KELIAHfLIT] Or HOLDING TIME M EASLRh.M EXTS KM 



is then, 



~~/- (single period error). 



Illustrative Kxamplc. If calls of approximately 1.^5 seconds holdiiif; time 

 are to be switch counted at ?> minute intervals by 1 hour [)eriods, how many 

 such periods will be required to give us an assurance of P = .90 that the 

 resulting holding time estimate does not difTer from the true by more than 3 

 per cent? Assume an average of 325 calls per hour over the group, and that 

 end effect corrections (a) will be made, and (b) will not be made. 



Solution (a) W'e first read on Fig. 19 that q ~ 1.165. Turning to Fig. 

 21, we find that opposite n = 325 and F = .90 we have an error of 9.2 per 

 cent, which we carry over to the C scale of the nomograph. Laying a 

 straight-edge across this point and q — 1.165 determines a point on D 

 somewhat above the 10 per cent line. Projecting this point across to the 

 desired 3 per cent error line and dropping to the lower edge of the chart 

 we find that 12.7, say 13, such one-hour observation periods will be necessary 

 to meet the accuracy specifications of the problem. This is the effort re- 

 quired when the end effect corrections are made. 



(b) If the end effect corrections are to be ignored, we determine our 

 factor from Fig. 20 to be q' ~ 1.268. Proceeding on Fig. 21 exactly as 

 before we find that the number of one-hour observation periods required 

 is increased to 15.1, say 15. Thus a failure to make the end effect correc- 

 tions causes us to increase our switch counts by about 20 per cent. It is 

 by such comparisons as these that one decides the practical desirability of 

 making the end effect corrections. 



Summary of Suitch Count Procedures for Exponential Holding Times 



The choice of the size of unit observation period should rest primarily 

 on the considerations discussed in Section II, that is the homogeneity of 

 the holding time data from hour to hour, day to day, etc. Other things 

 being equal, we should select the longest period consistent with the view 

 that enough periods must be included so that representative sampling 

 of all known or suspected major variations in holding time character is 

 accomplished. The length of the switch count interval will likely already 

 have been decided by the equipment at hand or by other considerations. 

 If a choice is available, however, a short interval will produce more reliable 

 results than a long one, by the amounts indicated on Figs. 19 and 20. With 

 these matters decided, Fig. 21 is consulted to see how many periods must be 

 switch counted in order to obtain the desired accuracy. 



Having actually made the switch counts, exercising the cautions we have 

 mentioned, the average holding time /'' for each period is obtained from 

 equation (35) if the correction of the counts for the end effects in each 



