Inference of exponentiated Teissier parameters from adaptive progressively type-II hybrid censored data

Refah Alotaibi; Mazen Nassar; Ahmed Elshahhat; Refah Alotaibi; Mazen Nassar; Ahmed Elshahhat

doi:10.3934/math.2025525

AIMS Mathematics

2025, Volume 10, Issue 5: 11556-11591. doi: 10.3934/math.2025525

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Inference of exponentiated Teissier parameters from adaptive progressively type-II hybrid censored data

1.
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
2.
Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
3.
Faculty of Technology and Development, Zagazig University, Zagazig 44519, Egypt

Received: 02 February 2025 Revised: 03 May 2025 Accepted: 12 May 2025 Published: 20 May 2025
MSC : 62F10, 62F15, 62N01, 62N05

Reliability evaluation holds significant importance in multiple fields, especially in engineering. Given the fast-paced advancement of modern products, researchers face the challenge of gathering a suitable amount of observed data on products that exhibit high reliability. An adaptive progressively Type-II hybrid censoring strategy is a commonly used form of censorship that helps to improve the accuracy of statistical tests by ending the experiment after getting a predetermined number of observed data. In this paper, we use this technique when the parent distribution of the population under consideration is the exponentiated Teissier distribution. We use the likelihood method to calculate point and interval estimates for model parameters and reliability indices. To determine the required interval ranges for various parameters, we use both the normal approximation of likelihood estimates and the normal approximation of their logarithm. Additionally, the Bayesian estimation method is employed to obtain point estimates and two types of credible intervals by sampling from the full conditional distributions. A simulation experiment is carried out to compare different approaches through varied experimental plans, effective number of failures, and priors. Two engineering applications are considered by analyzing the failure times of electronic components and aircraft windshields.
- exponentiated Teissier,
- adaptive progressive censoring,
- likelihood and Bayesian estimation,
- reliability estimation
Citation: Refah Alotaibi, Mazen Nassar, Ahmed Elshahhat. Inference of exponentiated Teissier parameters from adaptive progressively type-II hybrid censored data[J]. AIMS Mathematics, 2025, 10(5): 11556-11591. doi: 10.3934/math.2025525

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Abstract

Reliability evaluation holds significant importance in multiple fields, especially in engineering. Given the fast-paced advancement of modern products, researchers face the challenge of gathering a suitable amount of observed data on products that exhibit high reliability. An adaptive progressively Type-II hybrid censoring strategy is a commonly used form of censorship that helps to improve the accuracy of statistical tests by ending the experiment after getting a predetermined number of observed data. In this paper, we use this technique when the parent distribution of the population under consideration is the exponentiated Teissier distribution. We use the likelihood method to calculate point and interval estimates for model parameters and reliability indices. To determine the required interval ranges for various parameters, we use both the normal approximation of likelihood estimates and the normal approximation of their logarithm. Additionally, the Bayesian estimation method is employed to obtain point estimates and two types of credible intervals by sampling from the full conditional distributions. A simulation experiment is carried out to compare different approaches through varied experimental plans, effective number of failures, and priors. Two engineering applications are considered by analyzing the failure times of electronic components and aircraft windshields.

References

[1]	G. Teissier, Recherches sur le vieillissement et sur les lois de mortalite, Ann. Physiol. Physicochim. Biol., 10 (1934), 237–284.
[2]	A. G. Laurent, Failure and mortality from wear and ageing. The Teissier model, In: G. P. Patil, S. Kotz, J. K. Ord, A modern course on statistical distributions in scientific work, NATO Advanced Study Institutes Series, Springer, Dordrecht, 17 (1975), 301–320. https://doi.org/10.1007/978-94-010-1845-6_22
[3]	E. J. Muth, Reliability models with positive memory derived from the mean residual life function, Theory Appl. Reliabil., 2 (1977), 401–435.
[4]	P. Jodra, M. D. Jimenez-Gamero, On the Muth distribution, Math. Model. Anal., 20 (2015), 291–310. https://doi.org/10.3846/13926292.2015.1048540 doi: 10.3846/13926292.2015.1048540
[5]	P. Jodra, H. W. Gomez, M. D. Jimenez-Gamero, M. V. Alba-Fernandez, The power Muth distribution, Math. Model. Anal., 22 (2017), 186–201, https://doi.org/10.3846/13926292.2017.1289481 doi: 10.3846/13926292.2017.1289481
[6]	V. K. Sharma, S. V. Singh, K. Shekhawat, Exponentiated Teissier distribution with increasing, decreasing and bathtub hazard functions, J. Appl. Stat., 49 (2022), 371–393, https://doi.org/10.1080/02664763.2020.1813694 doi: 10.1080/02664763.2020.1813694
[7]	H. Pasha-Zanoosi, A. Pourdarvish, A. Asgharzadeh, Multicomponent stress-strength reliability with exponentiated Teissier distribution, Austrian J. Stat., 51 (2022), 35–59, https://doi.org/10.17713/ajs.v51i4.1327 doi: 10.17713/ajs.v51i4.1327
[8]	H. Pasha-Zanoosi, Reliability of stress-strength model for exponentiated Teissier distribution based on lower record values, Jpn. J. Stat. Data Sci., 7 (2024), 57–81, https://doi.org/10.1007/s42081-023-00229-8 doi: 10.1007/s42081-023-00229-8
[9]	W. R. Blischke, D. P. Murthy, Reliability: modeling, prediction, and optimization, John Wiley & Sons, 2000. https://doi.org/10.1002/9781118150481
[10]	R. Aggarwala, N. Balakrishnan, Some properties of progressive censored order statistics from arbitrary and uniform distributions with applications to inference and simulation, J. Stat. Plan. Infer., 70 (1998), 35–49, https://doi.org/10.1016/S0378-3758(97)00173-0 doi: 10.1016/S0378-3758(97)00173-0
[11]	S. Anwar, S. A. Lone, A. Khan, S. Almutlak, Stress-strength reliability estimation for the inverted exponentiated Rayleigh distribution under unified progressive hybrid censoring with application, Electron. Res. Arch., 31 (2023), 4011–4033. https://doi.org/10.3934/era.2023204 doi: 10.3934/era.2023204
[12]	S. A. Lone, H. Panahi, S. Anwar, S. Shahab, Inference of reliability model with Burr type XII distribution under two sample balanced progressive censored samples, Phys. Scr., 99 (2024), 025019. https://doi.org/10.1088/1402-4896/ad1c29 doi: 10.1088/1402-4896/ad1c29
[13]	D. Kundu, A. Joarder, Analysis of Type-II progressively hybrid censored data, Comput. Stat. Data Anal., 50 (2006), 2509–2528. https://doi.org/10.1016/j.csda.2005.05.002 doi: 10.1016/j.csda.2005.05.002
[14]	H. K. T. Ng, D. Kundu, P. S. Chan, Statistical analysis of exponential lifetimes under an adaptive Type-II progressive censoring scheme, Nav. Res. Log., 56 (2009), 687–698. https://doi.org/10.1002/nav.20371 doi: 10.1002/nav.20371
[15]	M. Nassar, O. E. Abo-Kasem, Estimation of the inverse Weibull parameters under adaptive type-II progressive hybrid censoring scheme, J. Comput. Appl. Math., 315 (2017), 228–239. https://doi.org/10.1016/j.cam.2016.11.012 doi: 10.1016/j.cam.2016.11.012
[16]	H. Panahi, N. Moradi, Estimation of the inverted exponentiated Rayleigh distribution based on adaptive Type II progressive hybrid censored sample, J. Comput. Appl. Math., 364 (2020), 112345. https://doi.org/10.1016/j.cam.2019.112345 doi: 10.1016/j.cam.2019.112345
[17]	A. Elshahhat, M. Nassar, Bayesian survival analysis for adaptive Type-II progressive hybrid censored Hjorth data, Comput. Stat., 36 (2021), 1965–1990. https://doi.org/10.1007/s00180-021-01065-8 doi: 10.1007/s00180-021-01065-8
[18]	A. Elshahhat, O. E. Abo-Kasem, H. S. Mohammed, Survival analysis of the PRC model from adaptive progressively hybrid type-II censoring and its engineering applications, Mathematics, 11 (2023), 3124, https://doi.org/10.3390/math11143124. doi: 10.3390/math11143124
[19]	A. Elshahhat, R. Alotaibi, M. Nassar, Statistical inference of the Birnbaum-Saunders model using adaptive progressively hybrid censored data and its applications, AIMS Math., 9 (2024), 11092–11121. https://doi.org/10.3934/math.2024544 doi: 10.3934/math.2024544
[20]	Q. Lv, Y. Tian, W. Gui, Statistical inference for Gompertz distribution under adaptive type-II progressive hybrid censoring, J. Appl. Stat., 51 (2024), 451–480, https://doi.org/10.1080/02664763.2022.2136147 doi: 10.1080/02664763.2022.2136147
[21]	N. Balakrishnan, N. Kannan, C. T. Lin, S. J. S. Wu, Inference for the extreme value distribution under progressive Type-II censoring, J. Stat. Comput. Simul., 74 (2004), 25–45, https://doi.org/10.1080/0094965031000105881 doi: 10.1080/0094965031000105881
[22]	A. Henningsen, O. Toomet, maxLik: a package for maximum likelihood estimation in R, Comput. Stat., 26 (2011), 443–458, https://doi.org/10.1007/s00180-010-0217-1 doi: 10.1007/s00180-010-0217-1
[23]	D. Kundu, Bayesian inference and life testing plan for the Weibull distribution in presence of progressive censoring, Technometrics, 50 (2008), 144–154, https://doi.org/10.1198/004017008000000217 doi: 10.1198/004017008000000217
[24]	M. Plummer, N. Best, K. Cowles, K. Vines, CODA: convergence diagnosis and output analysis for MCMC, R News, 6 (2006), 7–11.
[25]	J. F. Lawless, Statistical models and methods for lifetime data, 2 Eds., Hoboken, NJ, USA: John Wiley and Sons, 2011.
[26]	A. Mahdavi, D. Kundu, A new method for generating distributions with an application to exponential distribution, Commun. Stat.-Theory Methods, 46 (2017), 6543–6557. https://doi.org/10.1080/03610926.2015.1130839 doi: 10.1080/03610926.2015.1130839
[27]	R. D. Gupta, D. Kundu, Generalized exponential distribution: different method of estimations, J. Stat. Comput. Simul., 69 (2001), 315–337. https://doi.org/10.1080/00949650108812098 doi: 10.1080/00949650108812098
[28]	S. Nadarajah, F. Haghighi, An extension of the exponential distribution, Statistics, 45 (2011), 543–558, https://doi.org/10.1080/02331881003678678. doi: 10.1080/02331881003678678
[29]	W. Weibull, A statistical distribution function of wide applicability, J. Appl. Mech., 18 (1951), 293–297.
[30]	N. L. Johnson, S. Kotz, N. Balakrishnan, Continuous univariate distributions, 2 Eds., John Wiley and Sons, 1995.
[31]	P. R. D. Marinho, R. B. Silva, M. Bourguignon, G. M. Cordeiro, S. Nadarajah, AdequacyModel: an R package for probability distributions and general purpose optimization, PloS One, 14 (2019), e0221487. https://doi.org/10.1371/journal.pone.0221487 doi: 10.1371/journal.pone.0221487
[32]	D. N. P. Murthy, M. Xie, R. Jiang, Weibull models, Wiley Series in Probability and Statistics, Hoboken: Wiley, 2004.

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