Statistical Inference for Harmonic New Better Than Renewal Used in Expectation Class of Life Distributions Under Random Progressive Censoring
DOI:
https://doi.org/10.13052/jrss0974-8024.1926Keywords:
HNBRUE, HNWRUE, progressive Type II censoring, life distributions, simulation model, bootstrap confidence intervals, power analysis, small-sample robustnessAbstract
This paper extends the theoretical framework and testing methodology for the Harmonic New Better (or Worse) than Renewal Used in Expectation classes of life distributions. We revisit and refine empirical test statistics under random censoring, incorporating progressive Type II censoring schemes to enhance applicability. Modern lifetime distributions, including Lognormal, Gumbel, and Weibull models, are incorporated into the power analysis, with results strengthened through Monte Carlo simulations, bootstrap confidence intervals, and variance estimates. The findings highlight the robustness and practical value of the proposed methods, particularly in small-sample scenarios, and provide guidance for implementation through readily available software tools.
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References
Elkahlout, G. R. (2005). On testing statistics of harmonic new better than renewal used in expectation class of life distributions. Umm Al-Qura University Journal of Science, Medicine and Engineering, 17(2), 183–198.
Balakrishnan, N., and Zhao, Y. (2020). Progressive censoring: Theory, methods, and applications. Academic Press.
Wang, X., and Zhang, Y. (2019). Bootstrap testing procedures for aging classes under right censoring. Computational Statistics & Data Analysis, 135, 107–122. https://doi.org/10.1016/j.csda.2019.04.003.
Belzunce, F., Franco, M., and Ruiz, J. M. (2016). Characterizations of new, better-than-used properties in the harmonic mean sense. Journal of Applied Probability, 53(2), 499–511. https://doi.org/10.1017/jpr. 2016.21.
Abouammoh, A. M., and Elkahlout, G. R. (1999). Tests of new better than renewal used with randomly censored samples. Parishankhyan Samikha, 6(1&2), 47–63.
Elsawah, S., Ryan, M. J., and Abdullah, A. (2021). Reliability modeling of cyber-physical systems with reset behavior: A systems engineering perspective. Reliability Engineering & System Safety, 210, 107522. https://doi.org/10.1016/j.ress.2021.107522.
Kundu, D., and Manglick, A. (2013). Testing exponentiality under hybrid censoring. Communications in Statistics – Simulation and Computation, 42(6), 1401–1423. https://doi.org/10.1080/03610918.2012.686424.
Al-Zahrani, B. M., and Stoyanov, J. (2010). Moment inequalities for HNBRUE with hypothesis testing application. Statistical Methodology, 7(1), 58–67. https://doi.org/10.1016/j.stamet.2009.09.004.
Cramer, E. (2025). Structure of hybrid censoring schemes and its implications. Metrika, 88(3), 393–417. https://doi.org/10.1007/s00184-024-00960-6.
Asadi, S., Panahi, H., Swarup, C., and Lone, S. A. (2022). Inference on adaptive progressive hybrid censored accelerated life test for Gompertz distribution and its evaluation for virus-containing micro droplets data. Alexandria Engineering Journal, 61(12), 10071–10084. https://doi.org/10.1016/j.aej.2022.02.061.
Sudheesh, K. K., and Dewan, I. (2013). U-statistics approach to Hollander–Proschan test for NBUE alternatives. Statistics and Applications, 11(1–2), 87–92. https://doi.org/10.1007/s00362-016-0808-2.
Lodhi, C., Tripathi, Y. M., and Rastogi, M. K. (2019). Estimating the parameters of a truncated normal distribution under progressive type II censoring. Communications in Statistics – Simulation and Computation, Advance online publication. https://doi.org/10.1080/03610918.2019.1614619.
Abu Awwad, R. R., Raqab, M. Z., and Al-Mudahakha, I. M. (2015). Statistical inference based on progressively Type II censored data from Weibull model. Communications in Statistics – Simulation and Computation, 44(10), Article 12. https://doi.org/10.1080/03610918.2013.842589.
Khalifa, E. H., Ramadan, D. A., Alqifari, H. N., and El-Desouky, B. S. (2024). Bayesian inference for inverse power exponentiated Pareto distribution using progressive type-II censoring with application to flood-level data analysis. Symmetry, 16(3), Article 309. https://doi.org/10.3390/sym16030309.
Almetwally, E. M., Jawa, T. M., Sayed-Ahmed, N., Park, C., Zakarya, M., and Dey, S. (2022). Analysis of unit-Weibull based on progressive type-II censored with optimal scheme. Alexandria Engineering Journal, 63(1), 321–338. https://doi.org/10.1016/j.aej.2022.07.064.
Moharib Alsarray, R. M. M., Kazempoor, J., and Ahmadi Nadi, A. (2021). Monitoring the Weibull shape parameter under progressive censoring in the presence of independent competing risks. Journal of Applied Statistics, 50(4), 945–962. https://doi.org/10.1080/02664763.2021.2003760.
