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Front. Inform. Technol. Electron. Eng.  2013, Vol. 14 Issue (2): 143-154    DOI: 10.1631/jzus.C12a0241
    
Hypothesis testing for reliability with a three-parameter Weibull distribution using minimum weighted relative entropy norm and bootstrap
Xin-tao Xia, Yin-ping Jin, Yong-zhi Xu, Yan-tao Shang, Long Chen
School of Mechatronical Engineering, Henan University of Science and Technology, Luoyang 471003, China; School of Mechatronical Engineering, Northwestern Polytechnical University, Xi'an 710072, China
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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.

Key words： Reliability      Hypothesis testing      Three-parameter Weibull distribution      Weighted relative entropy      Norm      Bootstrap     
Received: 19 September 2012      Published: 31 January 2013
CLC:  TB114.3  
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Xin-tao Xia
Yin-ping Jin
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Long Chen
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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. Front. Inform. Technol. Electron. Eng., 2013, 14(2): 143-154.

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http://www.zjujournals.com/xueshu/fitee/10.1631/jzus.C12a0241     OR     http://www.zjujournals.com/xueshu/fitee/Y2013/V14/I2/143


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

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.

关键词： Reliability,  Hypothesis testing,  Three-parameter Weibull distribution,  Weighted relative entropy,  Norm,  Bootstrap 
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