This paper presents a sensor random deployment scheme to monitor 2-dimensional areas for constraining applications while providing a mathematical control of the coverage quality it allows. In addition, useful techniques to detect and repair sensor failures are also added to provide system robustness based on this scheme. In particular, mathematical formulas are developed to express the probability of complete coverage when the environment characteristics are varying, taking into account the deployment parameters. Moreover, a methodology is presented to adapt this scheme to the need of various WSN-based monitoring applications. A simulation is also performed to show the efficiency of the developed strategy, highlight some of its features, and assess its impact on the lifetime of the monitoring system it serves.