Systems and methods for activating a down hole tool in a wellbore. A piston is moveable from a first position to a second position for activating the down hole tool. The piston includes a first side exposed to an activation chamber, and a second side operatively coupled to the down hole tool. A rupture member has a first side exposed to the activation chamber and a second side exposed to the interior of a base pipe. The rupture member is configured to rupture when a pressure differential between the activation chamber and the interior reaches a predetermined threshold value, at which point the rupture member allows fluid communication between the interior and the activation chamber to pressurize the activation chamber and move the piston, thereby activating the down hole tool.