Shininglight,
If by tier 3 you mean that your tech is Ion Missile Engine with 3 points per MSP and Levitated-Pit Implosion Warhead: Strength: 4 x MSP then your not allocating nearly enough MSP to engines. At 50% MSP to engine your missile should be traveling at 30,000kps and have no trouble intercepting missiles doing only 12,500kps. With .25MSP allocated to warhead for the needed 1 damage point there is still plenty of MSP left for fuel and missile agility for an AMM that has 30 seconds of range (900,000km) and a better that 50% intercept probability if the agility tech is also "third tier" (ie 48 per msp).
The best approach I've found to missile design is a bit convoluted. It starts with identifying the speed of the missile to be intercepted. If that is not known the assume your own offensive missile speed. Missile range needs to allow for at least 3 intercept launches based on launcher fire rate. Much more range and you start running into issues with the active sensors required to detect incoming missiles becoming too large for practical use on a warship that is not a dedicated recon platform. The active sensor does need to be able to detect target missiles at a range sufficient to allow a max range intercept. The accompanying missile fire control is 1/3 the size of the detection sensor.
Example: Tech available: Fuel Efficiency 2. Fuel Usage x0.8; Missile Launcher Reload Rate 3; Ion Missile Drive: 3 per MSP; Levitated-Pit Implosion Warhead: Strength: 4 x MSP; Missile Agility 48 per MSP; Active Grav Sensor Strength 16; EM Sensor Sensitivity 8.
Expected target missile is size 6 and speed is 30,000kps.
size 1 AMM with .5msp engine, .25msp warhead, .004msp fuel, and rest is agility. This gives an AMM with speed 30,000kps, range 900,000km, 1 pt warhead, and an intercept chance against another missile traveling 30,000kps above 53.5%. It needs a resolution 1 active sensor of 13hs to detect a size 6 missile at 1,800,000km and resolution 1 missile fire control of 4.5hs to engage detected size 6 missiles. This of course assumes that the target missiles are not using ECM of any level.