REDUCING TIME IN RELIABILITY STUDIES 193 



E(T; 1, ^2) = — ; E{T; 2.088, 6^ = — ; 



n n (23) 



n 



For /.• > 2 the proposed procedure is an application of a general se- 

 quential rule for selecting the best of A- populations which is treated in 

 [1]. Proof that the probability specification is met and bounds on the 

 probability of a correct decision can be found there. 



CASE 2: COMMON KNOWN ^ > 



In order to obtain the properties of the sec^uential procedure R:>. for 

 this case it will be convenient to consider other sequential procedures. 

 Let (S = 1/6-2 — 1/^1 so that, since the di are ordered, jS ^ 0. Let us 

 assume that the experimenter can specify three constants a*, /3* and 

 P* such that a* > 1, /3* > and ^ 2 < -P* < 1 ai^d a procedure is de- 

 sired which will select the population with the largest scale parameter 

 with probability at least P* whenever we have both 



a ^ a* and i3 ^ /3* 



The following procedure meets this specification. 



Rule Rs': 



"Continue experimentation with replacement until the inec^uality 



fi «*-(^i-'-i>e-^*(^i-^i)^ (l_p*)/p* (24) 



1=2 



is satisfied. Then stop and select the population with the smallest nimiber 

 of failures as the one having the largest scale parameter. If, at stopping 

 time, two or more populations have the same value ri then select that 

 particular one of these with the largest Poisson life Li ." 



Remarks 



1 . For k = 2 the inequality reduces to 



(r, - n) In a* + (Li - L2) 13* ^ In [P*/a - P*)] (25) 



If <7 = then Li = Li for all t and the procedure R/ reduces to R3 . 



2. The procedure R/ may terminate not only at failures but also be- 

 tween failures. 



