Abstract
This paper is mainly according to Bayesian formula and using Bayesian method to estimate parameter truth-values of three-parameter Weibull distribution to achieve material reliability evaluation. The parameter values estimated by maximum likelihood method as the prior information of Bayesian estimation, assume that the parameter obeys a certain distribution and let the certain distribution as the prior distribution of parameter, and the three-parameter Weibull distribution is known, so the posterior distribution function of the parameter can be obtained. According to Bayesian estimation, the maximum posteriori estimation is chosen as the truth-value of the estimated parameter, the lifetime data are substituted into the truth-value estimated function of reliability and the theoretical values of the reliability can be got. Case study shows that the Bayesian method has general applicability to the material reliability evaluation. Key words: Material lifetime, test assessment, three-parameter Weibull distribution, Bayesian method.
Highlights
Material is the foundation and the forerunner of modern high-new technology and industry
This paper mainly discussed the application of Bayesian method in material reliability evaluation
Let the values of the parameters solved by maximum likelihood method as a priori information of Bayesian estimation, be assumed to obey a certain distribution and let the certain distribution be the prior distribution; the three-parameter Weibull distribution is known, the posterior distribution function of the parameter can be obtained (Mao, 1999)
Summary
Material is the foundation and the forerunner of modern high-new technology and industry. (2012) by raising the casting material performance, optimized the casting process, to ensure the reliability of the casting use, which is in the CRH2, CRH380A type trains of application. The material reliability method was used to research the above, thereby effectively enhancing the applicability and reliability of materials. This paper mainly discussed the application of Bayesian method in material reliability evaluation. For many products in engineering practice, the value of the Weibull parameter is unknown and needs to be found with the help of test evaluation. To this end, a lifetime experiment must be conducted. Assume that the lifetime data of a product are obtained by life tests as follows:
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