Bayesian analysis of the Xgamma distribution under type II censored accelerated life testing: Simulation-based Insights and Reliability applications

Abstract

This study introduces a robust Bayesian framework for simple-step stress accelerated life testing. For modeling lifetime characteristics, this study adopts the Xgamma distribution as the principal life model, Bayesian parameter estimation is conducted using the markov chain monte carlo method under three distinct loss functions: the squared error loss function, generalized entropy loss function, and linear exponential loss function. The resulting Bayesian estimators are analyzed and compared to those obtained through the classical maximum likelihood estimation method. Finally, the proposed methods are illustrated with the analysis of two real data sets.

Keywords

• Accelerated life testing
• Bayesian estimation
• Xgamma distribution
• type-II censoring

Supporting Institution

not applicable

Ethical Statement

The author declare that there are no conflict of interest regarding the publication of this paper

References

1. [1] I. Alam and A. Ahmed, Inference on maintenance service policy under step-stress partially accelerated life tests using progressive censoring, J. Stat. Comput. Simul. 92, 813–829, 2022.
2. [2] N. Hakamipour, Comparison between constant-stress and step-stress accelerated life tests under a cost constraint for progressive type I censoring, Seq. Analy 40 (1), 17–31, 2021.
3. [3] S.A Lone, H. Panahi and I. Shah, Bayesian prediction interval for constant- stress partially accelerated life test model under censored data, J. Taibah university for sciences 15 (1), 1178-1187, 2021.
4. [4] M. Kamal, A. Rahman, S. Zarrin and H. Kausar, Statistical Inference under Step Stress Partially accelerated life testing for adaptive type-II progressive hybrid censored data, J. Reli. Stat. Stud. 14 (2), 585–614, 2021.
5. [5] B. Liu, Y. Shi, J. Cai and R. Wang, Reliability analysis of masked data in adaptive step-stress partially accelerated lifetime tests with progressive removal, Commun. Stat. Theory Methods 46, 6174–6191, 2017.
6. [6] L.-S. Chen, M.-C. Yang and T. Liang, Curtailed Bayesian sampling plans for exponential distributions based on type-II censored samples, J. Stat. Comput. Simul. 87 (6), 1160–78, 2017.
7. [7] A.A. Abdel-Ghaly, A.F. Attia and M.M. Abdel-Ghani, The maximum likelihood estimates in step-stress partially accelerated Life tests for the weibull parameters in censored Data, Commun. Stat- Theory and Methods 31 (4), 551–73, 2002.
8. [8] S.A. Lone, Simulating Frechet distribution under multiply censored partially accelerated life testing, Ann. Data Sci. 10, 1447–1458, 2022.

9. [9] E.K. Al-Hussaini and A.H. Abdel-Hamid, Bayesian estimation of the parameters, reliability and hazard rate functions of mixtures under accelerated life tests, Commun. Stat. Simul. Comput. 33, 963–982, 2004.
10. [10] R.A. Rather and A. Afaq, Bayesian reliability estimation for Copoun distribution using type II censored step-stress accelerated life tests: methods and applications, Seq. Analy. 44 (4), 427-450, 2025.
11. [11] L.-S. Chen, T. Liang and M.-C. Yang, Designing efficient Bayesian sampling plans based on the simple step-stress test under random stress-change time for censored data, J. Stat. Comput. Simul. 93 (7), 1104–29, 2023.
12. [12] S.A Lone, I. Alam and A. Rehman, Statistical analysis under geometric process in accelerated life testing plans for generalized exponential distribution, Ann. Data Sci. 10, 1653-1665, 2021.
13. [13] F.-K. Wang, Y. Cheng and W. Lu, Partially accelerated life tests for Weibull distribution under multiply censored data, Commun. Stat. Simul. Comput. 41 (9), 1667–78, 2012.
14. [14] R.A. Rather and A. Afaq, Statistical inference of step-stress partially accelerated life tests for the Chris-Jerry distribution under type-I censored data with engineering applications, Hacet. J. Math. Stat. 54 (5), 2068-2085, 2025.
15. [15] S.A Lone, Multiple censored partially accelerated life testing for Power function model, Appl. Math. Inf. Sci. 15 (2), 147-152, 2021.
16. [16] A.A. Ismail, Parameter estimation under failure-censored constant-stress life testing model: A Bayesian approach, Seq. Analy. 34 (2), 264–76, 2015.
17. [17] S. Sen, SS. Maiti and N. Chandra, The Xgamma distribution: Statistical Properties and Application, J. Mod. Appl. Stat. Methods. 15 (1),38, 774–788, 2016.
18. [18] Q.W. Meeker and L.A. Escobar, Statistical Methods for Reliability Data, Wiley, New York, 1998.
19. [19] P. Hall, Theoretical comparison of bootstrap confidence intervals, Ann Stat. 16, 927–953, 1988.
20. [20] D. Samanta and D. Kundu, Order restricted inference of a multiple step-stress model, CSDA 117 (1), 62–75 2018.
21. [21] M.D. Nichols and W.J. Padgett, A bootstrap control chart for Weibull percentiles, Qual. Reliab. Eng. Int. 22 (2), 141–151, 2006.
22. [22] F. Proschan, Theoretical explanation of observed decreasing failure rate, Technometrics 5 (3), 375–383, 1963.