Maximum Likelihood Estimation for Step-Stress Partially Accelerated Life Tests based on Censored Data

N Chandra; Mashroor Ahmad Khan

doi:10.15415/mjis.2014.31004

Authors

N Chandra Department of Statistics, Ramanujan School of Mathematical Sciences, Pondicherry University, Pondicherry-605 014, India
Mashroor Ahmad Khan Department of Statistics, Ramanujan School of Mathematical Sciences, Pondicherry University, Pondicherry-605 014, India

DOI:

https://doi.org/10.15415/mjis.2014.31004

Keywords:

Step-stress partially accelerated life tests, Rayleigh distribution, Maximum likelihood estimation, Confidence interval, Type-I and Type-II censoring

Abstract

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

Download data is not yet available.

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