13-15] 



RELIABILITY 



719 





1.0 



0.5 



1 2 34 56 78 910 12 14 16 18 20 

 HOURS OF OPERATION *- 



Fig. 13-14 Representative Observed and Theoretical Reliability Functions. 



not as striking as in Fig. 13-14; however, the overall hypothesis of similarity 

 has been found to be a good one. Thus the familiar exponential reliability 

 law may be written: 



(13-16) 



R = e-'i'^ 



where R = reliability 



i = time during which satisfactory operation is desired 



T = equipment mean time to failure. 



The quantity r (hourly failure rate) is the reciprocal of T, giving rise to 

 the alternate form of the law: 



R 



(13-17) 



Let us return now to the measurement of reliability discussed earlier. 

 Field testing of equipment will yield the value of T needed for Equation 

 13-16. This is numerically equal to the sum of the operating hours divided 

 by the number of failures. It is important to realize that the soundness 

 of this procedure rests on the assumption that a unit once repaired is 

 equivalent to a new unit. It is further essential to use a sufficient number 

 of representative samples to ensuie generality of the results. Using Equa- 

 tion 13-16, a theoretical curve as shown in Fig. 13-14 can be generated by 

 substituting a continuum of/ values. 



As an example of how this law might be used, let us consider the hypo- 

 thetical AI radar problem treated in Chapter 2. The derived requirement 

 stated that a reliability of 90 per cent was required over a 3-hour operating 

 period. 



