Masked data are the system failure data when the exact cause of the failures might be unknown. That is, the cause of the system failures may be any one of the components. Additionally, to incorporate more information and provide more accurate analysis, modeling software fault detection and correction processes have attracted widespread research attention recently. However, stochastic fault correction time and masked data brings more difficulties in parameter estimation. In this paper, a framework of open source software growth reliability model with masked data considering both fault detection and correction processes is proposed. Furthermore, a novel Expectation Least Squares (ELS) method, an EM-like (Expectation Maximization) algorithm, is used to solve the problem of parameter estimation, because of its mathematical convenience and computational efficiency. It is note that the ELS procedure is easy to use and useful for practical applications, and it just needs more relaxed hidden assumptions. Finally, three data sets from real open source software project are applied to the proposed framework, and the results show that the proposed reliability model is useful and powerful.