962 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956 



be better appreciated when some quantitative aspects of the problem 

 are considered. 



QUANTITATIVE ASPECTS OF THE PROBLEM 



When the nationwide dial switching plan began to take shape some 8 

 or 10 3'ears ago, intensiA-e study of the transmission maintenance prob- 

 lem was undertaken. The existing situation was examined to determine 

 whether or not the plant ^^'ould continue to be satisfactory under the 

 changed conditions. This was done by analyzing the results of many 

 thousands of transmission measurements which had been made on a rou- 

 tine basis in toll test rooms all over the Bell System. Both the measured 

 and the assigned losses were available so the differences between them 

 could be derived and analyzed statistically. 



Although the distribution of differences expressed in db for an office 

 did not necessarily follow precisely a normal probability law, the distri- 

 butions were close enough to normal law so that they could be treated as 

 normal. The results were similar throughout the System. The differences 

 within an office were random as also were the means of the differeJnces 

 from office to office. However, the means tended to be biased in the direc- 

 tion of excess loss. The performance of trunks in multi-link connections 

 which would be set up by the switching machines could therefore be esti- 

 mated with reasonable accuracy. In the statistical analysis of measure- 

 ments on the group of trunks, the performance was expressed in terms 

 of "distribution grade" and "bias." In telephone transmission mainte- 

 nance terminology, bias is the algebraic average of the measured trans- 

 mission departures in db from individual specified net losses for the group 

 of trunks. The distribution grade is the standard deviation of the differ- 

 ences between measured and specified trunk losses about this bias value. 

 The distribution grades found in these studies were about as follows: 



For trunks under 500 miles — about 1.8 db. 



For longer trunks — about 2.5 db. 



Table II illustrates the effects of the distribution grades on connections 

 involving various combinations of these trunk links, assuming that bias 

 can be neglected. 



The design loss objective for a 4-link connection, say 1,000 miles long, 

 is abovit 7 or 8 db (including 2 db of connecting trunk or pad loss at each 

 end), ^rable II shows that, in an appreciable percentage of the 4-link con- 

 nections in\'olving the above type of plant, the \'ariations can he ex- 

 pected to exceed the design loss. Variations of this magnitude can result 

 in transmission impairment d\w to (H'ho, hollownoss, singing, crosstalk, 



