2-9] 



SYSTEM EFFECTIVENESS MODELS 



61 



the use of mathematical models. These interrelationships form the quanti- 

 tative bases for the choice of basic system parameters. 



The following paragraphs will develop a number of models designed to 

 expose some of the more important aspects of the task force air defense 

 problems. The techniques used to develop these models are illustrative of 

 the means by which any complex system problem may be broken down to 

 forms that can be handled by analytical means. 



2-9 SYSTEM EFFECTIVENESS MODELS 



The operational requirement (Fig. 2-8) specified the effectiveness of the 

 interceptor air defense system in terms of the degree of success which must 

 be achieved with a required reliability. For example, the probability of 

 destroying at least 16 of the 20 targets should exceed 90 per cent. 



The first step of the systems analysis must determine the nature of the 

 relationships between system eflFectiveness and the fixed and variable 

 elements of the defense system (Fig. 2-2). The following examples demon- 

 strate how such an analysis may be carried out. 



Assume that 40 interceptors may be brought to bear against the 20- 

 target raid previously assumed as the threat (A^ = 40). Each interceptor 

 can make only one attack with its two-missile salvo. Thus, when one 

 attack against a target fails, another interceptor will be assigned to that 

 target until either 40 attacks have been made or all the targets have been 

 destroyed. 



20 



18 



16 



Q 

 Ul 



d 14 

 \2 12 



C3 



^ 10 



20 40 60 



RELIABILITY (PER CENT) 



100 



Fig. 2-10 System Effectiveness Operating Characteristics. 



