Considering the impact of the popular energy management technique Dynamic Voltage and Frequency Scaling (DVFS) on system reliability, the Reliability-Aware Power Management (RA-PM) problem has been recently explored to save energy while maintaining system reliability. In this work, focusing on Rate Monotonic Scheduling (RMS) policy, we study static RA-PM schemes for periodic realtime tasks. After showing the intractability of the problem, we focus on two widely-known feasibility tests for RMS (namely, the Liu-Layland bound and Time Demand Analysis) and propose a number of heuristics based on the priority-monotonic speed assignment. The heuristics are evaluated through extensive simulations.