We focus on a cloud computing environment by using open source software such as OpenStack and Eucalyptus because of the unification management of data, and low cost. In this paper, we propose a new approach to software reliability assessment based on a jump diffusion model based on the stochastic differential equations in order to consider the interesting aspect of the numbers of components and users. In particular, we derive the confidence limits of jump range for the proposed jump diffusion model. Also, actual software fault-count data are analyzed in order to show numerical examples of software reliability assessment. Moreover, this paper shows that the proposed method of reliability analysis can assist quality improvement for the cloud computing.