E-Bayesian Estimation and Hierarchical Bayesian Estimation of Failure Probability

Abstract

This article introduces a new parameter estimation method, named E-Bayesian estimation, to estimate failure probability. The method is suitable for the censored or truncated data with small sample sizes and high reliability. The definition, properties and related simulation study of the E-Bayesian estimation are given. A real data set is also discussed. Through the examples, the efficiency and easiness of operation of this method are commended.

Keywords:

• E-Bayesian estimation
• Failure probability
• Hierarchical Bayesian estimation
• Reliability

Mathematics Subject Classification:

• 62F15
• 62N05

Acknowledgments

The author has benefited from Professor Xizhi Wu, who has checked the article and given the author very helpful suggestions. The author also wants to thank the referees for their helpful comments.

This work was supported partly by the Fujian Province Natural Science Foundation of China (No. 2009J01001).

Notes

Note: 5.64E − 05 = 5.64 × 10⁻⁵, and .

Note: , and is E-Bayesian estimate of the reliability at moment t, is hierarchical Bayesian estimate of the reliability at moment t.