RELIABILITY OF UOLDIMi IIME M LASV REM ENTS M?> 



The theoretical conclusions will he comjiared at various points with certain 

 data available. 



a. Errors at the Start of the Observation Period 



If the period of observation T be divided into ;■ equal intervals of length i, 

 and switch counts are made at the beginning (and end) of each interval, 

 we shall have a total of r + 1 observations. The ^ 1 count will give us 

 immediately the number of calls extending into the period from the pre- 



SWITCH COUNT 

 3 



2L 



TIME 



Fig. 6 — Diagram of switch counts at beginning of the period 



ceding hours. We have no means, however, of segregating their contribu- 

 tions to subsequent swatch counts, so a theoretical estimate of this amount 

 is required. 



If the average holding time of the calls is /, and they follow closely the 

 exponential law of distribution, we may reason as follows.' Consider the 

 case of a single call passing time at the start of the observation period 

 as in Fig. 6. Then the probability that it will be included only in switch 

 count number 1, that is that it ends between time and time /, is 



1 

 pi = P(<i) = 1 - e~^. 



^ Of course we do not know / exactly since that is the ultimate object of our study; 

 however, for the present purpose great accuracy will not be required, and / can usuallv 

 be taken as the first estimate of holding time obtained by the switch count method without 

 corrections. 



