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A simple Introduction into Reliability Metrics

Failure Rate, MTBF, Reliability, and Availability

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1. MTBF

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The most common (and also mostly misunderstood) reliability metric ist the MTBF, mean time between failure. MTBF has by no means any relationship with lifetime. The table below  shows some MTBF figures originating from an earlier version (mid 1990s) of the Telcordia SR 332 MTBF calculation standard. Therefore, the figures are quite dated. 

Assembly MTBF [h]
Personal computer 2.000
Computer-hard-disk-drive
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
Computer-color-monitor 8.000
Computer CD ROM drive 8.000

The table suggest that more complex devices tend to have lower MTBF compared to less complex devices. This is generally true, and in particular, MTBF can be viewed as a kind of complexity metric. More information on this can be found on the MTBF page. 

MTBF is a statistical metric characterizing a population of units. In order to illustrate this, we use the computer mouse in the above table. MTBF = 100.000 h does not mean that a specific mouse would fail every 100.000 h (not even on average), but if we consider, for example, 1.000 computer mice, we would expect a mouse failure every 1.00.000 cumulative operating hours on average, which is 1 mouse failure every 100 calendar hours on average ( ~ 4 calendar days). Since the MTBF concept comes with constant failure rate over time, we would expect the first mouse failure on the first few days, on average on the 4th day, to be precise. More on constant failure rate, in particular it's implications, can be found on the MTBF calculation page.

In order to understand the MTBF concept even better, and in particular to show the difference to lifetime, we consider the following, "extreme" examples:

    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:
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.

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2. Failure Rate

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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
Computer-hard-disk-drive 15.000
1E6/15.000 = 66,7 66.700
Computer mouse 100.000
10
10.000
Computer keyboard 25.000
40
40.000
Computer-color-monitor 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.

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3. Availability

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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
The most simplistic formula for Availability A is just uptime divided by total time:

Availability, MTTR, MTBF
 
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:
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4. Reliability

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Reliability is the probability that an item will perform 


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 non-occurrence 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.

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