Reliability
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under the curve is normalized, Eq. (4.1), knowing the whole area
ydx =
~exp |--~-|dx
(4.3)
~/2~t k z J
Therefore areas under portions of the curve can be interpreted
as
probabilities. Let the variable x be t, the integral
l f(t)dt = A
(4.4)
area
Dividing by A
if(t)
,
--~-at= 1
(4.5)
Therefore, any areas under thef(t) versus t curve also represent probability
and also represents the number of items tested if all failed during testing.
Reliability is the probability that a device will perform its specified
function for a specified time under specified operating conditions.
Take a time t~ on thef(t) curve Fig. 4.1 and note that to the left of the
line are the failures and to the right are the items which have not failed. In
computing the reliability
interest is in the percent of those which have
not failed up to time tl. Further, since the normalized area under the curve
is 1, the area under the curve from q.
R(tl, = Jf--~dt
(4.6)
tl
Another parameter, the Mean Time To Failure is useful.
0
0
III. RELIABILITY FOR A RATE OF FAILURE CURVE
The concept of time as applied to mathematical models for reliability may
refer to clock time (i.e. hours, minutes, etc.) or to the number of cycles
of operation (e.g., number of times used, cycles of stress, etc.). For the purposes of the following discussion, it will be assumed that the conditions