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In this paper, we study and model a crash-recovery target and its failure detector's probabilistic behavior. We extend quality of service (QoS) metrics to measure the recovery detection speed and the proportion of the detected failures of a crash-recovery failure detector. Then the impact of the dependability of the crash-recovery target on the QoS bounds for such a crash-recovery failure detector is analysed by adopting general dependability metrics such as MTTF and MTTR. In addition, we analyse how to estimate the failure detector's parameters to achieve the QoS from a requirement based on Chen's NFD-S algorithm. We also demonstrate how to execute the configuration procedure of this crash-recovery failure detector. The simulations are based on the revised NFD-S algorithm with various MTTF and MTTR. The simulation results show that the dependability of a recoverable monitored target could have significant impact on the QoS of such a failure detector and match our analysis results.