In this paper, after applying the Gamma family distribution (Erlang, Log-Logistic, Rayleigh) to the finite failure-type NHPP reliability model in which failures do not occur during flaw repair, the reliability performance of the software was evaluated by comparing with the Goel-Okumoto basic model. In this process, software failure time data collected randomly during the operation of the computer system was used, and the estimator solution of the applied NHPP model was performed by applying the numerical analysis (bisection method).Conclusively, first, as a result of calculating the criteria for efficient model selection, it was evaluated that the efficiency of the Rayleigh and Goel-Okumoto basic models was excellent. Second, as a result of analyzing the reliability attributes functions, the Rayleigh model showed the best performance. Third, as a result of future reliability testing, the Rayleigh model with the highest reliability was efficient. Thus, the Rayleigh model showed the best reliability performance in this work. Through this study, the software reliability performance of the Gamma family lifetime distribution was newly identified, and this analysis data can help software developers to utilize it as basic data for reliability improvement in the testing process.