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CLC number: TB114.3

On-line Access: 2013-01-31

Received: 2012-09-19

Revision Accepted: 2013-01-09

Crosschecked: 2013-01-10

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Journal of Zhejiang University SCIENCE C 2013 Vol.14 No.2 P.143-154

http://doi.org/10.1631/jzus.C12a0241


Hypothesis testing for reliability with a three-parameter Weibull distribution using minimum weighted relative entropy norm and bootstrap


Author(s):  Xin-tao Xia, Yin-ping Jin, Yong-zhi Xu, Yan-tao Shang, Long Chen

Affiliation(s):  School of Mechatronical Engineering, Henan University of Science and Technology, Luoyang 471003, China; more

Corresponding email(s):   xiaxt1957@163.com, xiaxt@mail.haust.edu.cn

Key Words:  Reliability, Hypothesis testing, Three-parameter Weibull distribution, Weighted relative entropy, Norm, Bootstrap


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Xin-tao Xia, Yin-ping Jin, Yong-zhi Xu, Yan-tao Shang, Long Chen. Hypothesis testing for reliability with a three-parameter Weibull distribution using minimum weighted relative entropy norm and bootstrap[J]. Journal of Zhejiang University Science C, 2013, 14(2): 143-154.

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author="Xin-tao Xia, Yin-ping Jin, Yong-zhi Xu, Yan-tao Shang, Long Chen",
journal="Journal of Zhejiang University Science C",
volume="14",
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pages="143-154",
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publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.C12a0241"
}

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%A Xin-tao Xia
%A Yin-ping Jin
%A Yong-zhi Xu
%A Yan-tao Shang
%A Long Chen
%J Journal of Zhejiang University SCIENCE C
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%I Zhejiang University Press & Springer
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T1 - Hypothesis testing for reliability with a three-parameter Weibull distribution using minimum weighted relative entropy norm and bootstrap
A1 - Xin-tao Xia
A1 - Yin-ping Jin
A1 - Yong-zhi Xu
A1 - Yan-tao Shang
A1 - Long Chen
J0 - Journal of Zhejiang University Science C
VL - 14
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SP - 143
EP - 154
%@ 1869-1951
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PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.C12a0241


Abstract: 
With the help of relative entropy theory, norm theory, and bootstrap methodology, a new hypothesis testing method is proposed to verify reliability with a three-parameter Weibull distribution. Based on the relative difference information of the experimental value vector to the theoretical value vector of reliability, six criteria of the minimum weighted relative entropy norm are established to extract the optimal information vector of the Weibull parameters in the reliability experiment of product lifetime. The rejection region used in the hypothesis testing is deduced via the area of intersection set of the estimated truth-value function and its confidence interval function of the three-parameter Weibull distribution. The case studies of simulation lifetime, helicopter component failure, and ceramic material failure indicate that the proposed method is able to reflect the practical situation of the reliability experiment.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article

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