Statistical Techniques for Reducing the 

 Experiment Time in Reliability Studies 



By MILTON SOBEL 



(Manuscript received September 19, 1955) 



Given two or more processes, the units from which fail in accordance with 

 an exponential or delayed exponential law, the problem is to select the partic- 

 ular process with the smallest failure rate. It is assumed that there is a com- 

 mon guarantee period of zero or positive duration during which no failures 

 occur. This guarantee period may be known or unknown. It is desired to 

 accomplish the above goal in as short a time as possible without invalidating 

 certain predetermined probability specifications. Three statistical techniques 

 are considered for reducing the average experiment time needed to reach a 

 decision. 



1 . One technique is to increase the initial number of units put on test. 

 This technique will substantially shorten the average experiment time. Its 

 effect on the probability of a correct selection is generally negligible and in 

 some cases there is no effect. 



2. Another technique is to replace each failure immediately by a new 

 unit from the same process. This replacement technique adds to the book- 

 keeping of the test, but if any of the population variances is large (say in 

 comparison with the guarantee period) then this technique will result in a 

 substantial saving in the average experiment time. 



3. A third technique is to use an appropriate sequential procedure. In 

 many problems the sequential procedure results in a smaller average experi- 

 ment time than the best non-sequential procedure regardless of the true 

 failure rates. The amount of saving depends principally on the ^'distance'" 

 between the smallest and second smallest failure rates. 



For the special case of two processes, tables are given to show the proba- 

 bility of a correct selection and the average experiment time for each of three 

 types of procedures. 



Numerical estimates of the relative efficiency of the procedures are given 

 by computing the ratio of the average experiment time for two procedures of 

 different type with the same initial sample size and satisfying the same 

 probability specification. 



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