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

In this paper, a novel method of two-sided M-Bayesian credible limit is proposed to deal with the interval estimation problem of reliability parameters with exponential distribution in the case of zero-failure data. The properties of two-sided M-Bayesian limits of credibility are discussed and some new theorems are proven including the impact of the upper bound c of hyper parameters and the influence of different prior distributions of hyper parameters on two-sided M-Bayesian limits of credibility when the reliability of estimation was determined by the exponential distribution. The paper extended the conclusions drawn in two previous studies regarding the relationships among the many kinds of two-sided M-Bayesian limits of credibility and two-sided classical confidence. Finally, a real dataset about engines is discussed with different model parameters. By means of an example, the presented method of this paper is compared with the classical confidence limits. The results verify the properties of two-sided M-Bayesian limits of credibility and indicate that the method is efficient and easy to perform.