Last Updated on 13 September 2023
If you buy an asset, whether it’s a piece of machinery or a product, you can use Mean Time To Failure (MTTF) to know how long it’s expected to last. It is a key metric for the reliability of a non-reparable object.
It can be difficult to measure these by normal methods such as a run chart, as the data points are too far apart to show much useful information, and the number of peaks would depend as much on how many units are in use as how reliable they are.
Instead we use Mean Time To Failure, which instead of showing the number of failures, calculates the average length of time that the units last.
What is MTTF?
The mean time to failure definition is:
The Mean Time To Failure (MTTF) is the average amount of time that a machine or product will last before it is irreparably broken.
The average in the calculation is the arithmetic mean, i.e. add all the measurements together and divide by the number of units.
MTTF vs MTBF
The two failure metrics are often confused, and you will often find websites that have the wrong definitions:
- Mean Time To Failure is for irreparable assets (so when they break, they’re finished with, such as light bulbs), and will be calculated by averaging over different units.
- Mean Time Between Failures is for repairable assets (such as cars), and will be calculated by averaging over the same unit as it repeatedly fails and is repaired
Which you use is down to the asset you are monitoring, but the two operate in a similar way. They both show how long the asset will be ‘up and running for’ before it breaks. The only difference is that with MTBF, you will be able to get it back up and running again afterwards.
You can actually use MTTF for repairable assets too, but this is for their time to total failure, so the total life of a car, rather than the time between breakdowns. This then becomes the time until the first breakdown that you can’t repair.
When do you use MTTF?
Products are increasingly designed to be used to destruction, rather than be repaired. More and more products are therefore falling into the irreparable category, making this metric more useful.
The metric is often useful when you are trying to monitor and optimize the reliability of your products in the hands of the customer.
Machinery that wears out can quickly become one of the biggest costs in your operation, as they are often large amounts of capital expenditure. If you want to make the most of your capital investment, Mean Time To Failure can be used to measure the effects of your equipment maintenance efforts.
How do you calculate Mean Time To Failure?
To improve your reliability, you need to be able to calculate it. Fortunately the formula is relatively simple:
MTTF = Σ(age of product at failure) / number of products tested
The age of product is measured from when the item starts being used for its intended use. For a light bulb this is from when it is turned on, not when it is manufactured. The clock stops when it breaks and can’t be used for its intended purpose any more.
All you have to do is add up all of your measurements for the different products, and then divide by the number of products in your sample.
The Bathtub curve
If you have an item that you won’t have the failure times spread evenly over time or even clumped around the MTTF. Instead it follows what is called the ‘bathtub curve’. As you’d expect, it follows the shape of a bathtub:
In the early life stage you will have high failure rates, as poorly made products, manufacturing mistakes and improperly installed machinery has a high chance of breaking at this stage. Those that have no issues that will break it quickly usually then have a long useful life stage where they have a low risk of failure. You wouldn’t expect many units to fail during this stage. Eventually they will reach the wear out stage as the components age and get less reliable. As this stage, the units will start to fail over a relatively short window.
Your MTTF calculation is therefore likely to have a large number of results in these the early life and wear out areas. Most of your lifetime results will be in the ‘wear out’ stage, but the Mean Time To Failure figure you calculate will be dragged down by those which fail in the Early Life stage, such as through manufacturing or installation issues.
How to improve your Mean Time To Failure
MTTF is usually calculated for your products, and the failures are often due to manufacturing defects. To improve your Mean Time To Failure you need to remove the defects from your products. This is best done by proper diagnosis, prioritization and improvement through a Six Sigma DMAIC project.
Some failures will be due to incorrect installation and usage, and can’t be improved by improving the product quality. This can be improved by creating high quality documentation to go with the product, and training your customers in their use. You can also use Poka Yoke (mistake proofing) to make it impossible to use the product incorrectly.
For machinery rather than products, the best way to improve MTTF is to keep your machinery in good working order. This includes keeping the item clean, lubricated and maintained. There is a framework to do this, which is Total Productive Maintenance.
The classic example is light bulbs. To calculate MTTF for a batch of 5 light bulbs that last the following times (rounding to the nearest hour):
1 hour, 1,563 hours, 27,583 hours, 32,523 hours and 33,562 hours.
The Mean Time To Failure for this example would be:
MTTF = (1+15,263+27,583+32,823+33,662) / 5 = 21,866
This shows the bathtub curve and its effect. There is a high chance of failure at early life (the first couple of thousand hours) and in the wear out stage (towards 35,000 hours).
You can’t say you would expect the bulb to last 22,000 hours, in fact none of the bulbs lasted close to that level. They were either higher (wear out phase) or failed early (early phase).
The mean is pulled lower by the few items that break during the ‘early life’ stage. In this example that’s the bulb that died after 1 hour. Without the early failures, the mean would be 31,356.