Existing real-time research focuses on how to formulate. model and enforce timeliness guarantees for task sets whose correctness has a temporal aspect. However; the resulting systems often exhibit poor resource utilization due to the resource scheduler reserving more resources than required in order to ensure that admitted schedules can be satisfied under worst case conditions. Weakening the guarantees leads to the known concepts of firm and soft real-time tasks, butt we think the paradigm needs to be shifted further,: reifying efficient utilization. With Quality-Assuring Scheduling (QAS) we presented such an algorithm. However: its practical applicability is restricted to uniform and harmonic periods, due to its complexity for arbitrary periods. To overcome this limitation, we introduce Quality-Rate-Monotonic Scheduling (QRMS), which, although slightly more pessimistic, is less complex compared to QAS. Thee admission control is again based on a probabilistic model to ensure that a requested fraction of jobs is successfully executed. Thus the amount of missed deadlines can be externally controlled, even in sustained overload situations.