The M-Bayesian Credible Limits of the Reliability Derived from Binomial Distribution

Abstract

This article introduces a new method, M-Bayesian credible limit method, to estimate reliability derived from binomial distribution, in the case of zero-failure data. Firstly, the definition of one-sided and two-sided M-Bayesian credible limits are provided, and moreover, formulas of one-sided and two-sided M-Bayesian credible limits are also provided. secondly, properties of one-sided and two-sided M-Bayesian credible limits are discussed, and we will see that the M-Bayesian credible limit method is superior to the corresponding classical confidence limit method. Finally, the new estimation method is applied to a numerical example. Through the example the efficiency and easiness of operation of this method are commended.

Keywords:

• Classical confidence limit
• M-Bayesian credible limit
• Reliability
• Zero-failure data

Mathematics Subject Classification:

• 62F15
• 62N05

Acknowledgments

The author wishes to thank Professor Xizhi Wu, who checked the article and gave the author very helpful suggestions. The author also wishes to thank the referees for their helpful comments.

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