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Index of the two-parameter Weibull distribution parameters Bayes estimates and reliability analysis

Author: LiuChaoNan
Tutor: WangGuoFu
School: Central South University
Course: Probability Theory and Mathematical Statistics
Keywords: Bayes estimation Loss function Admissibility Zero Failure Data Reliability
CLC: O212.8
Type: Master's thesis
Year: 2008
Downloads: 267
Quote: 2
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Abstract


Bayes estimation is to fully utilize the existing prior information , sample information to estimate the overall parameters , and thus has excellent properties ; reliability assessment in reliability engineering occupies an important position in the situation of today 's high-reliability products , failure data is particularly important. Bayesian estimation, based on previous research the Admissibility and failure data reliability analysis , the index of the two-parameter Weibull distribution Brief Introduction of a three-pronged : First, given Censored , select the square loss the function entropy loss function and LINEX loss function , the index of the two-parameter Weibull distribution in which a parameter alpha known case , take the conjugate gamma distribution Ga ( a , b ) as a prior distribution , given the unknown parameter θ Baves estimated entropy loss function , for example , select a B super priori for the gamma distribution Ga ( c , d ) and evenly distributed , given θ hierarchical Bayes estimation ; Secondly, in the complete sample applications unknown parameter θ of the three loss function the Bayes estimates and its estimated allowable ; Finally, in the absence of failure data reliability index of the two-parameter Weibull distribution analysis , through mathematical proof , identified failure probability p 1 < / sub > of the prior distribution selected from the failure probability and reliability index using multi - priori Bayes method to get the failure probability p 1 estimates ( ? ) and reliability R 1 < / sub > of estimates ( ? ) with Virence algorithm and nonlinear regression method of least squares fitting failure probability and reliability of the data fitting method arrival.

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CLC: > Mathematical sciences and chemical > Mathematics > Probability Theory and Mathematical Statistics > Mathematical Statistics > Bayesian statistics
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