Since reliability can be defined as the probability that an item will perform a required function under stated conditionsfor a stated period of time, it can be modeled as a probability distribution. The probability of a component surviving to a time (t) is the reliability (R(t)).
R(t) = 
number surviving at instant t
number at time t = 0 
The failure rate can be expressed as f(t) below.
f(t)= 
number failing per unit time at instant t
number surviving at instant t 
Thus, the failure rate can be defined as the probability of failure in unit time of a component that is still working satisfactorily. For a constant failure rate f, R(t) varies exponentially as a function of time as given below.
R(t) = ef(t)
The failure rate, f(t), is given as the number of units failing per unit time. Since the number of components failing is typically very low, the units are usually reported as the percent (%) failure per 1x106 hours, or as the number of devices failing in 1x109 hours. This unit is referred to as the FIT (failures in time).
1 FIT = 1 failure per 1x109 device hours
Another common method for reporting component reliability is defined by the MTBF. Assuming that the failures occur randomly at a constant failure rate, the MTBF is given below.
MTBF = 1/ f
This may also be written as the probability of success (P(s)), or zero failures.
P(s) = e (t / MTBF) where t = time
Figure 42 shows P(s) versus time as normalized to the MTBF. From this plot it can be seen that after 1/2 MTBF, the probability of no failures is 60% and after 1 MTBF, the probability of no failures is 37%.
In summary, military electronics systems and the accompanying semiconductor devices, particularly GaAs, require thorough reliability testing. This includes both SPC monitoring to observe and improve the key characteristics and acceleratedlife testing to gather failure rate data to characterize MTBF and FIT over the long term life of the component and system.
References
1) Mouradian, George, "Basic Elements of Reliability" American University of Armenia, http://www.archassociates.com
2) Kayali, S., Ponchak, G., Shaw, R., eds., GaAs MMIC
Reliability Assurance Guideline, JPL Publication 9625, NASA Lewis Research Center, 1996, pp. 10.
