391 BELL SVSTEAP TECHNICAL JOURNAL 



20 trunks for a period of one hour, finding m = 7 and w — 13 as the number 

 of calls up at the beginning and the end of the hour, respectively. Suppose 

 also we have a total oi s = 680 switch counts, which includes the first 

 count of 7 at time zero. If the register recording number of calls originated 

 in the hour reads 282, what is the best estimate of the average holding time 

 of the n calls, and what is the probability that the true holding time is 

 within 3 seconds of this estimate? 

 We find our initial estimate for / from 



{^j-m)i ^ (673)60 ^ 143.19 seconds. 

 n 282 



Substituting in (35) and (36) we find 



t' = 145.65 seconds, 



a-f = 2.685 seconds. 



Then from Fig. 16 we read that the probability that this estimate of t is 



.3 

 more than 3 seconds, that is — = 1.12 standard deviations, in error is .263. 



o-'t' 



Likewise we may read that the probability is .94 that the error in the average 



is not over 5 seconds. 



As something of a final and overall comparison of theor}^ and observation, 

 the actual errors in holding times when estimated, by the switch count 

 method for the 31 busy hours in Newark have been tabulated in Table III. 

 The analysis of these pen register records was complicated by the fact that 

 the intervals i varied somewhat from switch count to switch count, and 

 even more from hour to hour, so that the last switch count often came near 

 the midpoint of the 60th minute. To some extent these irregularities of 

 counting correspond more closely to the timing variations in manual switch 

 counts than if they had been taken by machine at perfectly uniform inter- 

 vals. Such corrections as could be managed by the application of equations 

 (12) and (13) were made to the individual hours. In spite of these precau- 

 tions the actual errors were somewhat larger than those which could be 

 explained by theory although all large discrepancies were run down and 

 accounted for. The absolute errors are shown plotted in Fig. 17a in terms 

 of the theoretical standard deviations for each hour and in 17b in per 

 cent of the observed holding times. This case will again serve to show 

 that the switch count method is quite sensitive to variations from a perfect 

 application of the rules, and that very considerable care is required to remain 

 within the error limits indicated by the theory. 



It is interesting to see what portion of the error is contributed by the two 

 end effects and what by the errors made through "measuring" the calls by 



