Linear Wireless Sensor Networks (LWSNs) are used in applications where deployment scenarios necessitate sensor nodes to be placed over a line topology. However, such a deployment raises reliability concerns because almost all the nodes in the network are critical with respect to the survivability of the LWSN. It is possible that an LWSN can stay connected even if a subset of the nodes are eliminated, yet, the potential reduction in Network Lifetime (NL) due to such an occurrence can be significant. In this study, after presenting a concise survey of the literature on LWSN reliability, we present an elaborate optimization framework to model the operation of an LWSN, which is built upon a comprehensive system model. Our framework encompasses three transmission power and packet size assignment strategies, which are instrumental in characterizing LWSN behavior. Furthermore, we utilized two-node failure models (i.e., random and coordinated) to assess the vulnerability of LWSNs from multiple perspectives. The results of this study reveal that the impact of coordinated node failures on NL is more severe than the impact of random node failures to such extent that in strongly connected LWSNs, the percentage decrease in NL due to coordinated node failures can be more than a magnitude higher than the NL decrease due to random node failures.