MTBF and MTTR: formulas, calculation and a practical example

Definitions: MTBF, MTTR, MTTF

• MTBF: average operating time between one failure and the next, for machines that get repaired. The higher it is, the less often the machine breaks down.
• MTTR: average time from the failure stop to the restart. The lower it is, the faster maintenance gets the machine running again.
• MTTF (Mean Time To Failure): average operating time until failure, for components that are not repaired but replaced, such as a bearing or a fuse.

Watch the R in MTTR: in some contexts it means repair, the repair time only, in others restore or recovery, the whole time from the stop to the restart, waiting for the technician and finding the spare part included. For production the second one is what counts, because it is the time the line really loses. Whichever you choose, write it down and keep it the same for all machines.

Formulas

The last two lines hold if failures are random, that is with a constant rate over time (exponential distribution). That is a reasonable approximation for a machine with many components, not for a single part that wears out: there the risk of failure grows with wear and other models are needed.

Some texts define MTBF as the time between the start of two consecutive failures, repair included: in that case MTBF = MTTF + MTTR and availability becomes MTTF ÷ MTBF. The two conventions give the same availability; only what is called MTBF changes.

Example over a month of downtime

A press works 22 days on two 8-hour shifts: 352 planned hours in the month. The maintenance log records six failures.

With an MTBF of 56.7 hours the failure rate is about 0.018 failures per hour. If failures are random, the probability of finishing an 8-hour shift without a failure is e^(−8 ÷ 56.7) = 86.8%: about one shift in eight will have a failure.

Two of the six failures alone account for 7 of the 12 hours of downtime: the hydraulic leak and the proportional valve. This is the first practical use of MTTR: an average MTTR of 2 hours hides half-hour failures and half-day failures, and a Pareto by cause tells you where you need spare parts in stock or an instruction for the night shift.

From availability to OEE

Availability calculated with MTBF and MTTR considers failures only. OEE availability is broader: it also includes changeovers, adjustments and waiting, that is every stop that was not planned as a break. If the same press had 18 hours of die changes in the month, OEE availability is (352 − 12 − 18) ÷ 352 = 91.5%, against 96.6% for failures alone.

The two measures serve different people: MTBF and MTTR serve maintenance, to decide which components and which procedures to work on; OEE availability serves production, to understand how much planned time is lost and for what reasons. Micro-stops enter neither: they weigh on performance, as the guide on the six big losses explains.

Common mistakes when counting downtime

• Counting micro-stops as failures: it lowers MTBF and MTTR together and makes the numbers incomparable across machines. Below a written threshold, for example 5 minutes, a stop is not a failure.
• Putting no-order hours or breaks into operating time: MTBF looks better than it is. Count only the time in which the machine was supposed to work.
• Closing the failure when the technician arrives instead of at the restart: MTTR looks lower, but the line stayed stopped all the same.
• Calculating MTBF over a period with one or two failures: the number swings wildly. Better a rolling period of three or six months, or at least five failures.
• Mixing up MTBF and MTTF: for a component replaced every time there is no time between failures of the same unit, there is the time to failure.

The rule that avoids almost all of these mistakes is to take the times from the machine, not from the memory of whoever fills in the log: the start and end of a stop are in the PLC states. With Muvia Industrial the states arrive from the PLCs through the edge node, the intervention history from the ERP, and a query calculates MTBF and MTTR per machine and month for a maintenance dashboard. The use case on predictive maintenance shows how the same signals become deviations, a health index and an alarm.

Calculator

Enter the planned hours, the number of failures and the total repair time for the period: the calculator returns MTBF, MTTR, availability and the probability of finishing a shift without a failure. The starting values are those of the example.