A New Family of a prior Distributions for Exponential Reliability Growth Models

This paper introduces a new family of a prior distributions for four reliability growth testing scenarios with exponential failure data. The proposed prior is of conditional form, which can accord well with various actual situations in reliability growth tests. The expressions of corresponding conditional means and variances for all stages are obtained, and the relationship between the shape of a prior distributions and their parameters are discussed. These results are helpful for better incorporation of expert opinons. The posterior density and Bayesian estimators and Bayesian lower bound of the reliability at the end of the test are also given.