Research Article
BibTex RIS Cite

Parameter and Reliability Estimation for the Rayleigh Distribution under Improved Adaptive Type-II Progressive Censoring Scheme with Binomial Removals

Year 2026, Volume: 47 Issue: 1, 182 - 193, 27.02.2026

Hanefi Gezer , İlhan Usta

https://doi.org/10.17776/csj.1728252
https://izlik.org/JA38ZJ95EF

Abstract

In lifetime and reliability analyses, the Rayleigh distribution is extensively employed to model components or systems characterized by an increasing failure rate. On the other hand, in recent years, the improved adaptive Type-II progressive censoring scheme (IAT-II PCS) has gained considerable attention for its ability to ensure that the testing process concludes within a predetermined time. However, in many real-world applications, the number of units removed at each failure time cannot be predetermined precisely, which renders randomly determined removals a more realistic modeling assumption. Motivated by these considerations, this study focuses on estimating the scale parameter and reliability characteristics of the Rayleigh distribution under the IAT-II PCS with random removals. For this purpose, the maximum likelihood (ML) estimators are used alongside the Bayesian estimators derived under the squared error loss function. An extensive Monte Carlo simulation study is carried out to assess the performance of these estimators. Furthermore, a real data application is included to demonstrate the practical relevance of the proposed approaches. The results indicate that Bayesian estimators based on informative prior achieve better performance in terms of mean square error under the IAT-II PCS with binomial random removals

Keywords

Binomial removal Improved adaptive Type-II progressive censoring Point estimation Rayleigh distribution Reliability characteristics

References

  • [1] Al-Ameen, M., & Abdel-Aty, Y. (2022). Empirical Bayes inference for Rayleigh distribution. Journal of Statistics Applications & Probability, 11(2), 695–708. https://doi.org/10.18576/jsap/110226
  • [2] Alotaibi, R., Nassar, M., & Elshahhat, A. (2025). Reliability analysis of improved Type-II adaptive progressively inverse XLindley censored data. Axioms, 14, 437. https://doi.org/10.3390/axioms14060437
  • [3] Asgharzadeh, A., & Azizpour, M. (2016). Bayesian inference for Rayleigh distribution under hybrid censoring. International Journal of System Assurance Engineering and Management, 239–249. https://doi.org/10.1007/s13198-014-0313-7
  • [4] Balakrishnan, N., & Sandhu, R. (1995). A simple simulation algorithm for generating progressively Type-II censored sample. The American Statistician, 49(2), 229–230. https://doi.org/10.1080/00031305.1995.10476150
  • [5] Dey, S., & Dey, T. (2014). Statistical inference for the Rayleigh distribution under progressively Type-II censoring with binomial removal. Applied Mathematical Modelling, 38(3), 974–982. https://doi.org/10.1080/00949655.2011.590808
  • [6] Dutta, S., Alqifari, H. N., & Almohaimeed, A. (2024). Bayesian and non-Bayesian inference for logistic-exponential distribution using improved adaptive Type-II progressively censored data. PLoS ONE, 19(5), e0298638. https://doi.org/10.1371/journal.pone.0298638
  • [7] Dutta, S., & Kayal, S. (2023). Inference of a competing risks model with partially observed failure causes under improved adaptive Type-II progressive censoring. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 237, 765–780. https://doi.org/10.1177/1748006X221104
  • [8] Elbattal, I., Nassar, M., Ghorbal, A. B., & Elshahhat, A. (2024). Bayesian and E-bayesian reliability analysis of improved adaptive Type-II progressive censored inverted Lindley data. IEEE Access, 12, 99. https://doi.org/10.1109/ACCESS.2024.3408042
  • [9] Elshahhat, A., & Nassar, M. (2023). Inference of improved adaptive progressively censored competing risks data for Weibull lifetime models. Statistical Papers, 65, 1163–1196. https://doi.org/10.1007/s00362-023-01417-0
  • [10] Irfan, M., Dutta, S., & Sharma, A. (2025). Statistical inference and optimal plans for improved adaptive Type-II progressive censored data following Kumaraswamy-G family of distributions. Physica Scripta, 100, 025213. https://doi.org/10.1088/1402-4896/ada216
  • [11] Kaushik, A., & Mradula. (2019). Progressive interval Type-I censored life test plan for Rayleigh distribution. Austrian Journal of Statistics, 48, 76–86. https://doi.org/10.17713/ajs.v48i3.781
  • [12] Lawless, J. F. (1982). Statistical models and methods for lifetime data. John Wiley & Sons.
  • [13] Liao, H., & Gui, W. (2019). Statistical inference of the Rayleigh distribution based on progressively Type II censored competing risks data. Symmetry, 11(7), 898. https://doi.org/10.3390/sym11070898
  • [14] Lone, S. A. (2025). On estimation of Burr Type III model using improved adaptive progressive censoring with application to engineering data. Quality and Reliability Engineering International, 1–10. https://doi.org/10.1002/qre.70072
  • [15] Nassar, M., & Elshahhat, A. (2023). Estimation procedures and optimal censoring schemes for an improved adaptive progressively Type-II censored Weibull distribution. Journal of Applied Statistics, 51, 1664–1688. https://doi.org/10.1080/00264763.2023.2230536
  • [16] Noor, F., Sajid, A., Ghazal, M., Khan, I., Zaman, M., & Baig, I. (2020). Bayesian estimation of Rayleigh distribution in the presence of outliers using progressive censoring. Hacettepe Journal of Mathematics and Statistics, 49(6), 2119–2133. https://doi.org/10.15672/hujms.635684
  • [17] Pak, A., Parham, G. A., & Saraj, M. (2014). Inference for the Rayleigh distribution based on progressive Type-II fuzzy censored data. Journal of Modern Applied Statistical Methods, 13(1), 287–304. https://doi.org/10.22237/jmasm/1398917880
  • [18] Polovko, A. M. (1986). Fundamentals of reliability theory. Academic Press.
  • [19] Raqab, M., & Madi, M. (2002). Bayesian prediction of the total time on test using doubly censored Rayleigh data. Journal of Statistical Computation and Simulation, 72(10), 781–789. https://doi.org/10.1080/00949650214670
  • [20] Tse, S. K., Yang, C., & Yuen, H. K. (2010). Statistical analysis of Weibull distributed lifetime data under Type II progressive censoring with binomial removals. Journal of Applied Statistics, 27(8), 1033–1043. https://doi.org/10.1080/00031305.1995.10476150
  • [21] Yan, W., Li, P., & Yu, Y. (2021). Statistical inference for the reliability of Burr-XII distribution under improved adaptive Type-II progressive censoring. Applied Mathematical Modelling, 95, 38–52. https://doi.org/10.1016/j.apm.2021.01.050
  • [22] Zhang, L., & Yan, R. (2024). Parameter estimation of Chen distribution under improved adaptive Type-II progressive censoring. Journal of Statistical Computation and Simulation, 94, 2830–2861. https://doi.org/10.1080/00949655.2024.2358828
There are 22 citations in total.

Details

Primary Language English
Subjects Computational Statistics
Journal Section Research Article
Authors

Hanefi Gezer 0000-0002-8187-0299

İlhan Usta 0000-0001-5576-2027

Submission Date June 26, 2025
Acceptance Date December 4, 2025
Publication Date February 27, 2026
DOI https://doi.org/10.17776/csj.1728252
IZ https://izlik.org/JA38ZJ95EF
Published in Issue Year 2026 Volume: 47 Issue: 1

Cite

APA Gezer, H., & Usta, İ. (2026). Parameter and Reliability Estimation for the Rayleigh Distribution under Improved Adaptive Type-II Progressive Censoring Scheme with Binomial Removals. Cumhuriyet Science Journal, 47(1), 182-193. https://doi.org/10.17776/csj.1728252

As of 2026, Cumhuriyet Science Journal will be published in six issues per year, released in February, April, June, August, October, and December