ABSTRACT
Han introduced an E-Bayesian estimation method for estimating a system failure probability and revealed the relationship between the E-Bayesian estimates under three different prior distributions of hyperparameters in 2007. In this article, formulas of the hierarchical Bayesian estimation of a system failure probability are investigated and, furthermore, the relationship between hierarchical Bayesian estimation and E-Bayesian estimation is discussed. Finally, numerical example and application example are provided for illustrative purpose.
Acknowledgements
The author wishes to thank Professor Xizhi Wu, who checked the article and gave the author very helpful suggestions.
Funding
This work was supported partly by the Ningbo Natural Science Foundation (No. 2013A610108).