148 THE CALCULATION OF RADAR DETECTION PROBABILITY 



randomly from look to look because of their inability to judge accurately 

 the signal strength or to remember exactly the threshold level. Their 

 average threshold would also tend to increase with fatigue and inattention. 

 The net result of these deviations generally seems to be a loss in detection 

 efficiency of the human operator in comparison with that of a mathematical 

 threshold. This degradation is often introduced through an "operator 

 factor" or efficiency factor, ^q. The probability of detection obtained on the 

 basis of some threshold assumption is simply multiplied by />(, to give the 

 "realistic" probability of detection. Values ranging all the way from 0.05 

 to 0.8 have been specified for this factor at one time or another. 



It is quite possible that a degradation of this kind represents certain 

 detection operations quite well where the operators become fatigued or 

 bored. On the other hand there are many detection situations where the use 

 of an "operator factor" is very dubious. One such situation is that of the 

 operator of an AI radar on a vectored, 10-minute interception mission. It is 

 somewhat ridiculous to suppose that an operator on such a mission would 

 completely miss, say, 50 per cent of all targets no matter how brightly they 

 are painted on his scope. Another situation where the "operator factor" 

 concept is obviously not applicable is in connection with automatic equip- 

 ments. Here, the detection is directly accomplished through the use of a 

 threshold. 



In this chapter the "operator factor" concept will be abandoned in favor 

 of simply introducing an operator degradation of the signal-to-noise ratio. 

 This procedure is a standard one,^° and it leads to a somewhat simpler 

 formulation of the cumulative probability of detection. A typical value for 

 the degradation is given in the footnote reference as 2 db. 



The decision threshold is chosen to give a false-alarm probability, or 

 probability of detecting a target when none is present, which is compatible 

 with the cost of committing the radar or weapon system to such an alarm. 

 When such commitment costs can be established numerically, a selection of 

 false-alarm time can be made on the basis of minimizing total costs. Most 

 commonly, though, such costs cannot be established and the false-alarm 

 time is arbitrarily fixed after a thorough but subjective study of its effect 

 on the operational performance of the system. 



The number of independent samples of signal-plus-noise in the false- 

 alarm time is called the false-alarm number and is denoted by t?. With 

 false-alarm times varying from seconds to hours and pulse lengths varying 

 from fractions of a microsecond up to milliseconds, the false-alarm number 

 might have approximate upper and lower bounds of 10'- to 10^. The 

 probability of having a false alarm on a single trial is the reciprocal of the 

 false-alarm number. This probability, the probability that a noise sample 



lew. M. Hall, "Prediction of Pulse Radar Performance," Proc. IRE (Feb. 1956) 234-231. 



