A firing head assembly is described. The firing head assembly includes a tubular housing, upper piston and lower pistons, and a compressible member arranged within a lumen of the tubular housing and positioned between the upper and lower pistons. According to an aspect, the assembly includes a safety assembly that includes a sleeve having a zigzag shaped slot therein. The safety assembly may include a key that radially extends from a surface of one of the pistons, through the zigzag shaped slot. The distance between the upper and lower pistons may be adjusted by adjusting a pressure inside the tubular housing and a second pressure outside the tubular housing. The upper and lower pistons may function to operatively adjust the arrangement of the key within the zigzag shaped slot to activate the firing head assembly to either trigger an explosive reaction or to not trigger the explosive reaction.