OP, when you make an AMM sensor, you want to worry about the MCR range, thats for detecting size 6(and anything smaller) missiles.
As others noted, you have a 1HS range of 6mkm, but detection range is min(1,(max(MCR, tgt HS) / resolution))^2 * maximum range.
So, you have missiles incoming. Lets assume they are size 4, since we don't have them on active sensors, we don't know how big they are(unless we work it out from the thermal output...)
So lets plug everyting in:
min(1,(max(MCR, tgt HS) / resolution))^2 * maximum range
min(1,(max(0.3, s4 * 0.05HS) / 1HS))^2 * 6mkm
min(1,(max(0.3, 0.2) / 1))^2 * 6mkm
Note that a size 4 missile at 0.2 HS, is smaller than the minimum 0.3, so 0.3 is used.
min(1,(0.3 / 1))^2 * 6mkm
min(1,0.3)^2 * 6mkm
Note that this maxes out at 1.0, no bonus for bigger targets than the resolution.
0.3^2 * 6mkm
0.09 * 6mkm
0.54mkm
So you will not detect them until they are within half a million km.
Don't bother with the math every time, just use the MCR value in the sensor design window - thats what that math is for.