Reliability Engineering
OEM 2009
ESI 6321 –Applied Probability Methods in
Engineering
2
Reliability Engineering
Reliability
is the probability that a system
will perform properly for a specified
period of time.
Reliability depends on
Definition of “performing properly” (or
“failure”)
Operating conditions
Time (age of system)
Reliability as a function of time is
important system characteristic.

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3
Failure rate
Informally, we will define the
failure rate
of a system as the
rate at which the
system will fail
if
the system has not yet
failed for
t
time units.
We will formalize this later.
How do we expect this rate to vary over
time?
Increasing?
Decreasing?
Constant?
Mixed?
4
Failure rate
Nature of failures:
“Infant mortality” failure
Random failures
“Age-related” failures
A common assumption is therefore that
the failure rate follows a
bathtub curve
.

5
Time to failure
We will define
reliability
as it relates to
time through the following random
variable:
Let
F
denote the cumulative distribution
function (cdf) of this random variable:
T
=
time to failure
F
(
t
)
=
Pr(
T
!
t
)
=
probability that failure takes place
no later than time
t
6
Reliability
We then define
reliability
as a function of
time as
It is easy to see that
r
(0)
=
1
r
(
t
)
!
Pr(
T
>
t
)
=
1
"
F
(
t
)
=
probability that system operates without
failure for at least
t
time units
lim
t
!"
r
(
t
)
=
0

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