Many software reliability methods have been proposed for estimating and predicting reliability, and the method based on Bayesian framework is a popular one. However, the present Bayesian approaches are all based on the impractical assumption that the detected faults are corrected immediately with no debugging time delay. In this paper, we derive effective parameter estimation algorithms based on Bayesian framework not only for fault detection process, but also for combined detection and correction processes. To have a better understanding of the estimation performance, a simulation study and a practical example are conducted to investigate the performance of the proposed Bayesian approach.