180 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956 



INTRODUCTION 



This paper is concerned with a study of the advantages and disad- 

 vantages of three statistical techniques for reducing the average dura- 

 tion of hfe tests. These techniques are: 



1. Increasing the initial number of units on test. 



2. Using a replacement technique. 



3. Using a sequential procedure. 



To show the advantages of each of these techniques, we shall consider 

 the problem of deciding which of two processes has the smaller failure 

 rate. Three different types of procedures for making this decision will 

 be considered. They are: 



Ri , A nonsequential, nonreplacement type of procedure 

 E,2 , A nonsequential, replacement type of procedure 

 Rs , A sequential, replacement type of procedure 

 Within each type wq will consider different values of n, the initial 

 number of units on test for each process. The effect of replacement is 

 shown by comparing the average experiment time for procedures of 

 type 1 and 2 with the same value of n and comparable probabilities of a 

 correct selection. The effect of using a sequential rule is shown by com- 

 paring the average experiment time for procedures of type 2 and 3 with 

 the same value of n and comparable probabilities of a correct selection. 



ASSUMPTIONS 



1. It is assumed that failure is clearly defined and that failures are 

 recognized without any chance of error. 



2. The lifetime of individual units from either population is assumed 

 to follow an exponential density of the form 



f{x; e,g) =\ e-^^-")/" iov x -^ g 



f(x; e,g) = iorx<g 



where the location parameter g ^ represents the common guarantee 

 period and the scale parameter 6 > represents the unknown parameter 

 which distinguishes the two different processes. Let Ox ^ do denote the 

 ordered values of the unknown parameter 6 for the two processes; then 

 the ordered failure rates are given by 



Xi = 1/(01 + {/) ^ Xo = 1/(02 -f g) (2) 



3. It is not known which process has the parameter di and which has 

 the parameter dt . 



