Missile Detection Processor MR1-R5 (1) GPS 40 Range 1.4m km Resolution 5
Three thoughts,
1. Speed, speed, speed. As previously mentioned you cannot hit what you cannot catch.
2. Since your Missile Detection Processor has a resolution of 5, a Size 6 missile (0.33 HS) will only be detected at 6100 km, and you will never fire at it unless it's speed is less than 1000 km/s.
Range for objects less than the sensor resolution = (target HS/Resolution)
2Detection has to occur at 6 seconds to allow the beam fire control to fire in the next 5 second impulse.
For my beam armed ships I use a single active sensor, resolution 1 and range of 2mkm which lets me see everything I can take a shot at. As a reaction ship I would strip off the passive sensors and use DSTS's at my colony, or a dedicated senor ship.
3. Your beam fire control for you 20cm lasers has really poor accuracy, you
might be better off dropping one laser and having a fire control that has range and accuracy.