Software development based on the Open Source Software (OSS) model is being increasingly accepted to stand up servers and applications. In particular, Cloud OSS is now attracting attention as the next generation of software products due to cost efficiencies and quick delivery. This chapter focuses on the software reliability modeling and assessment for Cloud computing infrastructure software, especially open source software, such as OpenStack and Eucalyptus. In this chapter, the authors introduce a new approach to the Jump diffusion process based on stochastic differential equations in order to consider the interesting aspect of the numbers of components and users in the reliability model. In addition, the authors consider the network traffic of the Cloud in the reliability modeling and integrate the reliability model with a threshold-based neural network approach that estimates network traffic. Actual software fault-count data are analyzed in order to show numerical examples of software reliability assessment. This chapter also illustrates how the proposed method of reliability analysis can assist in quality improvement in Cloud computing software.