REUABILITY OF IJOLDIXG TIME MEASi'RE}fENTS 



391 



It may be noted that the unknown average holding time l enters into 

 both equations (35) and (36). They are not very sensitive to this value, 



however, and a iirst approximation obtained from / = will usually 



suffice. I'^urther refinement may be obtained by recalculating using the 

 new value ? found from equation (35). The form of the distribution 

 represented by the parameters of equations (35) and (36) is not known of 



0.5 1.0 1.5 2.0 2.5 3.0 



Z = NUMBER OF STANDARD DEVIATIONS ERROR (ABSOLUTE) 



Fig. 16 — Cumulative distribution of overall errors in average holding time, regardless 



of sign 



course, but since the errors are essentially the sum of three primary error 

 distributions w^hich are inclined to be unimodal themselves (except for very 

 small trunk groups), we shall probably be not far wrong to assume the 

 normal form for ? . If the magnitude only of the errors in the estimate t' 

 of the unknown true holding time / of the /; calls under observation is 

 desired, we can readily construct a distribution of these discrepancies 

 Figure 16 is the theoretical cumulative half-normal frequency curve, and 

 when (T is equated to (t, > found from equation (36), the probability of exceed- 

 ing any given error in the holding time estimate may be read off directly. 

 Example: Suppose we have made 6()-sccond switch counts on a group of 



