400 BRLI. SYSTEM TECHNICAL JOURNAL 



nid of each /-interval, the last one coming at the exact end ol tlie wliole 

 period. 1 This is the common case in which we merely sum all the switch 



counts, multiply by the counting interval and divide by the number of 

 calls shown on the peg count meter as originating in the period T. The 

 standard error for each end effect will then be approximately that given by 

 (x„, in equation (6') where no attention is paid to the end switch count values 

 of m and ic. Substituting a,„ for a,„ and a,,- in (2^) and following the same 

 analysis as before gives for </' (instead of q), 



'/ = 





2i i 

 If 



(42) 



A plot of this last expression is given in Fig. 20. By comparing points 

 on Fig. 20 with corresponding ones on Fig. 19, one obtains an idea of the 

 increase of error due to failure to correct the switch counts for the end ef- 

 fects as indicated in equation (35). For example, with 100-second calls 

 switch counted at 120-second intervals we find q = 1.134 while q' — 1.203, 

 indicating quite a marked increase in the overall error. The particular 

 errors resulting in any given circumstance coupled with the cost of making 

 the end effect corrections will determine the practical desirability of which 

 method to adopt, that is whether the factor for increasing the basic sampling 

 standard error shall be read from Fig. 19 or from Fig. 20. 



Finally, a chart has been drawn up as Fig. 21, by which a measure of the 

 overall error in estimating the unknown true holding time may readily be 

 determined. The right hand section of the chart is a redrawing of Fig. 5 

 given in section III for the sampling errors of individually measured calls. 

 Scale A is carried across and reproduced at C permitting the small nomo- 

 graph B C D to give easily the product of the sampling error and the q 

 (or q') factor at D. The left hand chart is based simply on the fact that 

 the overall error decreases inversely as the square root of the number of 

 periods switch counted. From it the number of periods required to obtain 

 any desired accuracy can be read. 



The estimate of the average holding time will be found from a simple 

 average of the estimates made for individual observation periods, 



r :^ ^ + ^^+ ••• ^'^'". (43) 



g 



If a certain per cent error in the estimated average holding time is ob- 

 tained for a single period the improvement for the combination of g periods 



