This paper proposes a regression model for estimating Bayesian parameters related to reliability point and interval estimations. It is demonstrated that, using these regression models, reliability predictions can be made efficiently based on limited available testing data. Reliability estimation using traditional approaches generally considers electronic system failure rates as fixed but unknown constants, which can be estimated from sample test data taken randomly from the population. Prior knowledge is not used. Bayesian reliability inference, on the other hand, considers the failure rates as random, not fixed, quantities. Bayesian methods allow the incorporation of one's prior knowledge into the estimating process. Combining one's prior knowledge and limited testing results, reliability can be estimated more effectively. However, Bayesian reliability analysis has not been extensively applied in industry. One major reason is the complexity of the procedure and the computational intensity involved. In this paper, empirical regression models are developed to estimate the parameters related to Bayesian reliability point and interval estimation procedures.