Does MTBF have any role in Maintenance?
No. You should not use MTBF when designing or scheduling maintenance programs or tasks. Furthermore, it is a very poor metric to monitor equipment performance.
The basic calculation of MTBF (or MTTF) and assuming the equipment time-to-failure distribution is the exponential distribution implies the equipment downing event occurs randomly. In other word the equipment doesn’t break in and actually lower it’s chance for failure over time, nor exhibit wear out or the increase of failure rates over time.
The chance of failure is constant over time and does not change given the time the system or component has been in service.
MTBF dose provide the average time between failures and does not provide any information about when the failures may occur if the actually failure do not occur randomly. Furthermore the exponential distribution has a memoryless feature, meaning a motor that is brand new and a similar motor with1,000,000 hours of service each have the same chance to fail in the next hour.
The MTBF calculation or vendor supplied value does not include information about how the failure rate may change over time.
Wear Out and Maintenance Planning
Let’s use a motor as an example for a simple maintenance planning exercise. Let’s say the motor has an MTBF of 100,000 hours provided by the vendor. There isn’t any maintenance on the motor, such as lubrication or alignment checks, yet we are planning to use 100 motors in the plant and need to plan for spares.
How many spares will we need over the next year to replace faulty motors.
Using just MTBF, we can use the probability of successful operation over the year, 8760 hours, and quickly estimate how many of the 100 motors will require replacement.
t is 8760 hours
θ is the MTBF or 100,000 hours
Thus, we find 91.6% of units should survive one year of operation. That means out of 100 installed motors, we expect about 8.4% to fail, or 8 or 9 units. Of course we could add a confidence bound to this calculation plus include the time the replacement unit operate for a bit more accuracy. For this example we’ll keep it simple.
Yet, we know based on experience with other similar motors that they rarely fail during the first year. With a little work we find the motors do actually wear out primarily due to bearing wear. And another call to the vendor we find they recommend using the Weibull distribution with β of 2 and η of 90,000 hours.
The reliability function for the Weibull distribution is
Where η is the characteristic life, in this case 90,000 hours
And, β is 2.
Thus over one year we would expect 99% of the motors to survive, meaning only 1 is expected to fail.
Using MTBF would have us buy 7 or 8 extra spares unnecessarily.
We know that motors wear out. Given only MTBF and the exponential distribution assumption we do not have sufficient information to schedule motor replacements.
If the motors actually failed randomly, as assumed, then our only strategy is to replace motors as they fail. Since the chance to fail each hour remains constant arbitrarily replacing motors at a any point in time will not avert or change the chance of failure the next hour.
When we model the wear out behavior, I.e. Weibull distribution with β of 2, then we can calculate the time at which the chance of failure is economically unacceptable. For example, if we typically operation in 1 week shifts of 168 hours then have time for maintenance tasks, we can calculate the chance of failure over a week period after one year, two years, etc. And determine when the chance of failure becomes unacceptable.
Knowing how the failure rate changes over time we can schedule replacements and maintain a relatively lower overall failure rate.
Find or estimate the information concerning the changing rate of failure over time. Ignoring wear out or early failures by using MTBF only will cost you and your plant money.
Understanding and modeling the wear out patterns allows you to secure spares as needed. You can avoid costly downtime by doing replacements before the chance of failure is too high.
PS: I’m working on examples and update to the draft book on MTBF to include more maintenance reliability specifics.