The technological improvements in hardware and extensive standardization efforts in software development allow Wireless Sensor Networks (WSN) to be employed more widely and extend its application areas. The main challenge of the WSN studied in the literature is achieving the longest node lifetime given the limited battery capacities of the nodes. However, the lack of physical protection and inadequate security mechanisms make WSNs also vulnerable against different types of attacks and natural phenomena. In this thesis, we analyze the fact that not all the nodes have the same impact on the network performance in case of their incapacitation. Indeed, there are some critical nodes in the WSN, i.e. nodes that, once incapacitated, causes the most deterioration on the network performance. In this work, the focus is on two crucial network performance metrics, namely the lifetime and the latency and we investigate the effect that the elimination of the critical nodes has on these metrics by using Mixed Integer Programming (MIP) models. Furthermore, we introduce a novel method of adding spare node to compensate the destructive effects of failure of critical nodes on network performance. Numerical evaluations show the high impact these critical nodes have on lifetime and latency and prove how important is their identification for improving the network maintenance and for the adjustment of the service tolerance. Moreover, the addition of spare node could mitigate the effects of critical nodes failure significantly.