MTBF, MTTR and availability: three numbers, three different questions

In a maintenance meeting, "our MTBF is 500 hours" says little on its own. The same machine can have an MTTR of 3 hours or of 30; availability is very different in the two cases. Three numbers answer three separate questions: how often does it fail, how quickly does it recover, how much time is left for production.

1. Definitions

• MTBF (mean time between failures) = total operating time / number of operating intervals. Repair time is not counted as operating time.
• MTTR (mean time to repair) = total repair time / number of failures.
• Availability = MTBF / (MTBF + MTTR). This is inherent availability, which counts only failures and repairs; planned maintenance and waiting for material are not included.

2. Example

Assume a filling line ran 2,000 hours in a quarter, had 4 unplanned failures in that time, and the repairs took 12 hours in total.

• MTBF = 2,000 / 4 = 500 hours
• MTTR = 12 / 4 = 3 hours
• Availability = 500 / (500 + 3) = 99.40%

The failure rate λ = 1 / MTBF = 0.002 failures per hour. Under a constant failure rate, the probability of getting through a 100-hour block of shifts without a failure is exp(−100/500) = 81.9%; the probability of 500 failure-free hours is exp(−1) = 36.8%. So MTBF does not mean "one failure every 500 hours"; the probability of surviving one MTBF without a failure is only 36.8%.

3. Which number supports which decision?

• A low MTBF points to design, operating conditions or part quality; preventive and predictive maintenance work on this.
• A high MTTR points to organization: spare parts, diagnosis time, reaching a qualified technician. In the example, cutting MTTR from 3 hours to 1.5 raises availability from 99.40% to 99.70%. The same gain comes from halving the failures from 4 to 2 (MTBF 1,000 hours). Both give the same result, but one is an investment in the maintenance plan, the other in spares and diagnostics.
• On a serial line availabilities multiply: three of the same machine in sequence give a line availability of 0.9940³ = 98.22%. Two machines in parallel with redundancy (one running is enough) give 1 − (1 − 0.9940)² = 99.996%. This assumes independent failures and a perfect switchover; in reality the switchover takes time.

4. Four common mistakes

• Counting repair time as operating time. MTBF is inflated and availability looks better than it is.
• Counting work orders instead of failures. One failure may have three work orders; MTBF drops to a third.
• Deriving MTBF from a single quarter. The 500 hours calculated from 4 failures become 1,000 hours next quarter with 2 failures; follow the trend, not the number. For equipment with few failures, at least 10–12 months of records are needed.
• Applying the constant-failure-rate assumption to wearing parts. For bearings, belts and seals the failure rate rises with time; there exp(−t/MTBF) is optimistic and a Weibull analysis is needed.

Try it with your own records

The MTBF / MTTR calculator works from summary figures or from a failure log (start–end date-times); the data stays in your browser. To have your failure log interpreted, get in touch.