# Journal of Statistical Theory and Applications

Volume 17, Issue 2, June 2018, Pages 242 - 260

# Estimating the Modified Weibull Parameters in Presence of Constant-Stress Partially Accelerated Life Testing

Authors
Mohamed A. W. Mahmoudmawmahmoud11@yahoo.com
Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City (11884), Cairo, Egypt.
Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City (11884), Cairo, Egypt.
Amr M. Abou-Sennaamr.abosenna@yahoo.com
Mathematics Department, Faculty of Engineering, Shoubra, Benha University, Cairo, Egypt.
Received 14 July 2017, Accepted 10 January 2018, Available Online 30 June 2018.
DOI
10.2991/jsta.2018.17.2.5How to use a DOI?
Keywords
Modified Weilbull distribution; Constant-partially accelerated life testing; Progressive Type-II censoring; Asymptotic confidence intervals; Bootstrap; Bayesian estimation
Abstract

Accelerated life testing is very important in life testing experiments because it saves time and cost. In this paper, assuming that the lifetime of items under use condition follows the modified Weilbull distribution, partially accelerated life tests based on progressive Type-II censored samples are considered. The likelihood equations are to be solved numerically to obtain the maximum likelihood estimates. Based on normal approximation to the asymptotic distribution of maximum likelihood estimates, the approximate confidence intervals for the parameters are derived. Two bootstrap confidence intervals called bootstrap-p and bootstrap-t are also discussed. It is difficult to get explicit form for Bayes estimates, so we use Markov chain Monte Carlo method to solve this problem, which gives us flexibility to construct the credible intervals for parameters. Finally, a simulation study is performed to compare between MLEs and Bayes estimates.

Open Access
This is an open access article under the CC BY-NC license (http://creativecommons.org/licences/by-nc/4.0/).

Journal
Journal of Statistical Theory and Applications
Volume-Issue
17 - 2
Pages
242 - 260
Publication Date
2018/06/30
ISSN (Online)
2214-1766
ISSN (Print)
1538-7887
DOI
10.2991/jsta.2018.17.2.5How to use a DOI?
Open Access
This is an open access article under the CC BY-NC license (http://creativecommons.org/licences/by-nc/4.0/).

TY  - JOUR
AU  - Mohamed A. W. Mahmoud
AU  - Amr M. Abou-Senna
PY  - 2018
DA  - 2018/06/30
TI  - Estimating the Modified Weibull Parameters in Presence of Constant-Stress Partially Accelerated Life Testing
JO  - Journal of Statistical Theory and Applications
SP  - 242
EP  - 260
VL  - 17
IS  - 2
SN  - 2214-1766
UR  - https://doi.org/10.2991/jsta.2018.17.2.5
DO  - 10.2991/jsta.2018.17.2.5
ID  - Mahmoud2018
ER  -