390 



BELL SYSTEM TECHNICAL JOURNAL 



We now obtain immediately a preliminary ligure for the average holfling 

 time of the n calls as 



/; = 



SI 



and a standard deviation of this average by 



<^a = 



n 



(30) 



(31) 



This last standard deviation comprehends the uncertainty in the holding 

 time average caused by our inability to measure exactly the number of 

 switch counts which properly should be associated with the n calls. We 

 must now modify this measure of dispersion by the added fluctuation 

 inherent in the method of switch counting at finite intervals. These varia- 

 tions were found to cause no change in the "expected" or most likely value 

 of the average holding time (as shown by .c = in equations (18), (22) 

 and (26)), but the ax's, of equations (19), (23) and (27) showed sizeable 

 uncertainties which must be included. Since ax is for errors in the measure- 

 ment of individual calls we obtain the standard error of the average as 



■\/i 



(32) 



This error is built up on each call throughout the period and hence is 

 practically independent of those errors arising at the ends of the hour. 

 Their joint effects are additive so we obtain the estimates of the final param- 

 eters of the average holding time as 



r = /; -^ 



(s — 5,„ + sji 



-v/2 , 2 1a//2, 2\.2, 2 



(XI, = V ai' + (Tavg = - V [a^ -\- ay,)l -\- WCx . 



i^i) 



(34) 



If the holding times are exponential these equations may be written as 



/' = 



s + 



(35) 



ai' = 



(l - e-l) 



\{m + w)f- -f niiTt + /)(l - c 7)? ' 



- nlili - i)\\ - el). (36) 



