Hierarchical Bayesian Reliability Analysis of Binomial Distribution based on Zero-Failure Data

Abstract

The aim of this paper is to develop a new hierarchical Bayesian estimation method under symmetric entropy loss function for reliability of the binomial distribution. With the rapid development of manufacturing techniques, some electric products are highly reliable, and thus zero-failure data often occur when putting them in censored lifetime tests. Based on zero-failure data, the reliability analysis is very important for manufacturing. The hierarchical Bayesian estimator is regarded as a robust estimating method, but many existing robust Bayes estimators are complex and difficult to be utilized in practice. The contribution of this article is to present an easy hierarchical Bayesian estimator for reliability of the binomial distribution when reliability has a negative log-gamma prior distribution. Finally, a practical example is provided to show the feasibility and robustness of different estimators.

Two-sided M-Bayesian limits of credibility of reliability parameters in the case of zero-failure data and a case study

“…Han (2016) discussed the M-Bayesian lower credible limit method and its properties, and proved Bayesian lower credible limit method is superior to the corresponding classical lower confidence limit method. Xiao and Ren (2018) presented an easy hierarchical Bayesian estimator for reliability of the binomial distribution based on zero-failure data. Also, there are many other contributions on the failure problem, such as Han (2003Han ( , 2004Han ( , 2005.…”