One of the essential requirements of embedded systems is a guaranteed level of reliability. In this regard, fault-tolerance techniques are broadly applied to these systems to enhance reliability. However, fault-tolerance techniques may increase power consumption due to their inherent redundancy. For this purpose, power management techniques are applied, along with fault-tolerance techniques, which generally prolong the system lifespan by decreasing the temperature and leading to an aging rate reduction. Yet, some power management techniques, such as Dynamic Voltage and Frequency Scaling (DVFS), increase the transient fault rate and timing error. For this reason, heterogeneous multicore platforms have received much attention due to their ability to make a trade-off between power consumption and performance. Still, it is more complicated to map and schedule tasks in a heterogeneous multicore system. In this paper, for the first time, we propose a power management method for a heterogeneous multicore system that reduces power consumption and tolerates both transient and permanent faults through primary/backup technique while considering core-level power constraint, real-time constraint, and aging effect. Experimental evaluations demonstrate the efficiency of our proposed method in terms of reducing power consumption compared to the state-of-the-art schemes, together with guaranteeing reliability and considering the aging effect.