2-23] PROBABILITY OF RELIABLE OPERATION 103 



Throughout all of the phases of operation, an equipment failure can cause 

 the interception to fail. To account for this, we define a fourth probability: 



Pr = probability that the interceptor system equipment (fire-control 

 system, aircraft, communications, etc.) will operate satisfac- 

 factorily until weapon impact on the target. 



The interceptor kill probability Po may be defined as the likelihood that 

 the complete sequence of events will be completed successfully for any inter- 

 ceptor operating under the expected tactical conditions. Mathematically, 

 this statement has the form: 



Po (achieved) = PmXPcXP.X Pr. (2-38) 



Thus, the basic model is established. We will now demonstrate how 

 quantitative models may be derived and manipulated for each phase of 

 operation to produce specifications for the variable elements of the inter- 

 ceptor weapons system (AI Radar, Computer, Display, and Missile 

 Guidance Tie-in). First, we make an estimate of the expected contribution 

 of each phase of system operation to the overall kill probability. For 

 instance, in the hypothetical example, we may substitute specified input 

 values in Equation 2-38 and write 



Po = 0.50 = O.lSPcPvPr (2-39) 



0.667 = PcPvPr. 



Any combination of P^, P„, and Pr which yields this result will satisfy 

 the requirement. For preliminary design purposes, we shall select one of the 

 possible combinations to provide a criterion for the performance of each 

 phase: 



Pr = 0.85 



P. = 0.95 (2-40) 



Pc = 0.825 



Note that Po = (0.85) (0.95) (0.825) = 0.50. 



This choice is somewhat arbitrary. In an actual analysis a number of 

 different combinations might be assumed to establish trade-offs between 

 the contributions of each phase of system operation. 



2-23 PROBABILITY OF RELIABLE OPERATION 



The analysis of the tactical situation showed that the total air battle 

 lasted less than one-half hour. The total number of interceptors in the air 



