For monitoring critical applications by using wireless sensor networks (WSNs), users usually care about the false positive (false alarm) probability and false negative (detection miss) probability of a WSN, which are defined as quality of surveillance (QoSu) in this paper. To mask faulty sensors, the K-coverage configuration is widely exploited to ensure that each location is covered by at least K sensors. However, increasing K effectively reduces detection misses but incurs high false alarm rate. Little work evaluates the K-coverage configuration in terms of explicit metrics. In this paper, we propose a fault-tolerant model, which determines the value of K according to a desired QoSu while maximizing the system lifetime. Experimental results show that (1) the K-coverage configuration is insufficient to meet the QoSu without adopting any fusion scheme, and (2) the derived configuration minimizes power consumption while meeting the QoSu.