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Software reliability modeling & estimation plays a critical role in software development, particularly during the software testing stage. Although there are many research papers on this subject, few of them address the realistic time delays between fault detection and fault correction processes. This paper investigates an approach to incorporate the time dependencies between the fault detection, and fault correction processes, focusing on the parameter estimations of the combined model. Maximum likelihood estimates of combined models are derived from an explicit likelihood formula under various time delay assumptions. Various characteristics of the combined model, like the predictive capability, are also analyzed, and compared with the traditional least squares estimation method. Furthermore, we study a direct, useful application of the proposed model & estimation method to the classical optimal release time problem faced by software decision makers. The results illustrate the effect of time delay on the optimal release policy, and the overall software development cost.