This paper explores the design and configuration of a sensor network for target detection. Subject to a budget limit for sensors, the network is required to secure a certain detection probability and to work for a reasonable long time. One novel model of randomly distributed network is presented to fulfill this requirement. A state switching scheme is developed for sensor to save energy. The functional relationships between detection probability and related parameters about sensor, network and target are analyzed. Moreover, a two-level optimization problem is formulated. At the lower level, we optimize the behavior of each sensor subject to its energy constraint and at the upper level, we maximize the lifetime of the network. Equilibrium solution of the two-level optimization problem is obtained by numerical method. An example is presented to illustrate the main results. (c) 2007 Elsevier Ltd. All rights reserved.