Survivability of a wireless sensor network (WSN) reflects the ability of the network to fulfill its mission despite the presence of abnormal events, such as failures. Given that sensor networks are receiving increasing attention due to the wide range of their applications, which include the critical areas of health, and military and security, survivability constitutes a key property for their study. This paper proposes a quantitative analysis for survivability evaluation of wireless sensors networks using probabilistic model checking. We define network survivability in line with four measures, namely, the frequency of failures, the data loss, the delay, and the compromised data due to a variety of failures. In particular, three types of failure events are considered, namely, node, link, and attack failures, which are due to power faults, communication faults, and black hole attacks, respectively. Then, we represent network's behavior with continuous-time Markov chains and randomly inject the aforementioned faults and attacks in the network to derive results that quantify the impact of them. Although the proposed study considers and provides results for a WSN architecture, it has the potential of being exploited in different networks with their own specifications.