62 



THE DEVELOPMENT OF WEAPONS SYSTEM REQUIREMENTS 



If the effectiveness of each interceptor is assumed to be P = 0.5, the 

 system operating characteristic shown in Fig. 2-10 may be calculated by 

 the application of simple probability theory. ^ As can be seen, the assumed 

 parameters allow the operational requirement to be met. 



To obtain a complete picture, other possibilities may be assumed and 

 analyzed in the same fashion. For example, the effectiveness level provided 

 by 25 interceptors, each with a kill probability of 0.7, is also shown in the 

 figure. This combination of parameter values fulfills only part of the 

 operational requirement. The probability that more than 16 targets will be 

 destroyed is less than that for the previous assumptions; thus, this system 

 would impose increased requirements on the back-up surface-to-air missile 

 system. 



Continuing in this fashion, trade-off curves between the number of 

 interceptors and the interceptor kill probability can be determined for each 

 point of the operational requirement. Such a curve is shown in Fig. 2-11. 

 Here all the combinations of the interceptor kill probability and number of 

 interceptions are shown which will kill at least 16 out of 20 targets with a 

 90 per cent reliability. 



10 20 30 40 50 60 70 80 

 N-NUMBER OF INTERCEPTIONS 



Fig. 2-11 Interceptor Kill Probability vs. Number of Interceptions Required to 

 Kill 16 or More Targets with 90 Per Cent Probability. 



^Grayson Merrill, Harold Goldberg, and Robert H. Helmholz, Operations Research, Jrma- 

 ment. Launching {Yv\nc\p\&s oi Guided Missile Design Series), D. Van Nostrand Co., Inc., 1956. 

 Chapters 6 and 7 provide an excellent discussion of the mathematical techniques involved. 



