic normality of classical estimators and delta method, approximate intervals are constructed via the observed Fisher information matrix. Following the assumption of independent gamma priors, the Bayes estimates of the scale parameters have closed expressions, but when the common shape parameter is unknown, the Bayes estimates cannot be formed explicitly. To solve this difficulty, we recommend using Markov chain Monte Carlo routine to compute the Bayes estimates and to construct credible intervals. A comprehensive Monte Carlo simulation is conducted to judge the behavior of the offered methods. Ultimately, analysis of electrodes data from the life-test of high-stress voltage endurance is provided to illustrate all proposed inferential procedures.

Suggested Citation

  • Ahmed Elshahhat & Mazen Nassar, 2024. "Inference of improved adaptive progressively censored competing risks data for Weibull lifetime models," Statistical Papers, Springer, vol. 65(3), pages 1163-1196, May.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:3:d:10.1007_s00362-023-01417-0
    DOI: 10.1007/s00362-023-01417-0
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    References listed on IDEAS

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    1. S. K. Ashour & M. Nassar, 2017. "Inference for Weibull distribution under adaptive Type-I progressive hybrid censored competing risks data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(10), pages 4756-4773, May.
    2. Mazen Nassar & Refah Alotaibi & Chunfang Zhang, 2022. "Estimation of Reliability Indices for Alpha Power Exponential Distribution Based on Progressively Censored Competing Risks Data," Mathematics, MDPI, vol. 10(13), pages 1-25, June.
    3. Ahmed Elshahhat & Mazen Nassar, 2021. "Bayesian survival analysis for adaptive Type-II progressive hybrid censored Hjorth data," Computational Statistics, Springer, vol. 36(3), pages 1965-1990, September.
    4. Debasis Kundu & Rameshwar Gupta, 2007. "Analysis of Hybrid Life-tests in Presence of Competing Risks," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 65(2), pages 159-170, February.
    5. Essam A. Ahmed & Ziyad Ali Alhussain & Mukhtar M. Salah & Hanan Haj Ahmed & M. S. Eliwa, 2020. "Inference of progressively type-II censored competing risks data from Chen distribution with an application," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(13-15), pages 2492-2524, November.
    6. Xiaolin Shi & Yanchao Liu & Yimin Shi, 2017. "Statistical analysis for masked hybrid system lifetime data in step-stress partially accelerated life test with progressive hybrid censoring," PLOS ONE, Public Library of Science, vol. 12(10), pages 1-15, October.
    7. 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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