RELIABILITY OF HOLDING TIME MEASUREMENTS 



385 



Example: An hour with 372 calls having a constant holding time per 

 call of // = 131.8 seconds was subjected to a 60 second switch count study, 

 records being kept of the errors in measurement on individual calls. As 

 shown in Fig. 12, 284 or 76.3^'^, gave counts of "2" with an error of 120 — 

 131.8 = —11.8 seconds. The remaining i^S calls, or 23. 7*^!^, received counts 



-60 -50 -40 -30 -20 -10 10 20 30 40 50 



X = ERROR IN MEASUREMENT IN SECONDS 



Fig. 12 — Error distribution for measurements on individual calls with constant 



holding times 



of "3", with errors of 180 — 131.8 = 48.2 seconds. Applying the theory 

 just developed to this case gives, 



p{2i - I,) = />(-11.8) = ^^ ~^^^'^ = .803, 



Pi^i - h) = />(48.2) = 



60 



60 - 48.2 

 " 60 



.197. 



As indicated on Fig. 12, these theoretical values check very satisfactorily 

 with the observations. The observed average holding time — 134.2 seconds 

 as against the true value of 131.8 seconds; the error of 2.4 seconds is quite 

 compatible with o-^- = \/l 1.8(48.2) = 23.85 seconds and the n = 372 calls 

 observed. 



{b). Equally Likely Dislrihution of Holding Times between Adjacent Multi- 

 ples of i 



Imagine a holding time distribution of any general form but with a 

 constant probability of occurrence between adjacent pairs of multiples of /, 



