Estimating and Prediction Accelerated Life Test Using Constant Stress for Marshall-Olkin Extended Burr Type X Distribution Based on Type-II Censoring | ||||
| Al-Azhar Bulletin of Science | ||||
| Article 4, Volume 32, Issue 1-B, June 2021, Page 45-59 PDF (1.28 MB) | ||||
| Document Type: Original Article | ||||
| DOI: 10.21608/absb.2021.61409.1099 | ||||
 View on SCiNiTO | ||||
| Author | ||||
reda Mohamed refaey 
| ||||
| statistic | ||||
| Abstract | ||||
| In this paper constant stress accelerated life tests are discussed based on Type II censored sampling from Marshall-Olkin extended Burr Type X Distribution. The model parameters and the acceleration factor are estimated using the maximum likelihood estimation method and two-sample predictions are considered for future order statistics. Further, the asymptotic confidence intervals for the model parameters are discussed. Numerical study is given, and some interesting comparisons are presented to illustrate the theoretical results. Moreover, the results are applied on real dataset. | ||||
| Keywords | ||||
| Marshall-Olkin extended Burr Type X Distribution; Type II censored samples; two-sample prediction; maximum likelihood estimation and prediction | ||||
| References | ||||
|
[1] Ismail A, Planning step stress life tests with Type II censored data. Sci. Res. Essays, 2011;(6) :4021-28. DOI: 10.5897/SRE10.1060
[2] Hassan A, AL-Thobety A, Optimal design of failure step stress partially accelerated life tests with Type II censored inverted Weibull data. Int. J Eng, 2012;(2): 3242-53.
[3] AL-Dayian GR., EL-Helbawy AA, Rezk HR, Statistical inference for a simple constant stress model based on censored sampling data from the Kumaraswamy Weibull distribution. IJSP. 2014; 3(3): 80-95.DOI:10.5539/ijsp. v3n3p80
[4] Basak I, Balakrishnan N. A note on the prediction of censored exponential lifetimes in a simple step-stress model with Type II censoring. Calcutta Stat. Assoc. Bull. 2018; (70): 57-73 https://doi.org/10.1177/0008068318769506.
[5] Burr IW. Cumulative frequency functions. Ann Math Stat, 1942; 13(2): 215–32. DOI:org/10.1214/aoms/1177731607
[6] Ahmad KE, Fakhry ME, Jaheen ZF. Empirical Bayes estimation of P (Y< X) and characterizations of Burr-type X model. J Stat Plan Inference, 1997; 64(2): 297–308. DOI: 10.1016/S0378-3758(97)00038-4
[7] Surles JG, Padgett WJ. Some properties of a scaled Burr type X distribution. J Stat Plann, 2005; 128(1): 271–80. DOI:org/10.1016/j.jspi.2003.10.003.
[8] Raqab MZ, Kundu D. Burr Type X distribution: revisited. 2006; 4(2): 179–193. https://www.researchgate.net/publication/228669869
[9] Aludaat KM, Alodat MT, Alodat TT. Parameter estimation of Burr Type X distribution for grouped data. Appl Math, 2008; 2(9): 415–23. DOI: 10.1214/aoms/ 1177731607
[10] Al-Saiari AY, Baharith LA, Mousa SA. Marshall-Olkin extended Burr Type X distribution. Sri Lankan J Appl Stat, 2017; 17(3): 217-31. DOI: http://doi.org/10.4038/sljastats.v17i3.7904 [11] Padgett WJ. Inference from accelerated life tests. Reliab. 1984; (39): 346-351. DOI: 10.1109/TR.2014.2314598
[12] Kaminsky KS, Rhodin LS. Maximum likelihood prediction. Ann Inst Stat Math, 1985; (37): 507-517.
[13] Ateya SF, Mohammed HS. Prediction under Burr-XII distribution based on generalized Type-II progressive hybrid censoring. J Egypt, Math, Soc, 2018; (26): 491-508. DOI:10.21608/joems.2018.3335.1075
[14] Raqab MZ, Alkhalfan LA., Bdair OM, Balakrishnan N. Maximum likelihood prediction of records from 3-parameter Weibull distribution and some approximations. J Comput Appl Math 2019; (356): 118-132. DOI:10.1016/j.cam.2019.02.006
[15] Lawless JF. Statistical Models and Methods for Lifetime Data. 2011. Edition 2, John Wiley & Sons. ISBN 0-471-37215-3
[16] Crowder MJ. Tests for a family of survival models based on extremes. In Recent Advances in Reliability Theory. Limnios N, Nikulin M. Edition. 2000: 307-321. Birkhauser, Boston. DOI https://doi.org/10.1007/978-1-4612-1384-0_20 | ||||
|
Statistics Article View: 173 PDF Download: 188 |
||||
