A
simple Introduction into Reliability
Metrics
Failure Rate, MTBF,
Reliability, and Availability
You are here:

Page Content

Assembly 
MTBF
[h]

Personal computer 
2.000

Computerharddiskdrive 
15.000
As of 2022, HDD manufacturers would communicate MTBF figures of
1.000.000 h or even higher.

Computer mouse 
100.000

Computer keyboard 
25.000

Computercolormonitor 
8.000

Computer CD ROM drive 
8.000

Rifleman, bullet:
A
rifleman shoots 1000 bullets onto a target. The flight
time of the bullet shall be 0,5 seconds.
We
assume that 2 out of 1000 shots would not work properly due to failures
related with the bullet.
> The lifetime of a bullet is
0,5 seconds.
> MTBF = (1000 x 0,5 s) / 2 = 250 seconds.
> MTBF is
substantially higher than lifetime.
This is generally true for units with low complexity.
Computer center with many servers:
A
computer center
is running nonstop with 1 failure per month on average. The design life
of the servers shall be 10
years.
> Server lifetime = 10 years, therefore the
lifetime of the computer center is also 10 years.
> MTBF = 1 month.
> MTBF
is substantially lower than lifetime. This is generally true for units
with high complexity.
Conclusion:
 MTBF
and lifetime are different metrics with no relationship between each
other.
 MTBF
is a statistical value that applies to a population of units, and not
to a single specific unit.
Remark:
Both above conclusions are true in more than 99% of all cases. In
order to keep this introduction simple, we will not dig into the
remaining 1% here. More information on this can be found on the MTBF
page.
There are more interesting aspects
about MTBF, but since we want to keep this introduction simple, we will
not
cover them here.
The failure rate
is just the reciprocal of the MTBF.
In general, a rate is a number of occurrences per time unit.
> Failure Rate = Number of failures per time unit.
Common time units are 1.000.000 hours (then expressed in units of
failures per million hours, fpmh) and 1.000.000.000 hours (then
expressed in units of failures in time, Fit).
Using failure rates instead of MTBF, the above computer equipment table
would look like this:
Assembly 
MTBF
[h]

Failure Rate
[fpmh]

Failure Rate
[Fit]

Personal computer 
2.000

1E6/2.000 =
500

1E9/2.000 =
500.000

Computerharddiskdrive 
15.000

1E6/15.000 =
66,7 
66.700

Computer mouse 
100.000

10

10.000

Computer keyboard 
25.000

40

40.000

Computercolormonitor 
8.000

125

125.000

Computer CD ROM drive 
8.000

125

125.000

We will learn more about failure rate in a later failure rate paragraph.
Both MTBF and failure rate just tell us "how often" units would fail.
Sometimes however we would not so much be interested in the number of
failures, but rather in the percentage of time the unit is in an
oparable condition.
The comoputer center described above is a good example. One failure per
month, or even many failures per month, may be tolerable as long as the
downtime remains sufficiently short. Therefore, Availability would be
the appropriate metric:
Availability is the
probability that an item will be operable
 under stated conditions
 for a stated period of time
The most simplistic formula for
Availability A is just uptime divided by total time:
MTBF is the mean time between failure and MTTR is the mean time to
repair.
MTTR ( = downtime) is the average time needed to perform a repair.
Availabiloity denoted as above is the so called "inherent" or
"intrinsic" availability.
We will learn further (and more realistic) formulas for availability in a later availability paraghraph.
Conclusion:
When uptime matters first, the number of failures per time is less
important. In particular:
 The failure rate of a unit may
be high, but if at the same time the repair time is sufficiently low,
the availability may still be acceptable (= sufficiently high).
 The other hand, ailure rate of a unit may be low, but
if at the same time the repair time is too high, the availability may
still be unacceptable (= too low).
Reliability is the probability that an item will perform
 a required function without failure
 under stated conditions
 for a stated period of time.
The phrase "without failure", which actually makes the difference
to availability. Hence, Reliability could also be expressed as the
probability of survival. The
focus of reliability lies clearly on the nonoccurrence of failures,
therefore, reliability is the metric of choice when interruption of
operation
matters. Common examples are military missions and flights.
We will learn more about reliability in a later reliability paragraph.
Next
Topic