Two-sided M-Bayesian credible limits of reliability parameters in the case of zero-failure data for exponential distribution

In this paper, we study the interval estimation of failure rate and reliability for exponential distribution, in the case of zero-failure data, using the method of two-sided Modified Bayesian (M-Bayesian) credible limit. We discuss the properties of two-sided M-Bayesian credible limits which include the impact of the value of upper bound c of hyper parameter, and the influence of different prior distributions of hyper parameter on two-sided M-Bayesian credible limits. The paper obtains the relationship between three kinds of two-sided M-Bayesian credible limits and two-sided classical confidence limits. Finally, we use a real data set to verify the properties of two-sided M-Bayesian credible limits, and the computing results indicate that the method is efficient and easy to operate.