A new metric for measuring the fault-tolerance capability of a multihop wireless sensor network is introduced in this paper. Most of the studies on fault-tolerance in sensor networks use connectivity as the metric of fault-tolerance. If the underlying network is k-connected, it can tolerate up to k - 1 failures. In measuring fault tolerance in terms of connectivity, no assumption regarding the locations of the failed sensor nodes is made - they may be very close to each other or very far from each other. In other words, the connectivity metric fails to capture any notion of locality of faults. However, in sensor networks, it is highly likely that the faults will be localized. This is particularly true in military applications, where an enemy bomb may inflict massive but localized damage to the sensor network. To capture the notion of locality in fault-tolerance, we introduce the notion of region-based connectivity. The region-based connectivity of a network may be informally defined to be the minimum number of nodes within a region whose failure will disconnect the network. Obviously, the notion of region-based connectivity is tied to the notion of a region. A region may be defined in several different ways and they are discussed in detail in the paper. The attractive feature of the region-based connectivity as the fault-tolerance metric is that it can achieve the same level of fault-tolerance as the traditional metric - connectivity, but requires much lower transmission power for the sensor nodes. We provide both analytical as well as extensive simulation results to support our claim.