Abstract
Reliability assessment of the braking system in a high-speed train under small sample size and zero-failure data is very important for safe operation. Traditional reliability assessment methods are only performed well under conditions of large sample size and complete failure data, which lead to large deviation under conditions of small sample size and zero-failure data. To improve this problem, a new Bayesian method is proposed. Based on the characteristics of the solenoid valve in the braking system of a high-speed train, the modified Weibull distribution is selected to describe the failure rate over the entire lifetime. Based on the assumption of a binomial distribution for the failure probability at censored time, a concave method is employed to obtain the relationships between accumulation failure probabilities. A numerical simulation is performed to compare the results of the proposed method with those obtained from maximum likelihood estimation, and to illustrate that the proposed Bayesian model exhibits a better accuracy for the expectation value when the sample size is less than 12. Finally, the robustness of the model is demonstrated by obtaining the reliability indicators for a numerical case involving the solenoid valve of the braking system, which shows that the change in the reliability and failure rate among the different hyperparameters is small. The method is provided to avoid misleading of subjective information and improve accuracy of reliability assessment under conditions of small sample size and zero-failure data.
Highlights
The statistical model employed and the available sample size have a significant effect on the estimation of parameters in reliability assessment
The method is provided to avoid misleading of subjective information and improve accuracy of reliability assessment under condi‐ tions of small sample size and zero-failure data
The normal distribution, lognormal distribution, exponential distribution, and Weibull distribution have served as commonly employed statistical models in reliability assessment
Summary
The statistical model employed and the available sample size have a significant effect on the estimation of parameters in reliability assessment. Owing to the long lifetimes, high cost, and complex structures of components in high-speed trains, it is necessary to develop reliability assessment theory and methods suitable under small sample size. The present study proposes a new approach that combines a Bayesian method with a subjective prior distribution for zero-failure data under small sample size, and experiments confirm that this approach can be safely applied to the reliability assessment of solenoid valves in the braking systems of highspeed trains. For lifetime experiments of the solenoid valve in high-speed train braking systems, the principle under zero-failure data can be described as follows.
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