718 



MECHANICAL DESIGN AND PACKAGING 



OPERATING TIME *- 



Fig. 13-13 The Failure Rate Curve. 



presenting the mathematics involved in this determination, it is first 

 necessary to discuss several of the basic concepts of reliability theory. 



Electronic equipment has been 

 found to exhibit a characteristic 

 failure behavior with time. This 

 behavior is represented schematical- 

 ly in Fig. 13-13. As can be seen Irom 

 the curve, the failure behavior can 

 be divided into three stages. Each 

 stage can be represented by a 

 distinct mathematical model, as well 

 as by a specific time period in the 

 operating life of the equipment. 

 Stage I is characterized by initial 

 failures incident to defective com- 

 ponent parts finding their way 

 into the equipment, rough handling 

 during shipment and installation, and perhaps initial debugging of the 

 equipment. This is analogous to the infant mortality phenomenon in 

 humans. Obviously, the time between and A is short relative to the 

 equipment's entire life. 



In Stage II (bounded by A and 5), most failures occur randomly in time 

 and at a relatively constant rate. These random failures are a result of 

 accidental, unexpected, and unusually severe conditions arising during the 

 operating period, as well as randomly occurring failures of parts. During 

 this period, the probability of the accidental failure of a given equipment 

 in any time interval is entirely independent of the time the equipment has 

 already operated. For the most part, reliability is measured during this 

 period and, as will be shown later, the prediction of future reliability is 

 based upon the existence of a long period of the equipment's life in which 

 the failure rate is constant. 



The final hump in the curve beyond B represents increased wear-out 

 failures which occur due to a large number of component parts gradually 

 reaching a more or less failed state as a result of deterioration of the physical 

 structure of the parts. 



If a large sample of identical electronic equipments were to be operated 

 in region II until all the equipments failed, a curve similar to the observed 

 curve in Fig. 13-14 could be generated. Superimposed over the observed 

 curve is a theoretical exponential decay curve with the same time constant 

 as the observed curve. It can be seen that the two curves are so clearly 

 comparable that it is reasonable to hypothesize that the differences between 

 them are caused by chance factors. In most cases, of course, the degree of 

 similarity between the observed and a theoretical reliability function are 



