MTBF and MTTR

What is the MTBF versus MTTR?

My understanding is:

According to the picture, TTR (Time to Failure) is the amount of time a machine or system works is "up" before it fails.

Example: If a machine operates for 200 hours before breaking down, the TTF for that is 200 hours.

In the picture, TTF is the time between when the machine is fixed and when it breaks again.

TBF (Time between Failures) is the total time from one failure to the next, which includes:

the time the machine is operational (TTF).
The time it is not operational (Downtime: Waiting time (WT) + Time to Repair (TTR)).

Formula:

$T B F = T T F + D o w n t i m e$

In the picture: TBF is the time from one failure to the next failure, covering both operational and downtime period.

3. MTTF (Mean time to failure)

The average time a machine operates before failure across multiple instances. It is essentially the average of multiple TTFs.

Formula:

$M T T F = \frac{S u m o f a l l T T F s}{N u m b e r o f f a i l u r e s}$

Use: MTTF focuses only on the operational time (up time) and is often used for system that do not undergo repairs (non-repairable).

4. MTBF (Mean Time between Failures)

The average time between two failures, including both operational time (TTF) and downtime (WT + TTR).

Formula:

$M T B F = \frac{S u m o f a l l T B F s}{N u m b e r o f f a i l u r e s}$

Use: MTBF is often used for repairable systems because it includes both "up time" and "down time".

Key Difference Between MTTF and MTBF:

MTTF only measures the average operational time before a failure.

MTBF includes both operational time and downtime in its calculation.

Practical Example:

Imagine a machine fails three times with the following data:

TTFs: 100, 150, 120 hours

Downtimes (WT + TTR): 10, 15, 20 hours

1. $M T T F = \frac{100 + 150 + 120}{3} = 123.33 h o u r s$ (only operational time).

2. $M T B F = \frac{(100 + 10) + (150 + 15) + (120 + 20)}{3} = 148.33$ (operational + downtime).

Answer:

So, what is the difference between MTTF and MTBF in this case? "A repairable system" or is it just overlapped?

My question is: What is the difference between MTTF and MTBF in a repairable system?

According to the answer the statement, "The difference 'downtime' minus 'up time' is the amount of time it was operating between two events," can be better understood with a focus on how operational and down time periods relate to one another in repairable systems.

Why is Time to Failure (TTF) calculate in this way?

Downtime refers to the period where the machine is not operational (e.g., waiting for repairs or being repaired).

Uptime (or operational time) refers to how long the machine successfully operates between failures (this is TTF).

Relation between downtime and uptime:

When says "downtime minus uptime", it highlights TTF is isolated from downtime.

In other words:

$T T F = T o t a l T i m e - D o w n t i m e$

This means the period we care about for TTF is purely how long the machine operates, not including the time it's broken or being repaired.

Example:

If a machine operates (uptime)for 100 hours (TTF) and then breaks down for 10 hours (downtime), the focus of TTF is only the 100 hours of operation. The downtime is accounted for separately in maintenance metrics like MDT or MTTR.

In short, TTF is calculated this way because it measures how long a machine can run before failing, purely focusing on its operational performance and excluding downtime for repairs or waiting.

Svara