REDUCING TIME IN RELIABILITY STUDIES 



185 



Table III — Value of r Required to Meet the Specification 

 (a*, P*) FOR Procedures of Type R2 (g = 0) 



It i.s also unnecessary to prepare a separate table for the average ex- 

 periment time for procedures of type R2 since for g = the exact values 

 can be obtained by substituting the appropriate value of n in the ex- 

 pressions appearing in Table II in the row marked n = oo . For example, 

 for /( = 2, /• = 1 and a = 1 the exact value for ^ = is 0.500 62/2 = 

 0.250 62 , and for n = 3, r = 4, a = 00 the exact value for g = is 

 4.000 62/3 = 1.333 62 . It should be noted that for procedures of type R2 

 we need not restrict our attention to the cases r ^ n but can also con- 

 sider r > //. 



Table III shows the value of r recjuired to meet the specilication 

 (a*, F*) with a procedure of type R2 for various selected values of a* 

 and P*. 



procedures of type R3 — sequential, replacement 



Let D{t) denote the absolute difference between the number of fail- 

 ures produced by the two processes at any time t. The sequential pro- 

 cedure is as follows: 



"Stop the test as soon as the inequality 



Dit) ^ 



In [P*/{1 - P*)] 



In 



a 



(3) 



is satisfied. Then select the population with the smaller number of fail- 

 ures as the better one." 



To get the best results we will choose (a*, P*) so that the right hand 

 member of the inequality (3) is an integer. Otherwise we would be operat- 

 ing with a higher value of P* (or a smaller value of a*) than was specified. 



