Maximum Likelihood Estimation for Step-Stress Partially Accelerated Life Tests based on Censored Data
DOI:
https://doi.org/10.15415/mjis.2014.31004Keywords:
Step-stress partially accelerated life tests, Rayleigh distribution, Maximum likelihood estimation, Confidence interval, Type-I and Type-II censoringAbstract
The aim of this article is to perform the estimation procedures on Rayleigh parameter in step-stress partially accelerated life tests (PALT) under both Type-I and Type-II censored samples in which all the test units are first to run simultaneously under normal conditions for a pre-specified time, and the surviving units are then run under accelerated conditions until a predetermined censoring reached. It is assumed that the lifetime of the test units follows Rayleigh distribution. The maximum likelihood estimates are obtained for the proposed model parameters and acceleration factor for each of Type-I and Type- II censored data. In addition, the asymptotic variances and covariance matrix of the estimators are presented, and confidence intervals of the estimators are
also given.
Downloads
References
A bd-Elfattah, A. M. and Al-Harbey, A. M. (2010). Inferences for Burr Parameters Based on Censored Samples in Accelerated Life Tests, Journal of King Abdulaziz
University: Sciences, Vol.22, 149-170. http://dx.doi.org/10.4197/sci.22-2.12
A bd-Elfattah, A. M., Soliman, A. H. and Nassr, S. G. (2008). Estimation in Step-Stress Partially Accelerated Life Tests for the Burr Type XII distribution Using
Type I censoring, Statistical Methodology, Vol.5, 502-514.http://dx.doi.org/10.1016/j.stamet.2007.12.001
]Abdel-Ghaly, A. A., Attia, A. F. and Abdel-Ghani, M. M. (2002). The Maximum Likelihood Estimates in Step Partially Accelerated life Tests for the Weibull
Parameters in Censored Data, Communications in Statistics, Theory, and Methods, Vol.31, 551-573. http://dx.doi.org/10.1081/STA-120003134
Bai, D. S. and Chung, S. W. (1992). Optimal Design of Partially Accelerated Life Tests for the Exponential distribution under type-1 censoring, IEEE Transactions on Reliability, Vol.41, 400-406. http://dx.doi.org/10.1109/24.159807
Bai, D. S., Chung, S. W. and Chun, Y. R. (1993). Optimal Design of Partially Accelerated Life Tests for the Lognormal Distribution under Type-1 censoring,
Reliability Engineering and System Safety, Vol.40, 85-92. http://dx.doi.org/10.1016/0951-8320(93)90122-F
Bessler, S., Chernoff, H. and Marshall, A. W. (1962). An optimal Sequential Accelerated Life Test, Technomenics, Vol.4, 367-379. http://dx.doi.org/10.1080/00401706.1962.10490019
Bhattacharyya, G. K. and Soejoeti, Z. A. (1989). Tampered Failure Rate Model for Step-Stress Accelerated Life Test, Communications in Statistics, Theory and
Methods, Vol.18, 1627-1643. http://dx.doi.org/10.1080/03610928908829990
Bora, J. S. (1979). Step-Stress Accelerated Life Testing of Diodes. Microelectronics Reliability, Vol.19, 279-280. http://dx.doi.org/10.1016/0026-2714(79)90349-4
Chandra, N. and Khan, M. A. (2012). A New Optimum Test Plan for Simple Step-Stress Accelerated Life Testing. Applications of Reliability Theory and Survival
Analysis. Ed. Navin Chandra and G. Gopal. Bonfring Publication, Coimbatore, India, pp.57-65.
Chandra, N. and Khan, M. A. (2013). Optimum Plan for Step-Stress Accelerated Life Testing Model under Type-I Censored Samples, Journal of Modern Mathematics and Statistics, Vol.7, Issue 5-6, 58-62.
Chandra, N., Khan, M. A. and Pandey, M. (2014). Optimum Test Plan for 3-Step, Step-Stress Accelerated Life Tests, International Journal of Performability Engineering, Vol.10, 03-14.
Chernoff, H. (1962). Optimal Accelerated Life Designs for Estimation, Technomenics, Vol.4, 381-408. http://dx.doi.org/10.1080/00401706.1962.10490020
DeGroot, M. H. and Goel, P. K. (1979). Bayesian estimation and Optimal Design in Partially Accelerated life Testing, Naval Research Logistics Quarterly, Vol.16,
-235. http://dx.doi.org/10.1002/nav.3800260204
Goel, P. K. (1971). Some Estimation Problems in the Study of Tampered Random Variables, Carnegie-Mellon University, Pittspurgh (Pennsylvania).
H unt, S. and Xu, X. (2012). Optimum Design for Accelerated Life Testing with Simple Step-Stress Plans. International Journal of Performability Engineering,
Vol.8, 575-579.
Miller, R. and Nelson, W. B. (1983). Optimum Simple Step-Stress Plans for Accelerated Life Testing, IEEE Transactions on Reliability, R-32, 59-65. http://dx.doi.org/10.1109/TR.1983.5221475
Nelson, W. B. (1990). Accelerated Life Testing: Statistical Models, Test Plans and Data Analysis, John Wiley and Sons, New York. http://dx.doi.org/10.1002/9780470316795
Nelson, W. B. and Meeker, W. Q. (1978). Theory for Optimum Accelerated Censored Life Tests for Weibull and Extreme Value Distributions. Technometrics,
Vol.20, 171-177. http://dx.doi.org/10.1080/00401706.1978.10489643
Vander Wiel, S. A. and Meeker, W. Q. (1990). Accuracy of Approximate Confidence Bounds using Censored Weibull Regression Data from Accelerated
Life Tests, IEEE Transaction on Reliability, Vol.39, 346-351. http://dx.doi.org/10.1109/24.103016
Wang, F. K., Cheng, Y. F. and Lu, W. L. (2012). Partially Accelerated Life Tests for the Weibull Distribution under Multiply Censored Data, Communications in
Statistics-Simulation and Computation, Vol.41, 1667-1678. http://dx.doi.org/10.1080/03610918.2011.615434
Downloads
Published
How to Cite
Issue
Section
License
Articles in Mathematical Journal of Interdisciplinary Sciences (Math. J. Interdiscip. Sci.) by Chitkara University Publications are Open Access articles that are published with licensed under a Creative Commons Attribution- CC-BY 4.0 International License. Based on a work at https://mjis.chitkara.edu.in. This license permits one to use, remix, tweak and reproduction in any medium, even commercially provided one give credit for the original creation.
View Legal Code of the above mentioned license, https://creativecommons.org/licenses/by/4.0/legalcode
View Licence Deed here https://creativecommons.org/licenses/by/4.0/
Mathematical Journal of Interdisciplinary Sciences by Chitkara University Publications is licensed under a Creative Commons Attribution 4.0 International License. Based on a work at https://mjis.chitkara.edu.in |