In the current digitalized world, Open Source Software (OSS) methodology provides greater value to users and leads to increased revenue for the OSS companies. This paper investigates reliability modeling for OSS. Most of software reliability models proposed in literature for OSS projects are based on closed-form methodology and do not consider the properties of OSS in the model structure. This paper models the rate of adoption of volunteers to OSS using diffusion theory and considered as fault detection rate. However, the fault detection rate may vary in such a testing environment; a modified SRGM based on Itô type Stochastic Differential Equation (SDE) is proposed to describe realistic situations. The proposed model have been verified on real data sets from open source projects, as the Apache project, which has been released in the market with new features. Results show the proposed model can describe the failure process for open source software accurately.