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Constant Stress-Partially Accelerated Life Tests of Vtub-Shaped Lifetime Distribution under Progressive Type II Censoring

Authors :
Aisha Fayomi
Asmaa A. Ahmed
Neama T. AL-Sayed
Sara M. Behairy
Asmaa M. Abd AL-Fattah
Gannat R. AL-Dayian
Abeer A. EL-Helbawy
Source :
Symmetry, Vol 16, Iss 9, p 1251 (2024)
Publication Year :
2024
Publisher :
MDPI AG, 2024.

Abstract

In lifetime tests, the waiting time for items to fail may be long under usual use conditions, particularly when the products have high reliability. To reduce the cost of testing without sacrificing the quality of the data obtained, the products are exposed to higher stress levels than normal, which quickly causes early failures. Therefore, accelerated life testing is essential since it saves costs and time. This paper considers constant stress-partially accelerated life tests under progressive Type II censored samples. This is realized under the claim that the lifetime of products under usual use conditions follows Vtub-shaped lifetime distribution, which is also known as log-log distribution. The log–log distribution is highly significant and has several real-world applications since it has distinct shapes of its probability density function and hazard rate function. A graphical description of the log–log distribution is exhibited, including plots of the probability density function and hazard rate. The log–log density has different shapes, such as decreasing, unimodal, and approximately symmetric. Several mathematical properties, such as quantiles, probability weighted moments, incomplete moments, moments of residual life, and reversed residual life functions, and entropy of the log–log distribution, are discussed. In addition, the maximum likelihood and maximum product spacing methods are used to obtain the interval and point estimators of the acceleration factor, as well as the model parameters. A simulation study is employed to assess the implementation of the estimation approaches under censoring schemes and different sample sizes. Finally, to demonstrate the viability of the various approaches, two real data sets are investigated.

Details

Language :
English
ISSN :
20738994
Volume :
16
Issue :
9
Database :
Directory of Open Access Journals
Journal :
Symmetry
Publication Type :
Academic Journal
Accession number :
edsdoj.b970993fa3d14f6d9650cfd6db222ce2
Document Type :
article
Full Text :
https://doi.org/10.3390/sym16091251