REDUCING TIME IN RELIABILITY STUDIES 181 



4. The parameter g is assumed to be the same for both processes. It 

 may be known or unknown. 



5. The initial number n of units put on test is the same for both pro- 

 cesses. 



6. All units have independent lifetimes, i.e., the test environment is 

 not such that the failure of one unit results in the failure of other units 

 on test. 



7. Replacements used in the test are assumed to come from the same 

 population as the units they replace. If the replacement units have to 

 sit on a shelf before being used then it is assumed that the replacements 

 are not affected by shelf-aging. 



CONCLUSIONS 



1. Increasing the initial sample size n has at most a negligible effect 

 on the probability of a correct selection. It has a substantial effect on the 

 average experiment time for all three types of procedures. If the value of 

 n is doubled, then the average time is reduced to a value less than or 

 equal to half of its original value. 



2. The technique of replacement always reduces the average experi- 

 ment time. This reduction is substantial when ^ = or when the popu- 

 lation variance of either process is large compared to the value of g. 

 This decrease in average experiment time must always be weighed against 

 the disadvantage of an increase in bookkeeping and the necessity of 

 having the replacement units available for use. 



3. The sequential procedure enables the experimenter to make rational 

 decisions as the evidence builds up without waiting for a predetermined 

 number of failures. It has a shorter average experiment time than non- 

 sequential procedures satisfying the same specification. This reduction 

 brought about by the sequential procedure increases as the ratio a of 

 the two failure rates increases. In addition the sequential procedure 

 always terminates with a decision that is clfearly convincing on the basis 

 of the observed results, i.e., the a posteriori probability of a correct 

 selection is always large at the termination of the experiment. 



SPECIFICATION OF THE TEST 



Each of the three types of procedures is set up so as to satisfy the 

 same specification described below. Let a denote the true value of the 

 ratio 61/62 which by definition must be greater than, or equal to, one. 

 It turns out that in each type of procedure the probability of a correct 

 selection depends on 6i and 62 only through their ratio a. 



