Ambient Assisted Living (AAL) aims to ease the daily living and working environmentfor disabled/elderly peopleat home. AAL use information and communication technology based on sensors data. These sensors are generally placed randomly without taking into account the layout of buildings and rooms. In this paper, we develop a mathematical model foroptimal sensor placement in order (i) to optimize the sensor number with regard to room features, (ii) to ensure a reliability level in sensor networkconsidering a sensor failure rate. This placement ensures the targettracking in smart home sinceoptimizing sensorplacement allow us to distinguish different zonesand consequently, to identify the target location, according to the activated sensors.