In this paper, we present an effective scheduling approach for a fault-tolerant IMA (integrated modular avionics)-based system. The system architecture consists of connected cabinets that are made of multiple line replaceable modules, such as core processor and I/O modules. To provide fault tolerance, the system is incorporated with fault resilient capability and executes replicated tasks on different cabinets. Thus application output will be ready after a task processing stage and a consistency checking stage. To schedule the two-stage operations at task processing nodes and at the voter, we adopt fixed priority executives and investigate two priority assignment algorithms. Several experiments have been conducted to measure the success ratios of finding feasible schedules under various conditions. The evaluation results reveal a proper design space in which feasible schedules can be found easily.