Wireless Sensor networks (WSN) are used to monitor long linear structures such as pipelines, rivers, railroads, international borders, and high power transmission cables. In this case a special type of WSN called linear wireless sensor network (LSN) is used. One of the main challenges of using LSN is the reliability of the connections across the nodes. Faults in a few contiguous nodes may cause the creation of holes (segments where nodes on either end of them cannot 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 network's sensing coverage. In this paper, we provide analysis of the different types of node faults in LSN and study their negative impact on the sensing coverage. We develop an analytical model to estimate the impact of faults on coverage in LSNs. We verify the correctness of the developed model through a number of simulation experiments to compare both calculated and simulated results under various network and fault scenarios.