This paper introduces a new service reliability metric based on service survivability when network components are vulnerable to disruptions. The network service reliability, i.e., its capability of providing service when requested, could be affected by intentional or natural disasters such as earthquakes, storms, terrorist attacks, etc. The proposed metric, termed mean network survivability, is an improvement over the existing reliability efficiency metric because it takes into consideration that nodes may have different service demands and edges may have different operational probabilities. Additionally, to calculate mean network survivability, the authors propose the use of an approximation to the real value of two-terminal reliability that is more accurate than other approximations that use either the most reliable route or lower bounds based on minimal paths, especially when edge operational probabilities are different. The proposed metric is important in characterizing the performance of a network and allows comparison among different topologies. Examples that illustrate the use of the proposed metric and compare it with other service reliability metrics are presented.