This paper presents a unified framework for software reliability modeling with non-homogeneous Poisson processes, where each software fault-detection time obeys the phasetype distribution and the initial number of inherent faults is given by a Poisson distributed random variable. However, it is worth noting that the resulting software reliability models, called phase-type software reliability models, generalize the existing models but may involve a number of model parameters in the phase-type software reliability model, so that the usual maximum likelihood estimation based on the Newton?s method or quasi-Newton?s method does not often function well. In this paper, we develop EM (Expectation- Maximization) algorithms for the phase-type software reliability models with two types of fault data: fault-detection time data and grouped data with arbitrary time intervals. In numerical examples, we compare the EM algorithms with the quasi-Newton?s method and illustrate the effectiveness on our unified model and parameter estimation method.