5.3.4 Exponential
Distribution
This is probably the most important distribution in reliability
work and is used almost exclusively for reliability prediction of electronic
equipment (Ref. MILHDBK217). It describes the situation wherein the hazard
rate is constant which can be shown to be generated by a Poisson process. This distribution is valuable if properly
used. It has the advantages of
(1) A single, easily estimated
parameter ( l)
(2) Is mathematically very
tractable
(3) Has fairly wide
applicability
(4) Is additive  that is, the
sum of a number of independent exponentially distributed variables is
exponentially distributed
Some particular applications of this model include
(1) Items whose failure rate does not change significantly
with age
(2) Complex and repairable equipment without excessive amounts
of redundancy
(3) Equipment for which the early failures or "infant
mortalities" have been eliminated by "burning in" the equipment for some
reasonable time period
The failure density function is



for t > 0, 
(5.37) 
where l is the hazard (failure)
rate, and the reliability function is


(5.38) 