84 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1957 



that the capacitor design selected would provide the degree of reliability 

 required, a number of capacitors were constructed and placed on test 

 at voltage stresses ranging from 1^ to 2j times the maximum stress ex- 

 pected in service. From the performance of these samples, a prediction 

 of performance vmder service conditions can be made as follows: 



The total equivalent exposure in terms of capacitor years at the maxi- 

 mimi ser^qce voltage can be computed for the samples under test by the 

 following summation : 



T = N.T. (I;)' + N.T. g)' +---+N,T. (.0' (1) 



where Ni , N2 , • • • Nr are the number of samples on test at voltage 

 stresses Vi , V2 and Vr , Ti , T2 , ■ • • Tr are the total times of the individ- 

 ual tests and Vs is the maximum voltage stress under service conditions. 

 If, as has been the case in the tests described above, there has been 

 only one failure in the total exposure T, we can estimate from probability 

 equations the limits or bounds within which the first failure will occur 

 in a system involving a given number of capacitors operating at a volt- 

 age stress Vs . These equations are: 



probability of no failures in exposure T = e" '^'^ (2) 



probability of more than one failure in exposure time T = 



l-(i + T)e-"' (3) 



where T is obtained from (1) and L is the total exposure in the same 

 units as T for the service conditions. The solutions of (2) and (3) for 

 L using any desired probability give the maximum and minimum ex- 

 posures in capacitor-years, within which the first failure may be ex- 

 pected to occur under service conditions. 



However, since the voltage on the capacitors varies from repeater to 

 repeater, it is necessary to determine the equivalent exposure of the sys- 

 tem in terms of capacitor-years per year of operation at the maximum 

 service voltage in order to estimate the time to the first failure in the 

 system. This is obtained from (1) for one-half of one cable by substitut- 

 ing the supply voltage at each repeater for Fi , y2 , etc., the maximum 

 service voltage for Vs and the number of capacitors per repeater for A^. 

 The total exposure for a two cable system is then 4 times this figure. 

 With the data which has been accumulated and the number of capacitors 

 and voltages of the transatlantic system, we estimate with a probability 

 of being correct nine times in ten that the first "wear-out" failure of a 



