With the development of science and technology, the products reliability is higher and higher. So for high reliability products, zero\|failure data situation appears often in the time ended reliability tests. In this ...With the development of science and technology, the products reliability is higher and higher. So for high reliability products, zero\|failure data situation appears often in the time ended reliability tests. In this paper, the hierarchical Bayesian estimation of the products reliability is given under the conditions of the Binomial distribution with zero\|failure data and the prior distribution of the reliability being quasi\|Beta distribution. The authors also give a practical calculating example using the theory.展开更多
Reliability assessment of the braking system in a high?speed train under small sample size and zero?failure data is veryimportant for safe operation. Traditional reliability assessment methods are only performed well ...Reliability assessment of the braking system in a high?speed train under small sample size and zero?failure data is veryimportant 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 prob?abilities. 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 di erent hyperparameters is small. 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.展开更多
文摘With the development of science and technology, the products reliability is higher and higher. So for high reliability products, zero\|failure data situation appears often in the time ended reliability tests. In this paper, the hierarchical Bayesian estimation of the products reliability is given under the conditions of the Binomial distribution with zero\|failure data and the prior distribution of the reliability being quasi\|Beta distribution. The authors also give a practical calculating example using the theory.
基金Supported by National Natural Science Foundation of China(Grant No.51175028)Great Scholars Training Project(Grant No.CIT&TCD20150312)Beijing Recognized Talent Project(Grant No.2014018)
文摘Reliability assessment of the braking system in a high?speed train under small sample size and zero?failure data is veryimportant 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 prob?abilities. 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 di erent hyperparameters is small. 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.
