196 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956 



r r - e-(— «)/«v"^^^^ dx dy 



Jg Jg 6-1 



Prob \z = -logSj 



^2 -0[92(n-l)+9l"l/9lfl2 _i_ ^1 -H9in+Bi(n-l)]l9ie2,) 



- e + - e /o9\ 



1 + 5 



Thus the OC and ASN functions under (27) with g > bear the same 

 relation to 5* and 5 as they do to a* and a when ^ = 0. Hence, letting 

 w denote the smallest integer greater than or equal to 



^ In [P*/(l - P*)] ^ \n[P*/{l-P*)] 



In 8* gl3* + In a* ^' ' 



we can write (omitting P* in the rule description) | 



7^15; /?/ («*, /5*){ ^ P{5; /^.^"(S*)! ^ ^-^^^ (34) 



<w. I ■ — - tor 5 > 1 {So) 



^ \8 - l/\5"' +1/ 



w~ for 5=1 



W'e can approximate the average time between failures by 



I 



and the average experiment time by « 



E{T; /?/(«*, ^*)} ^ E{F; R,'(a*, 0*)\ [^.^ f^'^ _^ ^'^, (37) 



n{Oi -T 02 -f- zg) 



Since 5 ^ 1 then 5"(1 + 5") is an increasing function of w and by 

 (33) it is a non-increashig function of 5*. By (28) 5* ^ a* and hence, 

 if we disregard the approximation (34), 



P{8; AV(«*)1 - ^!^{py^/_p.^y..n ^* ^ P{S;R/m} (38) 



Clearly the rules Ri{a*, P*) and R/ {a*, P*) are equivalent so that 

 for g > we haA-e 



P{8;R-s{a*)} ^ P{8;R/ia*)] (39) 



