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Statistical Analysis of Improved Type-II Adaptive Progressive Hybrid Censored NH Data

Author

Listed:
  • EL-Sayed A. El-Sherpieny

    (Cairo University)

  • Ahmed Elshahhat

    (Zagazig University)

  • Nader M. Abdallah

    (Cairo University)

Abstract

Recently, improved Type-II adaptive progressive censoring has been introduced to ensure that the experimental duration does not exceed a certain time and that the test concludes once a predetermined number of failures are recorded. This paper addresses the problem of estimating the unknown parameters as well as the reliability and hazard rate functions of the proposed lifetime Nadarajah-Haghighi distribution when the collected data are obtained from the proposed censoring plan. For each unknown parameter of life, using maximum likelihood and Bayes inference methods, both point and interval estimators are derived. The approximate confidence intervals are acquired based on the asymptotic normality of the maximum likelihood estimators. Under the assumption of independent gamma priors, the Bayes estimators cannot be obtained in closed form, therefore, the Markov-Chain Monte-Carlo approximation technique via the Metropolis–Hastings algorithm is utilized to evaluate the Bayes point estimates and to create their credible interval estimates. To compare the efficiency of the different proposed estimators, in terms of root mean squared-error, mean relative absolute bias, and average interval length values, extensive Monte Carlo simulations are implemented. Ultimately, to show how the acquired estimators can be applied in a real-life engineering scenario, a real data set consisting of eighteen failure times for electronic devices is analyzed.

Suggested Citation

  • EL-Sayed A. El-Sherpieny & Ahmed Elshahhat & Nader M. Abdallah, 2024. "Statistical Analysis of Improved Type-II Adaptive Progressive Hybrid Censored NH Data," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 86(2), pages 721-754, August.
    • Handle: RePEc:spr:sankha:v:86:y:2024:i:2:d:10.1007_s13171-024-00345-x
    DOI: 10.1007/s13171-024-00345-x
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    References listed on IDEAS

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    1. Samir K. Ashour & Ahmed A. El-Sheikh & Ahmed Elshahhat, 2022. "Inferences and Optimal Censoring Schemes for Progressively First-Failure Censored Nadarajah-Haghighi Distribution," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 885-923, August.
    2. Arne Henningsen & Ott Toomet, 2011. "maxLik: A package for maximum likelihood estimation in R," Computational Statistics, Springer, vol. 26(3), pages 443-458, September.
    3. Kundu, Debasis & Joarder, Avijit, 2006. "Analysis of Type-II progressively hybrid censored data," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2509-2528, June.
    4. Sanku Dey & Ahmed Elshahhat & Mazen Nassar, 2023. "Analysis of progressive type-II censored gamma distribution," Computational Statistics, Springer, vol. 38(1), pages 481-508, March.
    5. 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.
    6. Ahmed Elshahhat & Refah Alotaibi & Mazen Nassar, 2022. "Inferences for Nadarajah–Haghighi Parameters via Type-II Adaptive Progressive Hybrid Censoring with Applications," Mathematics, MDPI, vol. 10(20), pages 1-19, October.
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