It is well-known that accurate reliability estimates can be obtained by using software reliability models only in the later phase of software testing. However, prediction in the early phase is important for costeffective and timely management. Also this requirement can be achieved with information from previous releases or similar projects. This basic idea has been implemented with nonhomogenerous Poisson process (NHPP) models by assuming the same testing/debugging environment for similar projects or successive releases. In this paper we study an approach to using past fault-related data with Artificial Neural Network (ANN) models to improve reliability predictions in the early testing phase. Numerical examples are shown with both actual and simulated datasets. Better performance of early prediction is observed compared with original ANN model with no such historical fault-related data incorporated. Also, the problem of optimal switching point from the proposed approach to original ANN model is studied, with three numerical examples.