Definition of reliability
Reliability is the probability of a device performing its purpose adequately for the period of time intended under the operating conditions encountered.
A failure-rate curve of the type shown in Fig. 1 is called a "bath tub" curve.
The early-failure period O->A is also called the infant-mortality or burn-in period. Failure occurrence can be discerned by burn in or aging of the components.
The failure rate will decrease to a lower value ( Point C ) and remain fairly constant, defining the beginning of the normal operating period. During this period, random failure takes place at a specified rate. An important objective of the manufacturer is to reduce the normal operating failure rate as low as possible.
In general, if X represents a constant probability of failure per hour, the probability of an item surviving for H hours is (1-X )H. For small X one can approximate:
R(t)=exp (-HX ) where R(t) is the probability of survival after H hours.
and 1/X =MTBF ( Mean Time Between Failure )