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Many real-time systems have firm real-time requirements which allow occasional deadline violations but discard any jobs that are not finished by their deadlines. To measure the performance of such a system, a quality of service (QoS) metric is needed. Examples of often used QoS metrics for firm real-time systems are average deadline miss rates and (m, k)-firm constraints. However, for certain applications, these metrics may not be adequate measures of system performance. This paper introduces a novel QoS constraint for firm real-time systems. The new QoS constraint generalizes existing firm real-time constraints. Furthermore, using networked control system as an example, we show that this constraint can be directly related to the control system's performance. We then present three different scheduling approaches with respect to this QoS constraint. Experimental results are provided to show the effectiveness of these approaches.