Mean Time Before Failure (MTBF), Mean Time To Repair(MTTR) and Reliability Calculators
Mean time between failures, mean time to repair, failure rate and reliability equations are key tools for any manufacturing engineer. it allows you to monitor the performance of components or machinery and enables you to plan production, maintain machinery and predict failures.
MTBF Calculator (Mean Time Between Failure)Mean Time Before failure is a measure of total uptime of the components(s) divided by the total number of failures. See formula:
Total Uptime is the measure of the total time a system or component is working, this is measured by taking the total time the machine should be operational, less the amount of time taken up by time to repair. Number of failures is the number of failures within this time. Careful! Make sure the number of uptime sessions matches the number of failures! Otherwise you might find your results are skewed.


Failure Rate Calculator
Failure Rate is a simple calculation derived by taking the inverse of the mean time between failures:
Failure Rate is a common tool to use when planning and designing systems, it allows you to predict a component or systems performance. Failure rate is most commonly measured in number of failures per hour.
MTTR Calculator (Mean Time To Repair)Mean Time To Repair (MTTR) is a measure of the average downtime. the formula for which is:
This takes the downtime of the system and divides it by the number of failures. again, be sure to check downtime periods match failures.

MTTR can be a useful tool for Preventative maintenance and other maintenance repair processes. It allows you to effectively plan maintenance around the time taken to repair so you can optimise time spent on maintenance to minimise downtime.
Reliability CalculatorReliability is essentially the probability of a component or systems chance of failure and is calculated in one of two ways, if time is relatively small:
Or if the time is relatively large:
Calculating the reliability of a component allows you to design redundancy into a system. if a system exhibits a relatively high probability of failure you can place an identical component in parallel to increase total system reliability:

Total System Reliability CalculatorTotal System Reliability is a calculation which allows you to combine the reliabilities of several components to give a new value for system reliability. The formula for system reliability is:

MTBF Calculator Example:
A CNC machine in a machine shop operates for 1000 hours per year, and over the year, the Y axis motors have failed four times. Using the MTBF calculator, we can see that the Y axis motor on the CNC has a Mean Time Between Failures of 250 hours.
From this, we can then adjust our maintenance schedule to ensure that when we are approaching the 250 hour mark, we can be prepared to replace or repair the Y Axis Motor and minimise the downtime.
From this, we can then adjust our maintenance schedule to ensure that when we are approaching the 250 hour mark, we can be prepared to replace or repair the Y Axis Motor and minimise the downtime.
Failure Rate Calculator Example:
Failure rate is calculated as one over MTBF, which effectively gives you a probability of failure, in the case of the Y axis on the CNC machine, is 1/250 or a 0.4% chance of failure.
MTTR Calculator Example:
If we take the same example of the CNC Machine with the unreliable Y axis motor, we know that currently we have a Y axis motor that breaks down four times per year, and currently those breakdowns have resulted in 300 hours of downtime.
Using the mean time to repair calculator we can see that the average downtime is 75 hours (approximately 3 days).
As we can see the mean time to repair is a large proportion of the total uptime, and upon further analysis you find that the majority of the wait time is the lead time on parts, so if the machine shop were to preemptively buy the replacement parts, they may be able to reduce downtime to far less than previously.
Using the mean time to repair calculator we can see that the average downtime is 75 hours (approximately 3 days).
As we can see the mean time to repair is a large proportion of the total uptime, and upon further analysis you find that the majority of the wait time is the lead time on parts, so if the machine shop were to preemptively buy the replacement parts, they may be able to reduce downtime to far less than previously.
Reliability Calculator Example:
Using the Failure Rate and the total machine time, and given the relatively small amount of time the machine is operating, we can use the calculator to find the reliability of the motor to be 33.
Total System Reliability Calculator Example:
On the very same CNC machine, it turns out that the Y axis motor is identical to the X and Z axis, and as such the Z and Y have the same failure rates. using the Total System Reliability Equation we could find the total system reliability. This is a combination of all of the identical inline processes, and in this instance is equal to 33.