This paper investigates a self-repairable serial system with two components and a buffer. Competitive failure processes are considered due to the internal degradation and external shock processes of components. The system reliability is calculated based on the integration of the internal degradation process and external shock process. When one of the components deteriorates to the PM or CM thresholds, it is restored to an imperfect state under dynamic time limitations based on the previous internal degradation and external shocks. As for the other component, it needs to be repaired or not according to the reliability of the component; it needs to be shut down or not based on the buffer status and the allocation of the component in the system. The optimal initial buffer capacity setting and PM threshold at minimum cost are found by minimizing the system's total cost in a given running cycle. Finally, numerical and case studies are provided to demonstrate the feasibility and superiority of the presented model.