Large software systems require regular upgrading that tries to correct the reported faults in previous versions and add some functions to meet new requirements. It is thus necessary to investigate changes in reliability in the face of ongoing releases. However, the current modeling frameworks mostly rely on the idealized assumption that all faults will be removed instantaneously and perfectly. In this paper, the failure processes in testing multi-release software are investigated by taking into consideration the delays in fault repair time based on a proposed time delay model. The model is validated on real test datasets from the software that has been released three times with new features. A comprehensive analysis of optimal release times based on cost-efficiency is also provided, which could help project managers to determine the best time to release the software.