Mixed-Criticality (MC) systems have emerged as an effective solution in various industries, where multiple tasks with various real-time and safety requirements (different levels of criticality) are integrated onto a common hardware platform. In these systems, a fault may occur due to different reasons, e.g., hardware defects, software errors or the arrival of unexpected events. In order to tolerate faults in MC systems, the re-execution technique is typically employed, which may lead to overrun of high-criticality tasks (HCTs), which necessitates the drop of low-criticality tasks (LCTs) or degrading their quality. However, frequent drops or relatively long execution times of LCTs (especially mission-critical tasks) are not always desirable and it may impose a negative impact on the performance, or the functionality of MC systems. In this regard, this article proposes a realistic MC task model and develops a design-time task-drop aware schedulability analysis based on the Earliest Deadline First with Virtual Deadline (EDF-VD) algorithm. According to this analysis and the proposed scheduling policy based on the new MC task model, in the high-criticality (HI) mode, when an HCT overruns and the system switches to the HI mode, the number of drops per LCT is prohibited from passing a predefined threshold. ... mehrIn addition, to guarantee the real-time constraints and safety requirements of MC tasks in the presence of faults (assuming transient faults in this article), a corresponding scheduling mechanism has been developed. According to the obtained results from an extensive set of simulations, which have been validated through a realistic avionic application, the proposed method improves the acceptance ratio by up to 43.9% compared to state-of-the-art.