Non-homogeneous Poisson process software reliability growth models are well-known tools to assess the reliability of software systems. However, most prior models overlook the introduction of new defects in the test process. It is especially so for open source softwares, because many programmers participate in the test and the software platform is not bound to a particular party. Considering the introduction of new defects, this paper proposes a modified model to assess reliability of open source softwares. Empirical results suggest that our proposed model well fits the failure data and presents a high prediction capability.