Linear Wireless Sensor networks (LSN) are used to monitor long linear critical structures such as pipelines, rivers, railroads, international borders, and high power transmission cables. Due to the importance of these structures, the LSN must be designed with high reliability considerations. However, one of the main challenges of LSN design is the connection reliability among the nodes. Unlike in Wireless Sensor Networks (WSN) in which sinks can be reached through multiple existing paths which can be utilized to enhance the reliability, very few alternate paths are usually available in LSNs. Faults in a few contiguous nodes in a LSN may cause the creation of holes. The nodes on either side of a hole may not be able to reach each other which will result in dividing the network into multiple disconnected segments. As a result, sensor nodes that are located between holes may not be able to deliver their sensed information which negatively affects the network's sensing coverage. In this paper, we develop an analytical model to provide reliability analysis for LSNs. We use this model to demonstrate two design applications. The first application is to use the model to create periodic maintenance schedules for existing LSNs while the second application is to use the model for new LSN designs and to compare different possible alternative designs.