380 BELL SYSTEM TECHNICAL JOURNAL 



exactly half of the points within the ±50% lines reassures us that the 

 estimated parameters are probably quite good. (If instead we had calcu- 

 lated, say, ±99% limit lines based on the skew distribution f(vw) just 

 derived, it seems likely that even the two "unusual" points of Fig. 9 might 

 have fallen in the "reasonable" range.") 



At this point it will be well to point out that in making switch counts 

 considerable care needs to be exercised in two directions. First, switch 

 counts ^ 1 and j^ r -\- I should coincide very closely with the beginning 

 and end, respectively, of the observation period, the intermediate counts 

 of course being uniformly spaced. Second, each count should be taken as 

 quickly as possible so that a substantially instantaneous reading of calls in 

 progress is obtained. These two desiderata can usually be attained readily 

 in schemes using mechanical, electrical or photographic means for recording 

 the switch counts. Counts made by observers, however, may be subject 

 to highly variable errors since in some cases a substantial portion of the 

 interval i may be required to complete a count. Such uncertainties natu- 

 rally increase the end-effect errors, and, consequently, the overall error in an 

 average-holding-time determination. 



To estimate the magnitude of the increased errors resulting from failure 

 to meet the above switch count specifications would require a special study 

 for each kind and type of failure; these would probably differ in every appli- 

 cation. An idea of the sensitiveness of switch counting to such irregularities 

 and the likely order of magnitude of the increased errors may be gained by 

 examining certain of the Newark data. Here the last switch count in many 

 of the hours, although taken instantly, failed to coincide well with the end 

 of the observation period T. The last count fell at points varying from a 

 little after the period closed to nearly an interval i ahead of this instant as 

 shown in Fig. 10. In most hours this permitted a small number of calls 

 to mark up on the peg count register after the last switch count was taken. 



As a result, if corrections were not made, the estimate of switch counts 

 lost on calls extending beyond the end of the hour would have omitted 

 about a third of those properly included, with a consequent lowering of the 

 average holding time estimate by approximately one per cent. 



If the time / which has elapsed between the last switch count and the 

 end of the period T is known, certain corrections for this particular irregu- 

 larity can be attempted. We shall indicate the formulas required since 

 they will be useful in an analysis of the Newark data. If an average of 



7 



a = ~a calls are assumed to originate in the interval J, and they follow a 



X —a 



Poisson distribution . ^ , then the expected number of switch counts lost 



