The concern for software reliability has grown over a period of time especially with the advent of real life systems such as satellite and shuttle control, telephone, internet and banking services. In today’s life the computers are being used to monitor and control safety critical and civilian systems with a great demand for high-quality software products. So reliability is a primary concern for both software developers and software users. The new outlines of competition and collaboration that have arisen in software engineering as a result of the globalization process have an impact on the entire software process. The need is growing to estimate, risk assess, plan and manage the development of these complex software systems to ensure a smooth run of life. Therefore to capture the combined effect of testing time and testing coverage we propose a two dimensional software reliability growth model. We have used cobb-douglas production function to develop the two dimensional model incorporating the effect of testing time and testing coverage on the number of faults removed in the software system. In this paper, we present two software reliability growth models incorporating logistic distribution function and Exponentiated Exponential distribution function respectively. The model developed is validated on real data set.