374 BELL SYSTEM TECHNICAL JOURNAL 



that is between 137.4 and 163.2 seconds. (The best single estimate, of 

 course, is the observed average of 150.3 seconds.) Or conversely, if one 

 should desire to determine the true average holding time within 5 seconds 

 with a surety oi P — .90, he may use an approximate value of the standard 

 deviation (or the average holding time) based on past experience and 

 substitute in 



/1.645/V 



to obtain the number of calls to be measured. If /" = 150 seconds here, 

 n = 2421. 



The same information is contained in Fig. 5 which gives the per cent 

 error, ± 100 z p /\/«, in the observed average not exceeded with probabilityP. 



All this is based on the assumption that each of the n call lengths is 

 accurately enough measured so that no appreciable error is introduced from 

 this source. Obviously there is no point in expending much effort in care- 

 fully "proportioning" a sample so as to be representative of the vagaries 

 of the universe if each of the calls so chosen is not pretty accurately meas- 

 ured. This would be quite as futile as measuring very accurately the 

 holding times of a number of calls chosen during some short time period 

 which might turn out to be wholly untypical of certain of those important 

 periods coming earlier or later. For these direct measurement cases it will 

 probably be quite satisfactory if each call is measured with a maximum 

 error of not over one-tenth of l/\/ n. In our example of 900 calls this 

 would be .501 seconds, that is measurement of each call to the nearest 

 second. 



IV — Holding Times by Switch Count Methods 



If each call's holding time is not measured with considerable accuracy it 

 is immediately clear that additional calls must be observed in order to 

 compensate therefor. This is the situation in the method of switch counts 

 which is in effect a means for noting at regular intervals i whether a particu- 

 lar call does or does not exist. Thus none of the calls are at all closely 

 measured for their individual lengths. Other errors will also have to be 

 considered since at the beginning of the period some switch counts are 

 inevitably included on a number of calls from the preceding hour and at 

 the end of the period some of the calls registered on the peg count meter 

 will end beyond the period with the loss of part of their proper switch counts. 

 As a result there are in this method three distinct sources of holding time 

 error whose magnitudes we shall proceed to investigate in turn: 



a. Errors at the start of the observation period; 



b. Errors at the end of the observation period; 



c. Errors at the beginning and end of each call. 



