Receiver Operating Characteristics for Detection by Systems with Decision-Making Relay Stations

Assume that the performance of an observer is constrained by receiver operating characteristic (ROC) with (d′)1. The observer responds with YES or NO according to some criterion. Also assume that a signal is sent to a second observer when the first observer responds with YES. If NO, the signal is not sent in that observation interval. The ROC for the second observer is specified by (d′)2. Thus, a signal is relayed to a second observer by way of an intermediary who thereby introduces a threshold. An ROC for the over-all system shows the relation between the probability that the second observer responds YES, given that a signal was sent to the first observer, and the probability that the second observer responds YES, given that the signal was not sent to the first observer. The ROC for the over-all system may be generated by independently or jointly varying the criteria of the observers. ROCs are a function of (1) values of (d′)i; (2) criterion variations by the observers; (3) number of observers. [Supported by Air Force Office of Scientific Research.]