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We discuss the performability evaluation model for the computer-based system, introducing the concept of codesign. We assume that the computer system consists of one hardware, and one software subsystems; and consider both of hardware, and software failure & restoration characteristics. In particular, the reliability growth process, the upward tendency of difficulty in debugging, and the imperfect debugging environment are described for the software subsystem. Assuming that the system can process the multiple tasks simultaneously, and that the arrival process of the tasks follows a nonhomogeneous Poisson process (NHPP), we use infinite server queueing theory to analyze the distribution of the number of tasks whose processes can be completed within the processing time limit. We derive several performability measures considering the real-time property, which are given as the functions of time, and the number of debugging activities. Finally we illustrate several numerical examples of the measures to investigate the impact of hardware and software failure & restoration characteristics on the system performability evaluation.