When a researcher wants to perform a life-test comparison study of items made by two separate lines inside the same institution, joint censoring strategies are particularly important. In this paper, we present a new joint Type-Ⅰ hybrid censoring that enables an experimenter to stop the investigation as soon as a pre-specified number of failures or time is first achieved. In the context of newly censored data, the estimates of the unknown mean lifetimes of two different Rayleigh populations are acquired using maximum likelihood and Bayesian inferential techniques. The normality characteristic of classical estimators is used to offer asymptotic confidence interval bounds for each unknown parameter. Against gamma conjugate priors, the Bayes estimators and related credible intervals are gathered about symmetric and asymmetric loss functions. Since classical and Bayes estimators are acquired in closed form, simulation tests can be easily made to evaluate the effectiveness of the proposed methodologies. The efficiency of the suggested approaches is examined in terms of four metrics, namely: Root mean squared error, average relative absolute bias, average confidence length, and coverage probability. To demonstrate the applicability of the offered approaches to real events, two real applications employing data sets from the engineering area are analyzed. As a result, when the experimenter's primary goal is to complete the test as soon as the total number of failures or the threshold period is recorded, the numerical results reveal that the recommended strategy is adaptable and very helpful in completing the study.
Citation: Ahmed Elshahhat, Hanan Haj Ahmad, Ahmed Rabaiah, Osama E. Abo-Kasem. Analysis of a new jointly hybrid censored Rayleigh populations[J]. AIMS Mathematics, 2024, 9(2): 3740-3762. doi: 10.3934/math.2024184
When a researcher wants to perform a life-test comparison study of items made by two separate lines inside the same institution, joint censoring strategies are particularly important. In this paper, we present a new joint Type-Ⅰ hybrid censoring that enables an experimenter to stop the investigation as soon as a pre-specified number of failures or time is first achieved. In the context of newly censored data, the estimates of the unknown mean lifetimes of two different Rayleigh populations are acquired using maximum likelihood and Bayesian inferential techniques. The normality characteristic of classical estimators is used to offer asymptotic confidence interval bounds for each unknown parameter. Against gamma conjugate priors, the Bayes estimators and related credible intervals are gathered about symmetric and asymmetric loss functions. Since classical and Bayes estimators are acquired in closed form, simulation tests can be easily made to evaluate the effectiveness of the proposed methodologies. The efficiency of the suggested approaches is examined in terms of four metrics, namely: Root mean squared error, average relative absolute bias, average confidence length, and coverage probability. To demonstrate the applicability of the offered approaches to real events, two real applications employing data sets from the engineering area are analyzed. As a result, when the experimenter's primary goal is to complete the test as soon as the total number of failures or the threshold period is recorded, the numerical results reveal that the recommended strategy is adaptable and very helpful in completing the study.
| [1] | N. Balakrishnan, D. Kundu, Hybrid censoring: Models, inferential results and applications, Comput. Stat. Data Anal., 57 (2013), 166–209. |
| [2] |
N. Balakrishnan, A. Rasouli, Exact likelihood inference for two exponential populations under joint Type-Ⅱ censoring, Comput. Stat. Data Anal., 52 (2008), 2725–2738. https://doi.org/10.1016/j.csda.2007.10.005 doi: 10.1016/j.csda.2007.10.005
|
| [3] | F. Su, Exact likelihood inference for multiple exponential populations under joint censoring, Ph.D. Thesis. McMaster University: Hamilton, Ontario, 2013. |
| [4] |
F. Su, X. Zhu, Exact likelihood inference for two exponential populations based on a joint generalized Type-Ⅰ hybrid censored sample, J. Stat. Comput. Simul., 86 (2016), 1342–1362. https://doi.org/10.1080/00949655.2015.1062483 doi: 10.1080/00949655.2015.1062483
|
| [5] | A. R. Shafay, Exact likelihood inference for two exponential populations under joint Type-Ⅱ hybrid censoring scheme, Appl. Math. Inform. Sci., 16 (2022), 389–401. |
| [6] |
O. Abo-Kasem, A. Elshahhat, A new two sample generalized Type-Ⅱ hybrid censoring scheme, Am. J. Math. Manage. Sci., 41 (2022), 170–184. https://doi.org/10.1080/01966324.2021.1946666 doi: 10.1080/01966324.2021.1946666
|
| [7] | R. Chattamvelli, R. Shanmugam, Rayleigh distribution, In: Continuous Distributions in Engineering and the Applied Sciences, Part Ⅱ, Synthesis Lectures on Mathematics & Statistics, Springer, Cham, 2021. |
| [8] |
B. Kwon, K. Lee, Y. Cho, Estimation for the Rayleigh distribution based on Type Ⅰ hybrid censored sample, J. Korean Data Inform. Sci. Soc., 25 (2014), 431–438. https://doi.org/10.7465/jkdi.2014.25.2.431 doi: 10.7465/jkdi.2014.25.2.431
|
| [9] |
A. Asgharzadeh, M. Azizpour, Bayesian inference for Rayleigh distribution under hybrid censoring, Int. J. Syst. Assur. Eng., 7 (2016), 239–249. https://doi.org/10.1007/s13198-014-0313-7 doi: 10.1007/s13198-014-0313-7
|
| [10] |
Y. E. Jeon, S. B. Kang, Estimation of the Rayleigh distribution under unified hybrid censoring, Aust. J. Stat., 50 (2021), 59–73. https://doi.org/10.17713/ajs.v50i1.990 doi: 10.17713/ajs.v50i1.990
|
| [11] | B. N. Al-Matrafi, G. A. Abd-Elmougod, Statistical inferences with jointly Type-Ⅱ censored samples from two Rayleigh distributions, Global J. Pure Appl. Math., 13 (2017), 8361–8372. |
| [12] | J. F. Lawless, Statistical models and methods for lifetime data, 2 Eds., John Wiley and Sons, New Jersey, USA, 2003. |
| [13] | Njomen, Didier and Donfack, Thiery, Bayesian estimation under different loss functions in competitive risks, Global J. Pure Appl. Math., 17 (2021), 113–139. |
| [14] |
M. Hasan, A. Baizid, Bayesian estimation under different loss functions using gamma prior for the case of exponential distribution, J. Sci. Res., 9 (2017), 67. https://doi.org/10.3329/jsr.v1i1.29308 doi: 10.3329/jsr.v1i1.29308
|
| [15] | S. Ali, M. Aslam, S. M. A. Kazmi, A study of the effect of the loss function on Bayes estimate, posterior risk and hazard function for Lindley distribution, Appl. Math. Model., 37 (2013), 6068–6078. |
| [16] | A. Elshahhat, E. S. A. El-Sherpieny, A. S. Hassan, The Pareto-Poisson distribution: Characteristics, estimations and engineering applications, Sankhya A, 85 (2023), 1058–1099. |
| [17] |
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
|
| [18] | W. Nelson, Applied life data analysis, New York, Wiley, 1982. |
| [19] |
A. Elshahhat, O. E. Abo-Kasem, H. S. Mohammed, Reliability analysis and applications of generalized Type-Ⅱ progressively hybrid Maxwell-Boltzmann censored data, Axioms, 12 (2023), 618. https://doi.org/10.3390/axioms12070618 doi: 10.3390/axioms12070618
|
| [20] |
R. Alotaibi, A. Elshahhat, M. Nassar, Analysis of Muth parameters using generalized progressive hybrid censoring with application to sodium sulfur battery, J. Radiat. Res. Appl. Sci., 16 (2023), 100624. https://doi.org/10.1016/j.jrras.2023.100624 doi: 10.1016/j.jrras.2023.100624
|
| [21] | D. N. P. Murthy, M. Xie, R. Jiang, Weibull models, Wiley series in probability and statistics, Wiley, Hoboken, 2004. |
| [22] |
K. Maiti, S. Kayal, Estimation of parameters and reliability characteristics for a generalized Rayleigh distribution under progressive Type-Ⅱ censored sample, Commun. Stat.-Simul. Comput., 50 (2021), 3669–3698. https://doi.org/10.1080/03610918.2019.1630431 doi: 10.1080/03610918.2019.1630431
|
Figures(7) / Tables(12)
Ahmed Elshahhat, Hanan Haj Ahmad, Ahmed Rabaiah, Osama E. Abo-Kasem. Analysis of a new jointly hybrid censored Rayleigh populations[J]. AIMS Mathematics, 2024, 9(2): 3740-3762. doi: 10.3934/math.2024184
DownLoad: