RELIABILITY OF HOLDING TIME MEASUREMENTS 387 



give the isosceles triangular distribution of errors on indix-idual calls shown 

 in Fig. 14. Tn this the average error is 



X = 0, (22) 



and the standard deviation is 



ax = .408i. (23) 



(c). Holding Times Exponentially Distributed, fit) — ke' , ic'liere k = - 



With holding times of the exponential type the sum of the terms in the 

 brackets of equations (14) and (15) will depend on the particular magni- 

 tudes of the errors .v assumed. If in equation (14), we substitute ex- 

 ponential expressions for the /-functions, we have 



/>.5o(.r) dx - '-X^ {ke^"'-'' + ke^'"'-'' + .-^g-'-^-'-^^ -^ ■ ■ ■) dx 

 I 



= 'J^ ke'^ (1 + e"'' + e-'" -f- • • •) dx 

 I 



i + X I,:, 1 



= — ^- ke --. dx 



I 1 — e *' 



= k' L+J."' eTdx, (24) 



w lie re 



k' = 



l{\-e 



Similarly we find 



»' — X 



Px^o{x) dx = k' IJ^ e~~r dx. (25) 



t 



The mean and standard deviation of this unusual-shaped distribution of 

 x are found to be 



(26) 



{2i -\- i)e i - 21 + i 



\ - e i 



(27) 



In Fig. 15 is shown the distribution of the individual errors found by 

 60-second switch counts on 746 varying holding time calls (2 hours on the 



