Human-robot systems are increasingly employed across various industries, such as transportation, military, emergency response, and manufacturing. During human-robot collaboration, cognitive fatigue accumulation significantly impacts the human operator's performance, particularly in teleoperation and shared autonomy. This fatigue accumulation can be dangerous and may lead to incidents in robot operations. Consequently, modelling human performance is crucial for understanding and evaluating human-robot systems for risk mitigation and efficiency enhancement. In this work, we propose a prediction model for human-robot teams based on Fitts' Law and the SAFTE model. The model takes into account the operator's cognitive fatigue level and mission requirements to predict whether the operator is suitable for executing the mission and the time required for the human-robot team to complete it. Furthermore, we present a case study on a hypothetical scenario, drawing upon human study data, to assess the model's applicability.