Abstract
In order to solve the reliability assessment of braking system component of high-speed electric multiple units, this article, based on two-parameter exponential distribution, provides the maximum likelihood estimation and Bayes estimation under a type-I life test. First of all, we evaluate the failure probability value according to the classical estimation method and then obtain the maximum likelihood estimation of parameters of two-parameter exponential distribution by performing and using the modified likelihood function. On the other hand, based on Bayesian theory, this article also selects the beta and gamma distributions as the prior distribution, combines with the modified maximum likelihood function, and innovatively applies a Markov chain Monte Carlo algorithm to parameters assessment based on Bayes estimation method for two-parameter exponential distribution, so that two reliability mathematical models of the electromagnetic valve are obtained. Finally, through type-I life test, the failure rates according to maximum likelihood estimation and Bayes estimation method based on Markov chain Monte Carlo algorithm are, respectively, 2.650 × 10−5 and 3.037 × 10−5. Compared with the failure rate of a electromagnetic valve 3.005 × 10−5, it proves that the Bayes method can use a Markov chain Monte Carlo algorithm to estimate reliability for two-parameter exponential distribution and Bayes estimation is more closer to the value of electromagnetic valve. So, by fully integrating multi-source, Bayes estimation method can preferably modify and precisely estimate the parameters, which can provide a certain theoretical basis for the safety operation of high-speed electric multiple units.
Highlights
The continuous operating rate of high-speed electric multiple units (EMUs), which is one of the important railway transportations in China, has reached more than 350 km/h
High-speed EMUs braking system is composed of many components and subsystems which cooperate with each other, and the running safety of the vehicle will be influenced if one link fails
After a long operation time, reliability of the electromagnetic valve and other components of EMUs braking system which are prone to failure reduced
Summary
The continuous operating rate of high-speed electric multiple units (EMUs), which is one of the important railway transportations in China, has reached more than 350 km/h. For the braking system components with superior reliability, this article, based on the small sample and zero-failure data theory, carries on the type-I life test to make parameter estimation for two-parameter exponential distribution based on the two methods. Zero failure may occur during the test due to its high reliability and the limited test time, so research is conducted on zero-failure data under small sample To solve such problems, researchers generally adopt the Bayes estimation method for analysis so that the test cycle and cost can be reduced. The simplified Bayes formula can be expressed as follows h(ajx)}L(xja) 3 p(a) where h(ajx) means the posterior distribution which integrates prior information, sample information, and general information; L(xja) is the likelihood function containing current sample information and general information; and p(a) means prior distribution which includes all the prior information
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