190 



THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956 



Remarks 



1. Since P* > Y2 then (1 — P*)/P* < 1 and hence no two popula- 

 tions can have the same vahie ri at stopping time. 



2. For A: = 2 the inequality (6) reduces to the inequalitj^ (3). 



3. The procedure 7^3 terminates onl}^ at a failure time, never between 

 failures, since the left member of (G) depends on t only through the 

 quantities 7-i{t). 



4. After experimentation is completed one can make, at the lOOP per 

 cent confidence level, the confidence statement 



ds ^ di S a* 9, (or di/a"" 



^ ds S e,) 



(7) 



where 6s is the scale parameter of the selected population. 



Numerical Illustrations 



»l/4 



Suppose the preassigned constants are P* = 0.95 and a* = 19' 

 2.088 so that (1 - P*)/P* = ^9- Then for A; = 2 the procedure is to 

 stop when r-i — ri ^ 4. For A; = 3 it is easy to check that the procedure 

 reduces to the simple form: "Stop when ?'2 — ri ^ 5". For A; > 3 either 

 calculations can be carried out as experimentation progresses or a table 

 of stopping values can be constructed before experimentation starts. 

 For A: = 4 and A; = 5 see Table VIII. 



In the above form the proposed rule is to stop Avhen, for at least one 



Table VIII — Sequential Rule for P* = 0.95, a* = 19 

 A: = 4 fc = 5 



1/4 



* Starred rows can be omitted without affecting the test since every integer in 

 these rows is at least as great as the corresponding integer in the previous row. 

 They are shown here to ilhistrate a systematic method which insures that all the 

 necessary rows are included. 



