182 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1950 



1. The experimenter is asked to specify the smallest value of a (say 

 it is a* > I) that is worth detecting. Then the interval (1, a*) represents 

 a zone of indifference such that if the true ratio a lies therein then we 

 would still like to make a correct selection, but the loss due to a wrong 

 selection in this case is negligible. 



2. The experimenter is also asked to specify the minimum value P* > 

 \'2 that he desires for the probability of a correct selection whenever 

 a ^ a*. In each type of procedure the rules are set up so that the proba- 

 bility of a correct selection for a = a* is as close to P* as possible without 

 being less than P*. 



The two constants a* > 1 and \2 < P* < 1 are the only quantities 

 specified by the experimenter. Together they make up the specification 

 of the test procedure. 



EFFICIENCY 



If two procedures of different type have the same value of n and satisfy 

 the same specification then we shall regard them as comparable and 

 their relative efficiency will be measured by the ratio of their average 

 experiment times. This ratio is a function of the true a but we shall 

 consider it only for selected values of a, namely, a = 1, a = a* and 

 a = CO . 



PROCEDURES OF TYPE Ri — • NONSEQUENTIAL, NONREPLACEMENT 



"The same number n of units are put on test for each of the two pro- 

 cesses. Experimentation is continued until either one of the two samples 

 produces a predetermined number r (r ^ n) of failures. Experimenta- 

 tion is then stopped and the process with fewer than r failures is chosen 

 to be the better one." 



Table I — Probability of a Correct Selection — Procedure 



Type Ri 

 (a = 2, any g '^ 0, to be used to obtain r for a* = 2) 



Note: The value for ?• = is obviously 0.500 for any n. 



