2-9] SYSTEM EFFECTIVENESS MODELS 63 



Also shown are the limiting effects of the fixed problem elements pre- 

 viously outlined in Figs. 2-3 through 2-6. For example, the missile salvo 

 kill probability is 0.75; obviously the interceptor kill probability cannot 

 exceed this value. If the raid is engaged by six CAP interceptors and all 36 

 of the deck-ready interceptors, an interceptor kill probability of 0.48 is 

 required. If the tactics are changed to allow both CAP patrols to engage 

 the raid in addition to the 36 deck-ready interceptors, the individual inter- 

 ceptor kill probability required drops to 0.42. If the total complement of 

 66 interceptors could be used, a kill probability of only 0.3 would be 

 required. 



The basic parametric relationships between the number of interceptors 

 and system effectiveness now are established. The next phase of the sys- 

 tems analysis must determine the relationships between the number of 

 interceptors and the other fixed and variable elements. Completion of this 

 phase will provide the basic parametric data which will, in turn, allow 

 intelligent selection of the following system parameters (see Fig. 2-2). 



1. Number of interceptors (A^) 



2. Interceptor effectiveness (Po) 



3. Early-warning range {Raew)- 



The number of interceptors which can be used to defend a given raid, 

 and thus the required interceptor kill probability, is a function of initial 

 interceptor deployment, detection ranges, reaction times, and target and 

 interceptor speeds. These factors can be conveniently summarized in a 

 diagram similar to Fig. 2-12, which shows the sequence of events in a typical 

 raid. The interceptor and target performance characteristics were given 

 in Figs. 2-5 and 2-7. We assume, as an illustrative case, that the AEW 

 detection range is 250 n. mi. from the fleet center. Since the target has a 

 speed of 800 fps (474 knots), it will arrive at the fleet center 32 minutes 

 after detection. The target track is shown in Fig. 2-12 as the straight line 

 connecting 250 n. mi. at zero time to 32 minutes at zero range. 



The CAP interceptors stationed 100 n.mi. from the fleet center are 

 vectored to intercept the raid following a 3-minute time delay consumed by 

 the process of identification, acquisition, and assignment. The track of the 

 CAP aircraft is constructed as a line with a slope equal to the reciprocal of 

 their speeds (1200 fps or 710 knots). We observe that the intersection of 

 the two tracks occurs at 175 n.mi., the maximum range at which the raid 

 can be engaged. 



In accordance with defined tactical doctrine (Fig. 2-3), only one combat 

 air patrol (6 aircraft) is committed to the raid. The remaining CAP 

 maintains its station to guard against the possibility of attacks from other 

 directions. 



